%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%%     author          = "Nelson H. F. Beebe",
%%%     version         = "3.159",
%%%     date            = "23 March 2024",
%%%     time            = "16:20:42 MST",
%%%     filename        = "toms.bib",
%%%     address         = "University of Utah
%%%                        Department of Mathematics, 110 LCB
%%%                        155 S 1400 E RM 233
%%%                        Salt Lake City, UT 84112-0090
%%%                        USA",
%%%     telephone       = "+1 801 581 5254",
%%%     FAX             = "+1 801 581 4148",
%%%     URL             = "https://www.math.utah.edu/~beebe",
%%%     checksum        = "41254 63484 310016 3035820",
%%%     email           = "beebe at math.utah.edu, beebe at acm.org,
%%%                        beebe at computer.org (Internet)",
%%%     codetable       = "ISO/ASCII",
%%%     keywords        = "bibliography; mathematical software; TOMS;
%%%                        Transactions on Mathematical Software",
%%%     license         = "public domain",
%%%     supported       = "yes",
%%%     docstring       = "This is a BibTeX bibliography for ACM
%%%                        Transactions on Mathematical Software (TOMS)
%%%                        (CODEN ACMSCU, ISSN 0098-3500 (print),
%%%                        1557-7295 (electronic)), completely covering
%%%                        all issues from March 1975 -- date.  All
%%%                        papers, including editorials, policy
%%%                        statements, remarks, and corrigenda are
%%%                        included.
%%%
%%%                        The ACM maintains World Wide Web pages with
%%%                        journal tables of contents for 1985--date at
%%%
%%%                            http://dl.acm.org/pub.cfm?id=J782
%%%                            http://toms.acm.org/
%%%                            http://www.acm.org/dl/toc.html
%%%                            http://www.acm.org/toms/
%%%                            http://www.acm.org/pubs/contents/journals/toms/
%%%
%%%                        Source code for all ACM Algorithms from 1960
%%%                        to date is available at
%%%
%%%                            http://www.acm.org/calgo/contents/
%%%
%%%                        That data has been automatically converted to
%%%                        BibTeX form, corrected for spelling and page
%%%                        number errors, and merged into this file.
%%%
%%%                        At version 3.159, the COMPLETE year coverage
%%%                        looks like this:
%%%
%%%                             1960 (   1)    1982 (  34)    2004 (  28)
%%%                             1961 (   1)    1983 (  43)    2005 (  30)
%%%                             1962 (   1)    1984 (  46)    2006 (  34)
%%%                             1963 (   2)    1985 (  40)    2007 (  28)
%%%                             1964 (   2)    1986 (  34)    2008 (  23)
%%%                             1965 (   1)    1987 (  29)    2009 (  51)
%%%                             1966 (   1)    1988 (  40)    2010 (  37)
%%%                             1967 (   1)    1989 (  32)    2011 (  25)
%%%                             1968 (   1)    1990 (  34)    2012 (  21)
%%%                             1969 (   2)    1991 (  41)    2013 (  31)
%%%                             1970 (   2)    1992 (  36)    2014 (  29)
%%%                             1971 (   1)    1993 (  37)    2015 (  25)
%%%                             1972 (   4)    1994 (  38)    2016 (  54)
%%%                             1973 (   3)    1995 (  31)    2017 (  43)
%%%                             1974 (   7)    1996 (  33)    2018 (  25)
%%%                             1975 (  38)    1997 (  31)    2019 (  45)
%%%                             1976 (  49)    1998 (  31)    2020 (  38)
%%%                             1977 (  46)    1999 (  28)    2021 (  40)
%%%                             1978 (  43)    2000 (  33)    2022 (  48)
%%%                             1979 (  54)    2001 (  21)    2023 (  40)
%%%                             1980 (  57)    2002 (  24)    2024 (   8)
%%%                             1981 (  47)    2003 (  26)
%%%
%%%                             Article:       1807
%%%                             Misc:             1
%%%                             TechReport:       1
%%%
%%%                             Total entries: 1809
%%%
%%%                        Abstracts, Keywords, Categories and Subject
%%%                        Descriptors are available for some issues.
%%%                        Eventually, this coverage should be
%%%                        extended to the entire collection, in the
%%%                        interests of enhancing search capabilities.
%%%
%%%                        This bibliography includes ACM Algorithms
%%%                        493 -- 735 (or the latest), including
%%%                        Algorithm 568, published in ACM
%%%                        Transactions on Programming Languages and
%%%                        Systems (TOPLAS).  For ACM Algorithms 1 --
%%%                        492, see the companion bibliographies,
%%%                        cacm1960.bib and cacm1970.bib.
%%%
%%%                        All published Remarks and Corrigenda are
%%%                        cross-referenced in both directions, so
%%%                        that citing a paper will automatically
%%%                        generate citations for those Remarks and
%%%                        Corrigenda.  There is one important paper,
%%%                        on multiple-precision integer division,
%%%                        included from the journal Software ---
%%%                        Practice and Experience because it is
%%%                        cross-referenced to a TOMS paper.
%%%
%%%                        Algorithms published in Communications of
%%%                        the ACM, prior to the founding of TOMS in
%%%                        1975, are also included in this
%%%                        bibliography, if a TOMS paper contains
%%%                        Remarks or Corrigenda for them.
%%%
%%%                        Source code for ACM Algorithms from 380
%%%                        onwards, with some omissions, is available
%%%                        via netlib, and via anonymous ftp to
%%%
%%%                            ftp://netlib.bell-labs.com/netlib/toms
%%%
%%%                        ACM also markets a CD-ROM containing
%%%                        algorithms 495 (March 1975) through 798
%%%                        (December 1999): the ``CALGO Special Edition
%%%                        CD'', organized as a Web site (see entry
%%%                        ACM:2002:CSE at the end of this file).
%%%
%%%                        The initial draft of entries for 1981 -- 1990
%%%                        was extracted from the ACM Computing Archive
%%%                        CD ROM for the 1980s, with manual corrections
%%%                        and additions from bibliographies in the TeX
%%%                        User Group collection, the author's personal
%%%                        bibliography files, Aake Bjoerck's
%%%
%%%                            ftp://math.liu.se/pub/references/habook.bib
%%%
%%%                        G. W. Stewart's
%%%
%%%                            ftp://thales.cs.umd.edu/pub/references/ref.bib
%%%
%%%                        John R. Rice and Richard J. Hanson's
%%%                        Algorithm 620 (available as a BibTeX file via
%%%                        netlib, with additions up to Algorithm 678),
%%%                        and the very large Karlsruhe computer science
%%%                        bibliography collection at
%%%
%%%                            ftp://ftp.ira.uka.de/pub/bibliography/
%%%
%%%                        to which many people of have contributed.
%%%
%%%                        Math Review MRclass and MRnumber values for
%%%                        341 entries were supplied from a search of
%%%                        the American Mathematical Society's
%%%                        MathSciNet database for version 2.26
%%%                        [06-Dec-1996].  That search also turned up
%%%                        a few small errors in author names and
%%%                        title words; they have been corrected to
%%%                        match the original journal articles.
%%%
%%%                        Numerous errors in the sources noted above
%%%                        have been corrected.   Spelling has been
%%%                        verified with the UNIX spell and GNU ispell
%%%                        programs using the exception dictionary
%%%                        stored in the companion file with extension
%%%                        .sok.
%%%
%%%                        Numerous heuristic checks on the validity
%%%                        of the TOMS bibliography files have also
%%%                        been made using software developed by the
%%%                        author for maintenance of the TeX Users
%%%                        Group and BibNet bibliography collections.
%%%
%%%                        Every entry from March 1975 -- June 1994
%%%                        has been compared directly with the article
%%%                        cover pages in the original journal issues
%%%                        to ensure correctness.  Several errors were
%%%                        uncovered this way in earlier sources of
%%%                        BibTeX entries and citation data.
%%%
%%%                        Considerable effort has been expended to
%%%                        ensure accuracy of this bibliography,
%%%                        because it is expected to be widely used
%%%                        and distributed.  Capitalization of
%%%                        original titles, and use of initials or
%%%                        full names in author lists, should match
%%%                        the journal exactly, with two exceptions.
%%%                        (1) Algorithms have been sometimes entitled
%%%                        ``ALGORITHM xyz...'', and sometimes
%%%                        ``Algorithm xyz...''.  The latter usage has
%%%                        been adhered to throughout.  (2) Remarks
%%%                        and Corrigenda in the journal occasionally
%%%                        fail to cite the full title of the original
%%%                        paper; that has been rectified in the
%%%                        interests of clarity and consistency.
%%%
%%%                        ACM copyrights explicitly permit abstracting
%%%                        with credit, so article abstracts, keywords,
%%%                        and subject classifications have been
%%%                        included in this bibliography wherever
%%%                        available.  Article reviews have been
%%%                        omitted, until their copyright status has
%%%                        been clarified.
%%%
%%%                        bibsource keys in the bibliography entries
%%%                        below indicate the entry originally came
%%%                        from the computer science bibliography
%%%                        archive, even though it has likely since
%%%                        been corrected and updated.
%%%
%%%                        URL keys in the bibliography point to
%%%                        World Wide Web locations of additional
%%%                        information about the entry.
%%%
%%%                        BibTeX citation tags are uniformly chosen
%%%                        as name:year:abbrev, where name is the
%%%                        family name of the first author or editor,
%%%                        year is a 4-digit number, and abbrev is a
%%%                        3-letter condensation of important title
%%%                        words. Citation tags were automatically
%%%                        generated by software developed by the
%%%                        author for the BibNet Project.
%%%
%%%                        In this bibliography, entries are sorted
%%%                        by journal, and then by publication order,
%%%                        with the help of ``bibsort -byvolume''.  The
%%%                        bibsort utility is available from
%%%
%%%                            ftp://ftp.math.utah.edu/pub/bibsort
%%%
%%%                        The author will be grateful for reports of
%%%                        errors of any kind in this bibliography.
%%%
%%%                        The checksum field above contains a CRC-16
%%%                        checksum as the first value, followed by the
%%%                        equivalent of the standard UNIX wc (word
%%%                        count) utility output of lines, words, and
%%%                        characters.  This is produced by Robert
%%%                        Solovay's checksum utility."
%%%     }
%%% ====================================================================

@Preamble{"\input bibnames.sty"
 # "\hyphenation{Cher-kas-sky Cue-vas Ka-chit-vich-yan-u-kul Rich-ard Za-bo-row-ski}"
 # "\ifx \undefined \booktitle \def \booktitle #1{{{\em #1}}}   \fi"
 # "\ifx \undefined \circled   \def \circled #1{(#1)}           \fi"
 # "\ifx \undefined \k         \let \k = \c                     \fi"
 # "\ifx \undefined \mathbb    \def \mathbb  #1{{\bf #1}}       \fi"
 # "\ifx \undefined \ocirc     \def \ocirc   #1{{\accent'27#1}} \fi"
 # "\ifx \undefined \pkg       \def \pkg     #1{{{\tt #1}}}     \fi"
 # "\ifx \undefined \reg       \def \reg       {\circled{R}}    \fi"
 # "\ifx \undefined \TM        \def \TM        {${}^{\sc TM}$}  \fi"
}

%%% ====================================================================
%%% Acknowledgement abbreviations:

@String{ack-nhfb = "Nelson H. F. Beebe,
                    University of Utah,
                    Department of Mathematics, 110 LCB,
                    155 S 1400 E RM 233,
                    Salt Lake City, UT 84112-0090, USA,
                    Tel: +1 801 581 5254,
                    FAX: +1 801 581 4148,
                    e-mail: \path|beebe@math.utah.edu|,
                            \path|beebe@acm.org|,
                            \path|beebe@computer.org| (Internet),
                    URL: \path|https://www.math.utah.edu/~beebe/|"}

@String{ack-kr = "Karin Remington,
                  Celera Genomics
                  45 West Gude Drive
                  Rockville, Maryland 20850
                  Tel: +1 240 453-3038
                  FAX: +1 240 453-4375
                  e-mail: \path|remingka@celera.com|"}

@String{ack-nj = "Norbert Juffa,
                  2445 Mission College Blvd.
                  Santa Clara, CA 95054
                  USA
                  email: \path=norbert@iit.com="}

@String{ack-rfb = "Ronald F. Boisvert,
                  Applied and Computational Mathematics Division,
                  National Institute of Standards and Technology,
                  Gaithersburg, MD 20899, USA,
                  Tel: +1 301 975 3812,
                  e-mail: \path=boisvert@cam.nist.gov="}

%%% ====================================================================
%%% Journal abbreviations:

@String{j-CACM                  = "Communications of the ACM"}

@String{j-COMP-J                = "The Computer Journal"}

@String{j-COMP-STAT             = "Computational Statistics"}

@String{j-IEEE-TRANS-COMPUT     = "IEEE Transactions on Computers"}

@String{j-SIAM-J-SCI-COMP       = "SIAM Journal on Scientific Computing"}

@String{j-SPE                   = "Soft{\-}ware\emdash Prac{\-}tice
                                  and Experience"}

@String{j-J-STAT-COMPUT-SIMUL   = "Journal of Statistical Computation and
                                  Simulation"}

@String{j-TOMS                  = "ACM Transactions on Mathematical Software"}

@String{j-TOPLAS                = "ACM Transactions on Programming
                                  Languages and Systems"}

%%% ====================================================================
%%% Bibliography entries from Communications of the ACM.

@Article{Ellenberger:1960:NSP,
  author =       "K. W. Ellenberger",
  title =        "{ACM Algorithm 30}: Numerical Solution of the
                 Polynomial Equation",
  journal =      j-CACM,
  volume =       "3",
  number =       "12",
  pages =        "643--643",
  month =        dec,
  year =         "1960",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Feb 07 16:37:16 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Novotny:1985:RNS}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Herndon:1961:SNF,
  author =       "J. R. Herndon",
  title =        "{ACM Algorithm 49}: Spherical {Neumann} Function",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "179--179",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Coleman:1978:RSN}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Merner:1962:CEI,
  author =       "J. N. Merner",
  title =        "{ACM Algorithm 149}: Complete Elliptic Integral",
  journal =      j-CACM,
  volume =       "5",
  number =       "12",
  pages =        "605--605",
  month =        dec,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Skovgaard:1978:RCE}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ludwig:1963:IBR,
  author =       "O. G. Ludwig",
  title =        "{ACM Algorithm 179}: Incomplete Beta Ratio",
  journal =      j-CACM,
  volume =       "6",
  number =       "6",
  pages =        "314--314",
  month =        jun,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Pike:1976:RIB}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kase:1963:TOP,
  author =       "R. H. Kase",
  title =        "{ACM Algorithm 219}: Topological Ordering for {Pert}
                 Networks",
  journal =      j-CACM,
  volume =       "6",
  number =       "12",
  pages =        "738--739",
  month =        dec,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Tenney:1977:RTO}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gautschi:1964:AAB,
  author =       "W. Gautschi",
  title =        "{ACM Algorithm 236}: {Bessel} Functions of the First
                 Kind [{S17}]",
  journal =      j-CACM,
  volume =       "7",
  number =       "8",
  pages =        "479--480",
  month =        aug,
  year =         "1964",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355586.355587",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:55 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Skovgaard:1975:RBF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "http://portal.acm.org/browse_dl.cfm?idx=J79",
  keywords =     "$J_n(x)$; Bessel functions of the first kind; special
                 functions",
}

@Article{Boothroyd:1964:G,
  author =       "J. Boothroyd",
  title =        "{ACM Algorithm 246}: {Graycode}",
  journal =      j-CACM,
  volume =       "7",
  number =       "12",
  pages =        "701--701",
  month =        dec,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Sep 10 09:12:22 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Misra:1975:RG,Er:1985:RG}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gautschi:1965:LFA,
  author =       "W. Gautschi",
  title =        "{ACM Algorithm 259}: {Legendre} Functions for
                 Arguments Larger than One",
  journal =      j-CACM,
  volume =       "8",
  number =       "8",
  pages =        "488--492",
  month =        aug,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Jansen:1977:RLF}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fletcher:1966:ITB,
  author =       "W. Fletcher",
  title =        "{ACM Algorithm 284}: Interchange of Two Blocks of
                 Data",
  journal =      j-CACM,
  volume =       "9",
  number =       "5",
  pages =        "326--326",
  month =        may,
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Ito:1976:RIT}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hill:1967:CSI,
  author =       "I. D. Hill and M. C. Pike",
  title =        "{ACM Algorithm 299}: Chi-Squared Integral",
  journal =      j-CACM,
  volume =       "10",
  number =       "4",
  pages =        "243--244",
  month =        apr,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{elLozy:1976:RAC,Hill:1985:RCS}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bell:1968:NRD,
  author =       "J. R. Bell",
  title =        "{ACM Algorithm 334}: Normal Random Deviates",
  journal =      j-CACM,
  volume =       "11",
  number =       "7",
  pages =        "498--498",
  month =        jul,
  year =         "1968",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Tracht:1982:RNR}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Morris:1969:TP,
  author =       "J. Morris",
  title =        "{ACM Algorithm 346}: ${F}$-Test Probabilities",
  journal =      j-CACM,
  volume =       "12",
  number =       "3",
  pages =        "184--185",
  month =        mar,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Cormack:1988:RTP}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{TadeudeMedeiros:1969:APF,
  author =       "A. {Tadeu de Medeiros} and G. Schwachheim",
  title =        "{Algorithm 349}: Polygamma functions with arbitrary
                 precision",
  journal =      j-CACM,
  volume =       "12",
  number =       "4",
  pages =        "213--214",
  month =        apr,
  year =         "1969",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Jun 16 10:30:24 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See certification \cite{Lewis:1975:CPF}.",
  acknowledgement = ack-nhfb,
  classcodes =   "C7300 (Natural sciences computing)",
  corpsource =   "Centro Brasileiro de Pesquisas Fisicas, Rio de
                 Janeiro, Brazil",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "mathematics; subroutines",
}

@Article{Hill:1970:SD,
  author =       "G. W. Hill",
  title =        "{ACM Algorithm 395}: {Student}'s $t$-Distribution",
  journal =      j-CACM,
  volume =       "13",
  number =       "10",
  pages =        "617--619",
  month =        oct,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{elLozy:1979:RAS,Hill:1981:RSD}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hill:1970:SQ,
  author =       "G. W. Hill",
  title =        "{ACM Algorithm 396}: {Student}'s $t$-Quantiles",
  journal =      j-CACM,
  volume =       "13",
  number =       "10",
  pages =        "619--620",
  month =        oct,
  year =         "1970",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Apr 29 15:20:10 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remarks
                 \cite{Hill:1981:RSD,Hill:1981:RSQ,elLozy:1979:RAS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{McNamee:1971:SMP,
  author =       "J. M. McNamee",
  title =        "{ACM Algorithm 408}: a Sparse Matrix Package ({Part
                 I})",
  journal =      j-CACM,
  volume =       "14",
  number =       "4",
  pages =        "265--273",
  month =        apr,
  year =         "1971",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also
                 \cite{Sipala:1977:RSM,Gustavson:1978:RSM,Harms:1980:RSM}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gentleman:1972:CCQ,
  author =       "W. M. Gentleman",
  title =        "{ACM Algorithm 424}: {Clenshaw--Curtis} Quadrature",
  journal =      j-CACM,
  volume =       "15",
  number =       "5",
  pages =        "353--355",
  month =        may,
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Geddes:1979:RCC}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Akima:1972:ISC,
  author =       "H. Akima",
  title =        "{ACM Algorithm 433}: Interpolation and Smooth Curve
                 Fitting Based on Local Procedures",
  journal =      j-CACM,
  volume =       "15",
  number =       "10",
  pages =        "914--918",
  month =        oct,
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Anderson:1976:RIS}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{March:1972:EPT,
  author =       "D. L. March",
  title =        "{ACM Algorithm 434}: Exact Probabilities for
                 ${R\times{C}}$ Contingency Tables",
  journal =      j-CACM,
  volume =       "15",
  number =       "11",
  pages =        "991--992",
  month =        nov,
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Sep 09 14:13:19 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Boulton:1976:REP}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fullerton:1972:MIG,
  author =       "W. Fullerton",
  title =        "{ACM Algorithm 435}: Modified Incomplete Gamma
                 Function",
  journal =      j-CACM,
  volume =       "15",
  number =       "11",
  pages =        "993--995",
  month =        nov,
  year =         "1972",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Schoene:1978:RMI}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{MacHura:1973:RFM,
  author =       "M. MacHura and A. Mulawa",
  title =        "{ACM Algorithm 450}: {Rosenbrock} Function
                 Minimization",
  journal =      j-CACM,
  volume =       "16",
  number =       "8",
  pages =        "482--483",
  month =        aug,
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Davies:1976:RRF}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Brenner:1973:MTP,
  author =       "N. Brenner",
  title =        "{ACM Algorithm 467}: Matrix Transposition in Place",
  journal =      j-CACM,
  volume =       "16",
  number =       "11",
  pages =        "692--694",
  month =        nov,
  year =         "1973",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Leathers:1979:RAS}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Akima:1974:BIS,
  author =       "H. Akima",
  title =        "{ACM Algorithm 474}: Bivariate Interpolation and
                 Smooth Surface Fitting Based on Local Procedures",
  journal =      j-CACM,
  volume =       "17",
  number =       "1",
  pages =        "26--31",
  month =        jan,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:56 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Anderson:1979:RBI}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Loeser:1974:SPT,
  author =       "R. Loeser",
  title =        "Some Performance Tests of `Quicksort' and
                 Descendants",
  journal =      j-CACM,
  volume =       "17",
  number =       "3",
  pages =        "143--152",
  month =        mar,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Apr 29 15:23:43 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Mackay:1977:RPT}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Wright:1974:VSP,
  author =       "T. Wright",
  title =        "{ACM Algorithm 475}: Visible Surface Plotting
                 Program",
  journal =      j-CACM,
  volume =       "17",
  number =       "3",
  pages =        "152--155",
  month =        mar,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Duta:1976:RVS,vanSwieten:1979:RAV}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Page:1974:MST,
  author =       "R. L. Page",
  title =        "{ACM Algorithm 479}: a Minimal Spanning Tree
                 Clustering Method",
  journal =      j-CACM,
  volume =       "17",
  number =       "6",
  pages =        "321--323",
  month =        jun,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{White:1976:RMS}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Watkins:1974:MTD,
  author =       "S. L. Watkins",
  title =        "{ACM Algorithm 483}: Masked Three-Dimensional Plot
                 Program with Rotations",
  journal =      j-CACM,
  volume =       "17",
  number =       "9",
  pages =        "520--523",
  month =        sep,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Feinstein:1975:RMT}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Veillon:1974:NIL,
  author =       "F. Veillon",
  title =        "{ACM Algorithm 486}: Numerical Inversion of {Laplace}
                 Transform",
  journal =      j-CACM,
  volume =       "17",
  number =       "10",
  pages =        "587--589",
  month =        oct,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Koppelaar:1976:RNI,Veillon:1977:RNI}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pomeranz:1974:ECD,
  author =       "J. Pomeranz",
  title =        "{ACM Algorithm 487}: Exact Cumulative Distribution of
                 the {Kolmogorov--Smirnov} Statistic for Small Samples",
  journal =      j-CACM,
  volume =       "17",
  number =       "12",
  pages =        "703--704",
  month =        dec,
  year =         "1974",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Pomeranz:1976:REC}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Floyd:1975:ASF,
  author =       "R. W. Floyd and R. L. Rivest",
  title =        "{ACM Algorithm 489}: The Algorithm {SELECT} --- for
                 Finding the $i{\rm th}$ Smallest of $n$ Elements",
  journal =      j-CACM,
  volume =       "18",
  number =       "3",
  pages =        "173--173",
  month =        mar,
  year =         "1975",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Dec 04 12:25:43 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Brown:1976:RAS}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ginsberg:1975:DFR,
  author =       "E. S. Ginsberg and D. Zaborowski",
  title =        "{ACM Algorithm 490}: The Dilogarithm Function of a
                 Real Argument",
  journal =      j-CACM,
  volume =       "18",
  number =       "4",
  pages =        "200--202",
  month =        apr,
  year =         "1975",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Morris:1976:RDF}.",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

%%% ====================================================================
%%% Bibliography entries from IEEE Transactions on Computers

@Article{Kramer:1998:PWC,
  author =       "W. Kr{\"a}mer",
  title =        "A priori worst case error bounds for floating-point
                 computations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "7",
  pages =        "750--756",
  month =        jul,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.709374",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Tang:1992:TDI}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709374",
  abstract =     "A new technique for the a priori calculation of
                 rigorous error bounds for floating-point computations
                 is introduced. The theorems given in the paper combined
                 with interval arithmetic lead to the implementation of
                 reliable software routines, which enable the user to
                 compute the desired error bounds automatically by a
                 suitable computer program. As a prominent example, a
                 table-lookup algorithm for calculating the function
                 $exp(x) - 1$ that has been published by P. T. P. Tang
                 (1992) is analyzed using these new tools. The result
                 shows the high quality of the new approach",
  acknowledgement = ack-nhfb,
  author-dates = "1952--2014 (WK)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}

%%% ====================================================================
%%% Bibliography entries from Software---Practice and Experience

@Article{BrinchHansen:1994:MLD,
  author =       "Per {Brinch Hansen}",
  title =        "Multiple-length Division Revisited: a Tour of the
                 Minefield",
  journal =      j-SPE,
  volume =       "24",
  number =       "6",
  pages =        "579--601",
  month =        jun,
  year =         "1994",
  CODEN =        "SPEXBL",
  ISSN =         "0038-0644 (print), 1097-024X (electronic)",
  ISSN-L =       "0038-0644",
  bibdate =      "Thu Apr 29 15:16:58 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "This paper derives an algorithm for division of long
                 integers, and implements it as a literate program,
                 although without identifier cross-references. See also
                 related work \cite{Regener:1984:MID} on division.",
  acknowledgement = ack-nhfb,
  fjournal =     "Soft{\-}ware\emdash Prac{\-}tice and Experience",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-024X",
}

%%% ====================================================================
%%% Bibliography entries from ACM Transactions on Mathematical Software.

@Article{Rice:1975:PS,
  author =       "John R. Rice",
  title =        "Purpose and Scope",
  journal =      j-TOMS,
  volume =       "1",
  number =       "1",
  pages =        "1--3",
  month =        mar,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355626.355627",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 21:29:05 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Anonymous:1975:ADS,
  author =       "{Anonymous}",
  title =        "Algorithms Distribution Service",
  journal =      j-TOMS,
  volume =       "1",
  number =       "1",
  pages =        "4--4",
  month =        mar,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355626.355628",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 21:29:05 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/355626.355628;
                 http://www.acm.org/pubs/citations/journals/toms/1975-1-1/p4-no_author/",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fosdick:1975:AP,
  author =       "Lloyd D. Fosdick",
  title =        "Algorithms Policy",
  journal =      j-TOMS,
  volume =       "1",
  number =       "1",
  pages =        "5--6",
  month =        mar,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355626.355629",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 21:29:05 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Anonymous:1975:PMS,
  author =       "{Anonymous}",
  title =        "Papers from {Mathematical Software II}",
  journal =      j-TOMS,
  volume =       "1",
  number =       "1",
  pages =        "7--12",
  month =        mar,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355626.355630",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 21:29:05 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/355626.355630;
                 http://www.acm.org/pubs/citations/journals/toms/1975-1-1/p7-no_author/",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cody:1975:FPS,
  author =       "W. J. Cody",
  title =        "The {FUNPACK} Package of Special Function
                 Subroutines",
  journal =      j-TOMS,
  volume =       "1",
  number =       "1",
  pages =        "13--25",
  month =        mar,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355626.355631",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Jenkins:1975:PTP,
  author =       "M. A. Jenkins and J. F. Traub",
  title =        "Principles for Testing Polynomial Zerofinding
                 Programs",
  journal =      j-TOMS,
  volume =       "1",
  number =       "1",
  pages =        "26--34",
  month =        mar,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355626.355632",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68A10 (65H05)",
  MRnumber =     "53 #2009",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "James Howland",
}

@Article{Parlett:1975:ICC,
  author =       "B. N. Parlett and Y. Wang",
  title =        "The Influence of the Compiler on the Cost of
                 Mathematical Software\emdash in Particular on the Cost
                 of Triangular Factorization",
  journal =      j-TOMS,
  volume =       "1",
  number =       "1",
  pages =        "35--46",
  month =        mar,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355626.355633",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:35:13 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "cs; lud; nla; software",
}

@Article{Glover:1975:RWA,
  author =       "Fred Glover and Darwin Klingman",
  title =        "Real World Applications of Network Related Problems
                 and Breakthroughs in Solving Them Efficiently",
  journal =      j-TOMS,
  volume =       "1",
  number =       "1",
  pages =        "47--55",
  month =        mar,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355626.355634",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ng:1975:CCM,
  author =       "Edward W. Ng",
  title =        "A Comparison of Computational Methods and Algorithms
                 for the Complex Gamma Function",
  journal =      j-TOMS,
  volume =       "1",
  number =       "1",
  pages =        "56--70",
  month =        mar,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355626.355635",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "52 #2148",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "R. H. Bartels",
}

@Article{Byrne:1975:PNS,
  author =       "G. D. Byrne and A. C. Hindmarsh",
  title =        "A Polyalgorithm for the Numerical Solution of Ordinary
                 Differential Equations",
  journal =      j-TOMS,
  volume =       "1",
  number =       "1",
  pages =        "71--96",
  month =        mar,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355626.355636",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L99 (68A10)",
  MRnumber =     "51 #14600",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Sean McKee",
}

@Article{Powell:1975:VUM,
  author =       "M. J. D. Powell",
  title =        "A View of Unconstrained Minimization Algorithms that
                 Do Not Require Derivatives",
  journal =      j-TOMS,
  volume =       "1",
  number =       "2",
  pages =        "97--107",
  month =        jun,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355637.355638",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "(Reviewer: R. P. Brent (CR {17} \#29471)) 65K05",
  MRnumber =     "53 #14908",
  bibdate =      "Sat Dec 20 10:45:23 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Miller:1975:SRA,
  author =       "Webb Miller",
  title =        "Software for Roundoff Analysis",
  journal =      j-TOMS,
  volume =       "1",
  number =       "2",
  pages =        "108--128",
  month =        jun,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355637.355639",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G05",
  MRnumber =     "53 #9622",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "James H. Wilkinson",
}

@Article{Malcolm:1975:LVG,
  author =       "Michael A. Malcolm and R. Bruce Simpson",
  title =        "Local Versus Global Strategies for Adaptive
                 Quadrature",
  journal =      j-TOMS,
  volume =       "1",
  number =       "2",
  pages =        "129--146",
  month =        jun,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355637.355640",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30",
  MRnumber =     "51 #7248",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Thomas A. Atchison",
}

@Article{Stoutemyer:1975:AOU,
  author =       "David R. Stoutemyer",
  title =        "Analytical Optimization Using Computer Algebraic
                 Manipulation",
  journal =      j-TOMS,
  volume =       "1",
  number =       "2",
  pages =        "147--164",
  month =        jun,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355637.355641",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "90C99",
  MRnumber =     "58 #4363",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Barinka:1975:SEC,
  author =       "Lawrence L. Barinka",
  title =        "Some Experience with Constructing, Testing, and
                 Certifying a Standard Mathematical Subroutine Library",
  journal =      j-TOMS,
  volume =       "1",
  number =       "2",
  pages =        "165--177",
  month =        jun,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355637.355642",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Jenkins:1975:AZR,
  author =       "M. A. Jenkins",
  title =        "{Algorithm 493}: Zeros of a Real Polynomial [{C2}]",
  journal =      j-TOMS,
  volume =       "1",
  number =       "2",
  pages =        "178--189",
  month =        jun,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355637.355643",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:27:23 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rice:1975:SPP,
  author =       "John R. Rice",
  title =        "Software Package Policy",
  journal =      j-TOMS,
  volume =       "1",
  number =       "3",
  pages =        "193--195",
  month =        sep,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355644.355645",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bailey:1975:UAM,
  author =       "Carl B. Bailey and Rondall E. Jones",
  title =        "Usage and Argument Monitoring of Mathematical Library
                 Routines",
  journal =      j-TOMS,
  volume =       "1",
  number =       "3",
  pages =        "196--209",
  month =        sep,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355644.355646",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{George:1975:ARR,
  author =       "James E. George",
  title =        "Algorithms to Reveal the Representation of Characters,
                 Integers, and Floating-Point Numbers",
  journal =      j-TOMS,
  volume =       "1",
  number =       "3",
  pages =        "210--216",
  month =        sep,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355644.355647",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Aird:1975:CAU,
  author =       "T. J. Aird and Robert E. Lynch",
  title =        "Computable Accurate Upper and Lower Error Bounds for
                 Approximate Solutions of Linear Algebraic Systems",
  journal =      j-TOMS,
  volume =       "1",
  number =       "3",
  pages =        "217--231",
  month =        sep,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355644.355648",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F35",
  MRnumber =     "52 #2176",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Ian Gladwell",
}

@Article{Sincovec:1975:SNP,
  author =       "Richard F. Sincovec and Niel K. Madsen",
  title =        "Software for Nonlinear Partial Differential
                 Equations",
  journal =      j-TOMS,
  volume =       "1",
  number =       "3",
  pages =        "232--260",
  month =        sep,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355644.355649",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:44:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sincovec:1975:APS,
  author =       "Richard F. Sincovec and Niel K. Madsen",
  title =        "{Algorithm 494}: {PDEONE}, Solutions of Systems of
                 Partial Differential Equations [{D3}]",
  journal =      j-TOMS,
  volume =       "1",
  number =       "3",
  pages =        "261--263",
  month =        sep,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355644.355650",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 18:06:09 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Barrodale:1975:ASO,
  author =       "I. Barrodale and C. Phillips",
  title =        "{Algorithm 495}: Solution of an Overdetermined System
                 of Linear Equations in the {Chebychev} Norm [{F4}]",
  journal =      j-TOMS,
  volume =       "1",
  number =       "3",
  pages =        "264--270",
  month =        sep,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355644.355651",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 16:10:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Chebyshev approximation; nla",
}

@Article{Kaufman:1975:ALA,
  author =       "Linda Kaufman",
  title =        "{Algorithm 496}: The {LZ} Algorithm to Solve the
                 Generalized Eigenvalue Problem for Complex Matrices
                 [{F2}]",
  journal =      j-TOMS,
  volume =       "1",
  number =       "3",
  pages =        "271--281",
  month =        sep,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355644.355652",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 29 15:21:30 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Kaufman:1976:RLA}.",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Skovgaard:1975:RBF,
  author =       "Ove Skovgaard",
  title =        "Remark on ``{Algorithm 236}: {Bessel} Functions of the
                 First Kind [{S17}]''",
  journal =      j-TOMS,
  volume =       "1",
  number =       "3",
  pages =        "282--284",
  month =        sep,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355644.355653",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:11 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Gautschi:1964:AAB}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Feinstein:1975:RMT,
  author =       "Robert Feinstein",
  title =        "Remark on ``{Algorithm 483}: Masked Three-Dimensional
                 Plot Program with Rotations [{J6}]''",
  journal =      j-TOMS,
  volume =       "1",
  number =       "3",
  pages =        "285--285",
  month =        sep,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355644.355654",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:09 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Watkins:1974:MTD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Misra:1975:RG,
  author =       "Jayadev Misra",
  title =        "Remark on ``{Algorithm 246}: {Graycode} [{Z}]''",
  journal =      j-TOMS,
  volume =       "1",
  number =       "3",
  pages =        "285--285",
  month =        sep,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355644.356449",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 20:42:41 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Boothroyd:1964:G,Er:1985:RG}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Stone:1975:PTE,
  author =       "Harold S. Stone",
  title =        "Parallel Tridiagonal Equation Solvers",
  journal =      j-TOMS,
  volume =       "1",
  number =       "4",
  pages =        "289--307",
  month =        dec,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355656.355657",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68A10 (68A20)",
  MRnumber =     "52 #9676",
  bibdate =      "Fri Aug 26 23:35:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "nla; prll; tridiagonal matrix",
  reviewer =     "V. A. Valkovskii",
}

@Article{Lambiotte:1975:STL,
  author =       "Jules J. {Lambiotte, Jr.} and Robert G. Voigt",
  title =        "The Solution of Tridiagonal Linear Systems on the {CDC
                 STAR 100} Computer",
  journal =      j-TOMS,
  volume =       "1",
  number =       "4",
  pages =        "308--329",
  month =        dec,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355656.355658",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68A10 (68A20)",
  MRnumber =     "52 #9677",
  bibdate =      "Sat Aug 27 00:20:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "linear system; nla; tridiagonal matrix; vect",
  reviewer =     "V. A. Valkovskii",
}

@Article{Bus:1975:TEA,
  author =       "J. C. P. Bus and T. J. Dekker",
  title =        "Two Efficient Algorithms with Guaranteed Convergence
                 for Finding a Zero of a Function",
  journal =      j-TOMS,
  volume =       "1",
  number =       "4",
  pages =        "330--345",
  month =        dec,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355656.355659",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H05",
  MRnumber =     "52 #7112",
  bibdate =      "Fri Aug 26 23:12:30 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "nlop",
  reviewer =     "Ian Gladwell",
}

@Article{Norman:1975:CFP,
  author =       "A. C. Norman",
  title =        "Computing with Formal Power Series",
  journal =      j-TOMS,
  volume =       "1",
  number =       "4",
  pages =        "346--356",
  month =        dec,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355656.355660",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:22:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Neves:1975:AIF,
  author =       "Kenneth W. Neves",
  title =        "Automatic Integration of Functional Differential
                 Equations: An Approach",
  journal =      j-TOMS,
  volume =       "1",
  number =       "4",
  pages =        "357--368",
  month =        dec,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355656.355661",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65Q05",
  MRnumber =     "52 #7171",
  bibdate =      "Sat Aug 27 00:22:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "W. C. Rheinboldt",
}

@Article{Neves:1975:AAI,
  author =       "Kenneth W. Neves",
  title =        "{Algorithm 497}: Automatic Integration of Functional
                 Differential Equations [{D2}]",
  journal =      j-TOMS,
  volume =       "1",
  number =       "4",
  pages =        "369--371",
  month =        dec,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355656.355662",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:24:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Prince:1975:AAF,
  author =       "P. J. Prince",
  title =        "{Algorithm 498}: {Airy} Functions Using {Chebyshev}
                 Series Approximations",
  journal =      j-TOMS,
  volume =       "1",
  number =       "4",
  pages =        "372--379",
  month =        dec,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355656.355663",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:24:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Razaz:1981:RAF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lewis:1975:CPF,
  author =       "John Gregg Lewis",
  title =        "Certification of ``{Algorithm 349}: Polygamma
                 Functions with Arbitrary Precision''",
  journal =      j-TOMS,
  volume =       "1",
  number =       "4",
  pages =        "380--381",
  month =        dec,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355656.355664",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 11:10:19 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{TadeudeMedeiros:1969:APF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bromage:1975:CVS,
  author =       "Gordon E. Bromage",
  title =        "Certification of ``{Algorithm 475}: Visible Surface
                 Plotting Program [{J6}]''",
  journal =      j-TOMS,
  volume =       "1",
  number =       "4",
  pages =        "381--382",
  month =        dec,
  year =         "1975",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355656.355665",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:22:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rice:1976:PAA,
  author =       "John R. Rice",
  title =        "Parallel Algorithms for Adaptive Quadrature. {III}.
                 Program Correctness",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "1--30",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355666.355667",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30 (68A10)",
  MRnumber =     "54 #9058c",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Frederick N. Fritsch",
}

@Article{Griss:1976:ASS,
  author =       "Martin L. Griss",
  title =        "The Algebraic Solution of Sparse Linear Systems via
                 Minor Expansion",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "31--49",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355666.355668",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05",
  MRnumber =     "54 #4073",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Charles R. Johnson",
}

@Article{Duris:1976:GCP,
  author =       "Charles S. Duris",
  title =        "Generating and Compounding Product-Type
                 {Newton-Coates} Quadrature Formulas",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "50--58",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355666.355669",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30",
  MRnumber =     "53 #1919",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Thomas A. Atchison",
}

@Article{Bays:1976:IPR,
  author =       "Carter Bays and S. D. Durham",
  title =        "Improving a Poor Random Number Generator",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "59--64",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355666.355670",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lyness:1976:CNA,
  author =       "J. N. Lyness and J. J. Kaganove",
  title =        "Comments on the Nature of Automatic Quadrature
                 Routines",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "65--81",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355666.355671",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30",
  MRnumber =     "53 #1921",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Henning Esser",
}

@Article{Kinsner:1976:AES,
  author =       "W. Kinsner and E. Della Torre",
  title =        "{Algorithm 499}: An Efficient Scanning Technique
                 [{Z}]",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "82--86",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355666.355672",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:35:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Shanno:1976:AMU,
  author =       "D. F. Shanno and K. H. Phua",
  title =        "{Algorithm 500}: Minimization of Unconstrained
                 Multivariate Functions [{E4}]",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "87--94",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355666.355673",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 29 15:25:28 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remarks \cite{Dunham:1977:RMU,Shanno:1980:RMU}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Simpson:1976:AFT,
  author =       "Joseph C. Simpson",
  title =        "{Algorithm 501}: {Fortran} Translation of {Algorithm
                 409}, Discrete {Chebychev} Curve Fit [{E2}]",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "95--97",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355666.355674",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 23:07:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Futrell:1978:RTA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kubicek:1976:ADS,
  author =       "Milan Kub{\'\i}{\v{c}}ek",
  title =        "{Algorithm 502}: Dependence of Solution of Nonlinear
                 Systems on a Parameter [{C5}]",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "98--107",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355666.355675",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 18:03:58 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/355666.355675;
                 http://www.acm.org/pubs/citations/journals/toms/1976-2-1/p98-kubiviek/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Boulton:1976:REP,
  author =       "D. M. Boulton",
  title =        "Remark on ``{Algorithm 434}: Exact Probabilities for
                 ${R}\times{C}$ Contingency Tables [{G2}]''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "108--108",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355666.355676",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{March:1972:EPT}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Duta:1976:RVS,
  author =       "Lucian D. Duta",
  title =        "Remark on ``{Algorithm 475}: Visible Surface Plotting
                 Program [{J6}]''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "109--110",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355666.355677",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:22 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Wright:1974:VSP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{White:1976:RMS,
  author =       "G. M. White and S. Goudreau and J. L. Legros",
  title =        "Remark on ``{Algorithm 479}: a Minimal Spanning Tree
                 Clustering Method [{Z}]''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "110--111",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355666.355678",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Page:1974:MST}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pomeranz:1976:REC,
  author =       "J. Pomeranz",
  title =        "Remark on ``{Algorithm 487}: Exact Cumulative
                 Distribution of the {Kolmogorov--Smirnov} Statistic for
                 Small Samples [{S14}]''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "111--111",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355666.355679",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Pomeranz:1974:ECD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Morris:1976:RDF,
  author =       "Robert Morris",
  title =        "Remark on ``{Algorithm 490}: The Dilogarithm Function
                 of a Real Argument [{S22}]''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "1",
  pages =        "112--112",
  month =        mar,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355666.355680",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Ginsberg:1975:DFR}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rice:1976:TPS,
  author =       "John R. Rice",
  title =        "{TOMS} Policy Statement: The Rights of Program Authors
                 in the Evaluation of Programs",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "113--114",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355681.355682",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ford:1976:DSN,
  author =       "B. Ford and D. K. Sayers",
  title =        "Developing a Single Numerical Algorithms Library for
                 Different Machine Ranges",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "115--131",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355681.355683",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Paul:1976:SEF,
  author =       "George Paul and M. Wayne Wilson",
  title =        "Should the Elementary Function Library Be Incorporated
                 Into Computer Instruction Sets?",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "132--142",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355681.355684",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Janko:1976:LIS,
  author =       "Wolfgang Janko",
  title =        "A List Insertion Sort for Keys With Arbitrary Key
                 Distribution",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "143--153",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355681.355685",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Atkinson:1976:APL,
  author =       "Kendall Atkinson",
  title =        "An Automatic Program for Linear {Fredholm} Integral
                 Equations of the Second Kind",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "154--171",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355681.355686",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65R05",
  MRnumber =     "54 #6528",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Christopher T. H. Baker",
}

@Article{Shampine:1976:GEE,
  author =       "L. F. Shampine and H. A. Watts",
  title =        "Global Error Estimates for Ordinary Differential
                 Equations",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "172--186",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355681.355687",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05",
  MRnumber =     "54 #1621",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "J. Hurt",
}

@Article{Ericksen:1976:ICP,
  author =       "J. H. Ericksen and R. Wilhelmson",
  title =        "Implementation of a Convective Problem Requiring
                 Auxiliary Storage",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "187--195",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355681.355688",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 10:18:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Atkinson:1976:AAP,
  author =       "Kendall Atkinson",
  title =        "{Algorithm 503}: An Automatic Program for {Fredholm}
                 Integral Equations of the Second Kind [{D5}]",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "196--199",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355681.355689",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:51:30 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Shampine:1976:AGG,
  author =       "L. F. Shampine and H. A. Watts",
  title =        "{Algorithm 504}: {GERK}: Global Error Estimation For
                 Ordinary Differential Equations [{D}]",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "200--203",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355681.355690",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:52:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Janko:1976:ALI,
  author =       "Wolfgang Janko",
  title =        "{Algorithm 505}: a List Insertion Sort for Keys with
                 Arbitrary Key Distribution [{S20}]",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "204--206",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355681.355691",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:52:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pike:1976:RIB,
  author =       "Malcolm C. Pike and Jennie SooHoo and N. E. Bosten",
  title =        "Remark on ``{Algorithm 179}: Incomplete Beta Ratio
                 [{S14}]''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "207--208",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355681.355692",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Ludwig:1963:IBR}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Anderson:1976:RIS,
  author =       "Michael R. Anderson",
  title =        "Remark on ``{Algorithm 433}: Interpolation and Smooth
                 Curve Fitting Based on Local Procedures [{E2}]''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "2",
  pages =        "208--208",
  month =        jun,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355681.355693",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Akima:1972:ISC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Wyatt:1976:PEP,
  author =       "W. T. {Wyatt, Jr.} and D. W. Lozier and D. J. Orser",
  title =        "A Portable Extended Precision Arithmetic Package and
                 Library With {Fortran} Precompiler",
  journal =      j-TOMS,
  volume =       "2",
  number =       "3",
  pages =        "209--231",
  month =        sep,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355694.355695",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/355694.355695;
                 http://www.acm.org/pubs/citations/journals/toms/1976-2-3/p209-lozier/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gentleman:1976:AAC,
  author =       "W. M. Gentleman and S. C. Johnson",
  title =        "Analysis of Algorithms, a Case Study: Determinants
                 of Matrices with Polynomial Entries",
  journal =      j-TOMS,
  volume =       "2",
  number =       "3",
  pages =        "232--241",
  month =        sep,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355694.355696",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F30",
  MRnumber =     "54 #1575",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "K. Moszynski",
}

@Article{Barwell:1976:CAS,
  author =       "Victor Barwell and Alan George",
  title =        "A Comparison of Algorithms for Solving Symmetric
                 Indefinite Systems of Linear Equations",
  journal =      j-TOMS,
  volume =       "2",
  number =       "3",
  pages =        "242--251",
  month =        sep,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355694.355697",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05",
  MRnumber =     "54 #6472",
  bibdate =      "Fri Aug 26 23:35:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "indefinite system; linear system; nla; symmetric
                 matrix",
  reviewer =     "F. Szidarovszky",
}

@Article{Bartels:1976:HIU,
  author =       "Richard Bartels and Alec Steingart",
  title =        "{Hermite} Interpolation Using a Triangular Polynomial
                 Basis",
  journal =      j-TOMS,
  volume =       "2",
  number =       "3",
  pages =        "252--256",
  month =        sep,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355694.355698",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15 (65D20)",
  MRnumber =     "55 #4602",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Hwa-Shan Ho",
}

@Article{Hall:1976:NSS,
  author =       "C. A. Hall and R. W. Luczak and A. G. Serdy",
  title =        "Numerical Solution of Steady State Heat Flow Problems
                 Over Curved Domains",
  journal =      j-TOMS,
  volume =       "2",
  number =       "3",
  pages =        "257--274",
  month =        sep,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355694.355699",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65N10",
  MRnumber =     "54 #4135",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Stephen Hilbert",
}

@Article{Stewart:1976:AHE,
  author =       "G. W. Stewart",
  title =        "{Algorithm 506}: {HQR3} and {EXCHNG}: {Fortran}
                 Subroutines for Calculating and Ordering the
                 Eigenvalues of a Real Upper {Hessenberg} Matrix
                 [{F2}]",
  journal =      j-TOMS,
  volume =       "2",
  number =       "3",
  pages =        "275--280",
  month =        sep,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355694.355700",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 18:03:53 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Flamm:1982:RHE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "eig; Hessenberg matrix; nla; QR algorithm; software",
}

@Article{Herriot:1976:APQ,
  author =       "John G. Herriot and Christian H. Reinsch",
  title =        "{Algorithm 507}: Procedures for Quintic Natural Spline
                 Interpolation [{E1}]",
  journal =      j-TOMS,
  volume =       "2",
  number =       "3",
  pages =        "281--289",
  month =        sep,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355694.355701",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 01:01:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Hanson:1982:RPQ}.",
  acknowledgement = ack-nhfb,
  author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Loeser:1976:SAQ,
  author =       "Rudolf Loeser",
  title =        "Survey on Algorithms 347, 426, and Quicksort",
  journal =      j-TOMS,
  volume =       "2",
  number =       "3",
  pages =        "290--299",
  month =        sep,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355694.355702",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Davies:1976:RRF,
  author =       "Alan M. Davies",
  title =        "Remark on ``{Algorithm 450}: {Rosenbrock} Function
                 Minimization [{E4}]''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "3",
  pages =        "300--301",
  month =        sep,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355694.355703",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:28 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{MacHura:1973:RFM}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Brown:1976:RAS,
  author =       "Theodore Brown",
  title =        "Remark on ``{Algorithm 489}: The Algorithm
                 {SELECT}\emdash for Finding the $i$th Smallest of $n$
                 Elements [{M1}]''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "3",
  pages =        "301--304",
  month =        sep,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355694.355704",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:31 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Floyd:1975:ASF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pavlidis:1976:UAP,
  author =       "Theodosios Pavlidis",
  title =        "The Use of Algorithms of Piecewise Approximations for
                 Picture Processing Applications",
  journal =      j-TOMS,
  volume =       "2",
  number =       "4",
  pages =        "305--321",
  month =        dec,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355705.355706",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gibbs:1976:CSB,
  author =       "Norman E. Gibbs and William G. {Poole Jr.} and Paul K.
                 Stockmeyer",
  title =        "A Comparison of Several Bandwidth and Profile
                 Reduction Algorithms",
  journal =      j-TOMS,
  volume =       "2",
  number =       "4",
  pages =        "322--330",
  month =        dec,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355705.355707",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 01:07:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "band matrix; band reduction; nla; profile reduction;
                 sparse",
}

@Article{Mahendrarajah:1976:CTA,
  author =       "A. Mahendrarajah and F. Fiala",
  title =        "A Comparison of Three Algorithms for Linear Zero-One
                 Programs",
  journal =      j-TOMS,
  volume =       "2",
  number =       "4",
  pages =        "331--334",
  month =        dec,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355705.355708",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 01:08:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Weinberger:1976:FPA,
  author =       "P. J. Weinberger and L. P. Rothschild",
  title =        "Factoring Polynomials Over Algebraic Number Fields",
  journal =      j-TOMS,
  volume =       "2",
  number =       "4",
  pages =        "335--350",
  month =        dec,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355705.355709",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "12A20 (12-04)",
  MRnumber =     "56 #8521",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "I. Gerst",
}

@Article{Pinkert:1976:EMF,
  author =       "James R. Pinkert",
  title =        "An Exact Method for Finding the Roots of a Complex
                 Polynomial",
  journal =      j-TOMS,
  volume =       "2",
  number =       "4",
  pages =        "351--363",
  month =        dec,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355705.355710",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "12-04 (12D10 30A08 65H05)",
  MRnumber =     "56 #299",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "E. Frank",
}

@Article{Rubin:1976:PI,
  author =       "Frank Rubin",
  title =        "Partition of Integers",
  journal =      j-TOMS,
  volume =       "2",
  number =       "4",
  pages =        "364--374",
  month =        dec,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355705.355711",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68A10 (05A17 10A45)",
  MRnumber =     "57 #4605",
  bibdate =      "Sat Aug 27 00:30:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "S. Zaks",
}

@Article{Crane:1976:AMB,
  author =       "H. L. {Crane Jr.} and Norman E. Gibbs and William G.
                 {Poole Jr.} and Paul K. Stockmeyer",
  title =        "{Algorithm 508}: Matrix Bandwidth and Profile
                 Reduction [{F1}]",
  journal =      j-TOMS,
  volume =       "2",
  number =       "4",
  pages =        "375--377",
  month =        dec,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355705.355712",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 01:11:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Lewis:1982:RMB}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gibbs:1976:AHP,
  author =       "Norman E. Gibbs",
  title =        "{Algorithm 509}: a Hybrid Profile Reduction Algorithm
                 [{F1}]",
  journal =      j-TOMS,
  volume =       "2",
  number =       "4",
  pages =        "378--387",
  month =        dec,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355705.355713",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 01:11:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Lewis:1982:RMB}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Wilson:1976:APL,
  author =       "D. G. Wilson",
  title =        "{Algorithm 510}: Piecewise Linear Approximation to
                 Tabulated Data [{E2}]",
  journal =      j-TOMS,
  volume =       "2",
  number =       "4",
  pages =        "388--391",
  month =        dec,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355705.355714",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 01:12:13 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ito:1976:RIT,
  author =       "M. R. Ito",
  title =        "Remark on ``{Algorithm 284}: Interchange of Two Blocks
                 of Data [{K2}]''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "4",
  pages =        "392--393",
  month =        dec,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355705.355715",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Fletcher:1966:ITB}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{elLozy:1976:RAC,
  author =       "Mohamed {el Lozy}",
  title =        "Remark on ``{Algorithm 299}: Chi-Squared Integral
                 [{S15}]''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "4",
  pages =        "393--395",
  month =        dec,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355705.355716",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 11:04:46 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Hill:1967:CSI,Hill:1985:RCS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Koppelaar:1976:RNI,
  author =       "Henk Koppelaar and Peter Molenaar",
  title =        "Remark on ``{Algorithm 486}: Numerical Inversion of
                 {Laplace} Transform [{D5}]''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "4",
  pages =        "395--396",
  month =        dec,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355705.355717",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 29 15:27:20 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Veillon:1974:NIL,Piessens:1984:RNI}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kaufman:1976:RLA,
  author =       "Linda Kaufman",
  title =        "Remark on ``{Algorithm 496}: The {LZ} Algorithm to
                 Solve the Generalized Eigenvalue Problem for Complex
                 Matrices [{F2}]''",
  journal =      j-TOMS,
  volume =       "2",
  number =       "4",
  pages =        "396--396",
  month =        dec,
  year =         "1976",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355705.355718",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:42 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Kaufman:1975:ALA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{McClellan:1977:ESL,
  author =       "Michael T. McClellan",
  title =        "The Exact Solution of Linear Equations with Rational
                 Function Coefficients",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "1--25",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355720",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68A15",
  MRnumber =     "55 #11696",
  bibdate =      "Sat Aug 27 22:12:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Jo Ann Howell",
}

@Article{Stoutemyer:1977:AEA,
  author =       "David R. Stoutemyer",
  title =        "Automatic Error Analysis Using Computer Algebraic
                 Manipulation",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "26--43",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355721",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G05",
  MRnumber =     "55 #13765",
  bibdate =      "Fri Sep 02 22:30:11 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This paper shows how the inherent error and the
                 fixed-point or floating-point roundoff of chopoff error
                 of an expression can be determined automatically using
                 a computer algebra language such as {REDUCE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "R. P. Brent",
}

@Article{Shampine:1977:SND,
  author =       "L. F. Shampine",
  title =        "Stiff and Nonstiff Differential Equation Solvers,
                 {II}: Detecting Stiffness with {Runge--Kutta} Methods",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "44--53",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355722",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05",
  MRnumber =     "56 #4175",
  bibdate =      "Sat Aug 27 22:12:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "W. H. Enright",
}

@Article{Tran-Thong:1977:FPF,
  author =       "Tr{\^a}\`n-Th{\^o}\'ng and Bede Liu",
  title =        "Floating Point Fast {Fourier} Transform Computation
                 Using Double Precision Floating Point Accumulators",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "54--59",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355723",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65T05",
  MRnumber =     "55 #11658",
  bibdate =      "Sat Aug 27 22:12:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Most commonly available fast Fourier transform (FFT)
                 subroutines use single precision chopping arithmetic,
                 and the resulting normalized roundoff error, in
                 computing an $N$-point transform with $N = \prod_{i =
                 1}^M a_i$ is $O(M^2)$. This paper proposes a
                 modification of these subroutines for use on computers
                 with a hardwired double precision arithmetic unit. The
                 resulting normalized roundoff error is $O(M)$ and is
                 independent of the $a_i$. The modification leads to a
                 negligible increase in storage. For most computers, the
                 increase in the execution time is small. For certain
                 computers, such as IBM System/360 models 91 and 195,
                 the modification can result in a decrease in the
                 execution time.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "computer arithmetic; double-length summation; fast
                 Fourier transform; roundoff error",
}

@Article{Gonzalez:1977:EAK,
  author =       "Teofilo Gonzalez and Sartaj Sahni and W. R. Franta",
  title =        "An Efficient Algorithm for the {Kolmogorov--Smirnov}
                 and {Lilliefors} Tests",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "60--64",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355724",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65C99",
  MRnumber =     "55 #11561",
  bibdate =      "Sat Aug 27 22:12:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Hannah Chen",
}

@Article{Kaufman:1977:STQ,
  author =       "Linda Kaufman",
  title =        "Some Thoughts on the {QZ} Algorithm for Solving the
                 Generalized Eigenvalue Problem",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "65--75",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355725",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F15",
  MRnumber =     "55 #6814",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "gieg; nla; QZ algorithm",
  reviewer =     "W. Niethammer",
}

@Article{Amos:1977:CSI,
  author =       "D. E. Amos and S. L. Daniel and M. K. Weston",
  title =        "{CDC} 6600 Subroutines {IBESS} and {JBESS} for
                 {Bessel} Functions {$I_\nu(x)$} and {$J_\nu(x)$},
                 {$x\ge0,\nu\ge0$}",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "76--92",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355726",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "55 #6781",
  bibdate =      "Tue Sep 06 19:20:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Sven-{\AA}ke Gustafson",
}

@Article{Amos:1977:ACS,
  author =       "D. E. Amos and S. L. Daniel and M. K. Weston",
  title =        "{Algorithm 511}: {CDC} 6600 Subroutines {IBESS} and
                 {JBESS} for {Bessel} Functions {$I_\nu(x)$} and
                 {$J_\nu(x)$}, {$x \ge 0, \nu \ge 0$} [{S18}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "93--95",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355727",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 29 15:14:12 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See erratum \cite{Amos:1978:ECS}.",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Benson:1977:ANA,
  author =       "A. Benson and D. J. Evans",
  title =        "{Algorithm 512}: a Normalized Algorithm for Solution
                 of the Positive Definite Symmetric Quindiagonal Systems
                 of Linear Equations [{F4}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "96--103",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355728",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 22:22:47 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cate:1977:AAS,
  author =       "Esko G. Cate and David W. Twigg",
  title =        "{Algorithm 513}: Analysis of In-Situ Transposition
                 [{F1}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "104--110",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355729",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68A10",
  MRnumber =     "55 #13866",
  bibdate =      "Thu Apr 29 15:17:56 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Leathers:1979:RAS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Ralph A. Willoughby",
}

@Article{Veillon:1977:RNI,
  author =       "Fran{\c{c}}oise Veillon",
  title =        "Remark on ``{Algorithm 486}: Numerical Inversion of
                 {Laplace} Transform''",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "111--111",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355730",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:43 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Veillon:1974:NIL,Piessens:1984:RNI}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Dunham:1977:RMU,
  author =       "Charles Dunham",
  title =        "Remark on ``{Algorithm 500}: Minimization of
                 Unconstrained Multivariate Functions [{E4}]''",
  journal =      j-TOMS,
  volume =       "3",
  number =       "1",
  pages =        "112--112",
  month =        mar,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355719.355731",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:27:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Shanno:1976:AMU}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Aird:1977:PMS,
  author =       "Thomas J. Aird",
  title =        "Portability of Mathematical Software Coded in
                 {Fortran}",
  journal =      j-TOMS,
  volume =       "3",
  number =       "2",
  pages =        "113--127",
  month =        jun,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355732.355733",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 22:26:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Stoutemyer:1977:ASI,
  author =       "David R. Stoutemyer",
  title =        "Analytically Solving Integral Equations by Using
                 Computer Algebra",
  journal =      j-TOMS,
  volume =       "3",
  number =       "2",
  pages =        "128--146",
  month =        jun,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355732.355734",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65R05",
  MRnumber =     "56 #4205",
  bibdate =      "Sat Aug 27 22:26:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Sean McKee",
}

@Article{McClellan:1977:CAE,
  author =       "Michael T. McClellan",
  title =        "A Comparison of Algorithms for the Exact Solution of
                 Linear Equations",
  journal =      j-TOMS,
  volume =       "3",
  number =       "2",
  pages =        "147--158",
  month =        jun,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355732.355735",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05",
  MRnumber =     "55 #13753",
  bibdate =      "Sat Aug 27 22:26:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "H. R. Schwarz",
}

@Article{Farden:1977:SSS,
  author =       "David C. Farden",
  title =        "The Solution of a Special Set of {Hermitian}
                 {Toeplitz} Linear Equations",
  journal =      j-TOMS,
  volume =       "3",
  number =       "2",
  pages =        "159--163",
  month =        jun,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355732.355736",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 22:26:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ichida:1977:CFO,
  author =       "Kozo Ichida and Takeshi Kiyono and Fujiichi
                 Yoshimoto",
  title =        "Curve Fitting by a One-Pass Method With a Piecewise
                 Cubic Polynomial",
  journal =      j-TOMS,
  volume =       "3",
  number =       "2",
  pages =        "164--174",
  month =        jun,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355732.355737",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 22:26:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ellis:1977:ANM,
  author =       "T. M. R. Ellis and D. H. McLain",
  title =        "{Algorithm 514}: a New Method of Cubic Curve Fitting
                 Using Local Data [{E2}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "2",
  pages =        "175--179",
  month =        jun,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355732.355738",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Buckles:1977:AGV,
  author =       "B. P. Buckles and M. Lybanon",
  title =        "{Algorithm 515}: Generation of a Vector from the
                 Lexicographical Index [{G6}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "2",
  pages =        "180--182",
  month =        jun,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355732.355739",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{McKean:1977:AAO,
  author =       "J. W. McKean and T. A. {Ryan, Jr.}",
  title =        "{Algorithm 516}: An Algorithm for Obtaining Confidence
                 Intervals and Point Estimates Based on Ranks in the Two
                 Sample Location Problem [{G1}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "2",
  pages =        "183--185",
  month =        jun,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355732.355740",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Chan:1977:APC,
  author =       "S. P. Chan and R. Feldman and B. N. Parlett",
  title =        "{Algorithm 517}: a Program for Computing the Condition
                 Numbers of Matrix Eigenvalues Without Computing
                 Eigenvectors [{F2}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "2",
  pages =        "186--203",
  month =        jun,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355732.355741",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 22:34:22 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "condition estimation; eig; nla; nonsymmetric matrix;
                 pert; software",
}

@Article{Mackay:1977:RPT,
  author =       "M. Mackay and J. E. Radue",
  title =        "Remark on ``{Some} Performance Tests of `{Quicksort}'
                 and Descendants''",
  journal =      j-TOMS,
  volume =       "3",
  number =       "2",
  pages =        "204--204",
  month =        jun,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355732.355742",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:07:36 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Loeser:1974:SPT}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Jansen:1977:RLF,
  author =       "J. K. M. Jansen",
  title =        "Remark on ``{Algorithm 259}: {Legendre} Functions for
                 Arguments Larger than One''",
  journal =      j-TOMS,
  volume =       "3",
  number =       "2",
  pages =        "204--205",
  month =        jun,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355732.356467",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 00:59:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Gautschi:1965:LFA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Friedman:1977:AFB,
  author =       "Jerome H. Friedman and Jon Louis Bentley and Raphael
                 Ari Finkel",
  title =        "An Algorithm for Finding Best Matches in Logarithmic
                 Expected Time",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "209--226",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355745",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 22:53:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/355744.355745;
                 http://www.acm.org/pubs/citations/journals/toms/1977-3-3/p209-bentley/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ito:1977:MRP,
  author =       "Tetsuro Ito and Makoto Kizawa",
  title =        "The Matrix Rearrangement Procedure for
                 Graph-Theoretical Algorithms and Its Application to the
                 Generation of Fundamental Cycles",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "227--231",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355746",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 22:26:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cody:1977:CRF,
  author =       "W. J. Cody and Rose M. Motley and L. Wayne Fullerton",
  title =        "The Computation of Real Fractional Order {Bessel}
                 Functions of the Second Kind",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "232--239",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355747",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 22:26:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gautschi:1977:ERI,
  author =       "Walter Gautschi",
  title =        "Evaluation of Repeated Integrals of the Coerror
                 Function",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "240--252",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355748",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 22:26:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Walker:1977:EMG,
  author =       "Alastair J. Walker",
  title =        "An Efficient Method for Generating Discrete Random
                 Variables with General Distributions",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "253--256",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355749",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 22:26:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kinderman:1977:CGR,
  author =       "A. J. Kinderman and J. F. Monahan",
  title =        "Computer Generation of Random Variables Using the
                 Ratio of Uniform Deviates",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "257--260",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355750",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 22:58:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  country =      "USA",
  date =         "13/05/93",
  descriptors =  "RVG",
  enum =         "7496",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  language =     "English",
  location =     "SEL: Wi",
  references =   "0",
  revision =     "16/01/94",
}

@Article{Cohen:1977:SSF,
  author =       "Jacques Cohen and Joel Katcoff",
  title =        "Symbolic Solution of Finite-Difference Equations",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "261--271",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355751",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 22:26:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fateman:1977:ADC,
  author =       "Richard J. Fateman",
  title =        "An Algorithm for Deciding the Convergence of the
                 Rational Iteration $x_{n+1} = f(x_n)$",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "272--278",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355752",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 22:26:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hill:1977:AIB,
  author =       "G. W. Hill",
  title =        "{Algorithm 518}: Incomplete {Bessel} Function {$I_0$}.
                 {The von Mises} Distribution [{S14}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "279--284",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355753",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 24 15:46:06 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kallman:1977:ATA,
  author =       "Ralph Kallman",
  title =        "{Algorithm 519}: Three Algorithms for Computing
                 {Kolmogorov--Smirnov} Probabilities with Arbitrary
                 Boundaries and a Certification of {Algorithm 487}
                 [{S14}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "285--294",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355754",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:01:47 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Weglarz:1977:AAR,
  author =       "Jan Weglarz and Jacek Blazewicz and Wojciech Cellary
                 and Roman Slowinski",
  title =        "{Algorithm 520}: An Automatic Revised Simplex Method
                 for Constrained Resource Network Scheduling [{H}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "295--300",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355755",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gautschi:1977:ARI,
  author =       "Walter Gautschi",
  title =        "{Algorithm 521}: Repeated Integrals of the Coerror
                 Function [{S15}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "301--302",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355756",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:03:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sipala:1977:RSM,
  author =       "Paolo Sipala",
  title =        "Remark on ``{Algorithm 408}: a Sparse Matrix Package
                 ({Part I}) [{F4}]''",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "303--303",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.355757",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{McNamee:1971:SMP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Tenney:1977:RTO,
  author =       "Dennis Tenney",
  title =        "Remark on ``{Algorithm 219}: Topological Ordering for
                 {PERT} Networks''",
  journal =      j-TOMS,
  volume =       "3",
  number =       "3",
  pages =        "303--303",
  month =        sep,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355744.356472",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Kase:1963:TOP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hillstrom:1977:STA,
  author =       "Kenneth E. Hillstrom",
  title =        "A Simulation Test Approach to the Evaluation of
                 Nonlinear Optimization Algorithms",
  journal =      j-TOMS,
  volume =       "3",
  number =       "4",
  pages =        "305--315",
  month =        dec,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355759.355760",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:06:22 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Powell:1977:PQA,
  author =       "M. J. D. Powell and M. A. Sabin",
  title =        "Piecewise Quadratic Approximations on Triangles",
  journal =      j-TOMS,
  volume =       "3",
  number =       "4",
  pages =        "316--325",
  month =        dec,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355759.355761",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15",
  MRnumber =     "58 #3319",
  bibdate =      "Sat Aug 27 23:07:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Skeel:1977:BLM,
  author =       "Robert D. Skeel and Antony K. Kong",
  title =        "Blended Linear Multistep Methods",
  journal =      j-TOMS,
  volume =       "3",
  number =       "4",
  pages =        "326--345",
  month =        dec,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355759.355762",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05",
  MRnumber =     "57 #1904",
  bibdate =      "Fri Sep 30 01:01:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "R. Leonard Brown",
}

@Article{Payne:1977:NRN,
  author =       "W. H. Payne",
  title =        "Normal Random Numbers: Using Machine Analysis to
                 Choose the Best Algorithm",
  journal =      j-TOMS,
  volume =       "3",
  number =       "4",
  pages =        "346--358",
  month =        dec,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355759.355763",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65C10",
  MRnumber =     "57 #1827",
  bibdate =      "Sat Aug 27 23:09:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  country =      "USA",
  date =         "13/05/93",
  descriptors =  "RVG",
  enum =         "7752",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  language =     "English",
  location =     "SEL: Wi",
  references =   "0",
  reviewer =     "Artenio De Matteis",
  revision =     "16/01/94",
}

@Article{Boyce:1977:IPF,
  author =       "William M. Boyce",
  title =        "An Improved Program for the Full {Steiner} Tree
                 Problem",
  journal =      j-TOMS,
  volume =       "3",
  number =       "4",
  pages =        "359--385",
  month =        dec,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355759.355764",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "90B10 (05C30)",
  MRnumber =     "57 #11690",
  bibdate =      "Sat Aug 27 23:07:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Fan R. K. Chung",
}

@Article{Cabay:1977:CTE,
  author =       "S. Cabay and T. P. L. Lam",
  title =        "Congruence Techniques for the Exact Solution of
                 Integer Systems of Linear Equations",
  journal =      j-TOMS,
  volume =       "3",
  number =       "4",
  pages =        "386--397",
  month =        dec,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355759.355765",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05",
  MRnumber =     "57 #7962a",
  bibdate =      "Fri Sep 30 01:01:45 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "W. Borsch-Supan",
}

@Article{Eddy:1977:NCH,
  author =       "William F. Eddy",
  title =        "A New Convex Hull Algorithm for Planar Sets",
  journal =      j-TOMS,
  volume =       "3",
  number =       "4",
  pages =        "398--403",
  month =        dec,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355759.355766",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:07:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cabay:1977:AEC,
  author =       "S. Cabay and T. P. L. Lam",
  title =        "{Algorithm 522}: {ESOLVE}, Congruence Techniques for
                 the Exact Solution of Integer Systems of Linear
                 Equations [{F4}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "4",
  pages =        "404--410",
  month =        dec,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355759.355767",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05",
  MRnumber =     "57 #7962b",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "W. Borsch-Supan",
}

@Article{Eddy:1977:ACN,
  author =       "W. F. Eddy",
  title =        "{Algorithm 523}: {CONVEX}, a New Convex Hull
                 Algorithm for Planar Sets [{Z}]",
  journal =      j-TOMS,
  volume =       "3",
  number =       "4",
  pages =        "411--412",
  month =        dec,
  year =         "1977",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355759.355768",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Dinkel:1978:SAP,
  author =       "John J. Dinkel and Gary A. Kochenberger and S. N.
                 Wong",
  title =        "Sensitivity Analysis Procedures for Geometric
                 Programs: Computational Aspects",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "1--14",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355769.355770",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/355769.355770;
                 http://www.acm.org/pubs/citations/journals/toms/1978-4-1/p1-wong/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Blue:1978:PFP,
  author =       "James L. Blue",
  title =        "A Portable {Fortran} Program to Find the {Euclidean}
                 Norm of a Vector",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "15--23",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355769.355771",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68A10",
  MRnumber =     "57 \#18205",
  bibdate =      "Sat Aug 27 23:14:36 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "BLAS; floating-point arithmetic; floating-point
                 overflow; floating-point underflow; nla; norm;
                 software",
  reviewer =     "A. D. Booth",
}

@Article{Ivie:1978:SMP,
  author =       "John Ivie",
  title =        "Some {MACSYMA} Programs for Solving Recurrence
                 Relations",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "24--33",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355769.355772",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:42:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Celis:1984:RCE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lasdon:1978:DTG,
  author =       "L. S. Lasdon and A. D. Waren and A. Jain and M.
                 Ratner",
  title =        "Design and Testing of a Generalized Reduced Gradient
                 Code for Nonlinear Programming",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "34--50",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355769.355773",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Tsao:1978:MNI,
  author =       "Nai-Kuan Tsao and Rose Marie Prior",
  title =        "On Multipoint Numerical Interpolation",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "51--56",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355769.355774",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Brent:1978:FMP,
  author =       "Richard P. Brent",
  title =        "A {Fortran} Multiple-Precision Arithmetic Package",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "57--70",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355769.355775",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Brent:1978:AMF,
  author =       "Richard P. Brent",
  title =        "{Algorithm 524}: {MP}, {A Fortran} Multiple-Precision
                 Arithmetic Package [{A1}]",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "71--81",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355769.355776",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:35:50 1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran1.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also
                 \cite{Brent:1979:RMF,Brent:1980:AIB,Smith:1998:AMP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rice:1978:AAA,
  author =       "John R. Rice",
  title =        "{Algorithm 525}: {ADAPT}, Adaptive Smooth Curve
                 Fitting [{E2}]",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "82--94",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355769.355777",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Futrell:1978:RTA,
  author =       "R. Futrell",
  title =        "Remark on ``{Fortran} Translation of {Algorithm 409}:
                 Discrete {Chebychev} Curve Fit [{E2}]''",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "95--95",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355769.355778",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 23:07:36 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Simpson:1976:AFT}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Skovgaard:1978:RCE,
  author =       "Ove Skovgaard",
  title =        "Remark on ``{Algorithm 149}: Complete Elliptic
                 Integral [{S21}]''",
  journal =      j-TOMS,
  volume =       "4",
  number =       "1",
  pages =        "95--95",
  month =        mar,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355769.356473",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Merner:1962:CEI}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Krogh:1978:AP,
  author =       "Fred T. Krogh",
  title =        "Algorithms Policy",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "97--99",
  month =        jun,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355780.355781",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:23:41 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ford:1978:PET,
  author =       "Brian Ford",
  title =        "Parametrization of the Environment for Transportable
                 Numerical Software",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "100--103",
  month =        jun,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355780.355782",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fox:1978:PMS,
  author =       "P. A. Fox and A. D. Hall and N. L. Schryer",
  title =        "The {PORT} Mathematical Subroutine Library",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "104--126",
  month =        jun,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355780.355783",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  abstract =     "The development at Bell Laboratories of PORT, a
                 library of portable Fortran programs for numerical
                 computation, is discussed. Portability is achieved by
                 careful language specification, together with the key
                 technique of specifying computer classes by means of
                 predefined machine constants. The library is built
                 around an automatic error-handling facility and a
                 dynamic storage allocation scheme, both of which are
                 implemented portably. These, together with the modular
                 structure of the library, lead to simplified calling
                 sequences and ease of use.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "dynamic storage allocation; error handling; libraries;
                 numerical analysis; portability",
}

@Article{Enright:1978:IEM,
  author =       "W. H. Enright",
  title =        "Improving the Efficiency of Matrix Operations in the
                 Numerical Solution of Stiff Ordinary Differential
                 Equations",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "127--136",
  month =        jun,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355780.355784",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L10",
  MRnumber =     "58 #3483",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Henning Esser",
}

@Article{Duff:1978:ITA,
  author =       "I. S. Duff and J. K. Reid",
  title =        "An Implementation of {Tarjan}'s Algorithm for the
                 Block Triangularization of a Matrix",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "137--147",
  month =        jun,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355780.355785",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 19:40:23 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "graph; sparse",
}

@Article{Akima:1978:MBI,
  author =       "Hiroshi Akima",
  title =        "A Method of Bivariate Interpolation and Smooth Surface
                 Fitting for Irregularly Distributed Data Points",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "148--159",
  month =        jun,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355780.355786",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Akima:1978:ABI,
  author =       "Hiroshi Akima",
  title =        "{Algorithm 526}: Bivariate Interpolation and Smooth
                 Surface Fitting for Irregularly Distributed Data Points
                 [{E1}]",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "160--164",
  month =        jun,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355780.355787",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 4 20:54:19 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Akima:1979:RBI,Preusser:1985:RBI}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bank:1978:AFI,
  author =       "Randolph E. Bank",
  title =        "{Algorithm 527}: {A Fortran} Implementation of the
                 Generalized Marching Algorithm [{D3}]",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "165--176",
  month =        jun,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355780.355788",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:30:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fox:1978:AFP,
  author =       "P. A. Fox and A. D. Hall and N. L. Schryer",
  title =        "{Algorithm 528}: Framework for a Portable Library
                 [{Z}]",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "177--188",
  month =        jun,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355780.355789",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:30:46 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/gay-david-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  note =         "See remarks \cite{Fox:1979:RFP,Gay:1999:SAF}.",
  acknowledgement = ack-nhfb,
  annote =       "The three program packages presented here provide a
                 framework for a portable FORTRAN subroutine library.
                 They were developed for the BELL Laboratories library
                 PORT(1). The packages are: machine-dependent constants,
                 automatic error handling, and dynamic storage
                 allocation using a stack.",
  country =      "USA",
  date =         "19/03/80",
  descriptors =  "Reliability; program construction; mathematical
                 method; FORTRAN; portability; error handling; memory
                 management; library",
  enum =         "988",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  language =     "English",
  location =     "RWTH-AC-DFV: TELL",
  references =   "1",
  revision =     "20/03/92",
}

@Article{Duff:1978:APB,
  author =       "I. S. Duff and J. K. Reid",
  title =        "{Algorithm 529}: Permutations To Block Triangular Form
                 [{F1}]",
  journal =      j-TOMS,
  volume =       "4",
  number =       "2",
  pages =        "189--192",
  month =        jun,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355780.355790",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:31:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bailey:1978:ASS,
  author =       "P. B. Bailey and M. K. Gordon and L. F. Shampine",
  title =        "Automatic Solution of the {Sturm--Liouville} Problem",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "193--208",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355791.355792",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L15",
  MRnumber =     "80a:65181",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/355791.355792;
                 http://www.acm.org/pubs/citations/journals/toms/1978-4-3/p193-gordon/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Polak:1978:TPP,
  author =       "S. J. Polak and J. Schrooten and C. Barneveld
                 Binkhuysen",
  title =        "{TEDDY2}, a Program Package for Parabolic Composite
                 Region Problems",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "209--227",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355791.355793",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04",
  MRnumber =     "80a:65009",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Larson:1978:ECE,
  author =       "John Larson and Ahmed Sameh",
  title =        "Efficient Calculation of the Effects of Roundoff
                 Errors",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "228--236",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355791.355794",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G05",
  MRnumber =     "80a:65092a",
  bibdate =      "Thu Apr 29 15:22:59 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See errata \cite{Larson:1979:ECE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "na; rounding error",
}

@Article{Brown:1978:SPA,
  author =       "W. S. Brown",
  title =        "The Subresultant {PRS} Algorithm",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "237--249",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355791.355795",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "12-04 (68C20)",
  MRnumber =     "82g:12001",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gustavson:1978:TFA,
  author =       "Fred G. Gustavson",
  title =        "Two Fast Algorithms for Sparse Matrices:
                 Multiplication and Permuted Transposition",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "250--269",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355791.355796",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F30 (65-04)",
  MRnumber =     "80a:65086",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Chen:1978:PPB,
  author =       "S. C. Chen and D. J. Kuck and A. H. Sameh",
  title =        "Practical Parallel Band Triangular Systems Solvers",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "270--277",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355791.355797",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05 (65-04)",
  MRnumber =     "80a:65065",
  bibdate =      "Fri Aug 26 23:35:36 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "linear system; nla; prll; tridiagonal matrix",
}

@Article{Ward:1978:ECS,
  author =       "R. C. Ward and L. J. Gray",
  title =        "Eigensystem Computation for Skew-Symmetric and a Class
                 of Symmetric Matrices",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "278--285",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355791.355798",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F15",
  MRnumber =     "80a:65082",
  bibdate =      "Sat Aug 27 23:37:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "eig; nla; skew-symmetric matrix; symmetric matrix",
}

@Article{Ward:1978:AAC,
  author =       "R. C. Ward and L. J. Gray",
  title =        "{Algorithm 530}: An Algorithm for Computing the
                 Eigensystem of Skew-Symmetric Matrices and a Class of
                 Symmetric Matrices [{F2}]",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "286--289",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355791.355799",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:37:47 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Snyder:1978:ACP,
  author =       "William V. Snyder",
  title =        "{Algorithm 531}: Contour Plotting [{J6}]",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "290--294",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355791.355800",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:38:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Coleman:1978:RSN,
  author =       "John P. Coleman",
  title =        "Remark on ``{Algorithm 49}: Spherical {Neumann}
                 Function''",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "295--295",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355791.355801",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Herndon:1961:SNF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gustavson:1978:RSM,
  author =       "Fred G. Gustavson",
  title =        "Remark on ``{Algorithm 408}: a Sparse Matrix Package
                 ({Part I}) [{F4}]''",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "295--295",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355791.356474",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{McNamee:1971:SMP}.",
  URL =          "http://doi.acm.org/10.1145/355791.356474;
                 http://www.acm.org/pubs/citations/journals/toms/1978-4-3/p295-mcnamee/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Schoene:1978:RMI,
  author =       "Andrew Y. Schoene",
  title =        "Remark on ``{Algorithm 435}: Modified Incomplete Gamma
                 Function [{S14}]''",
  journal =      j-TOMS,
  volume =       "4",
  number =       "3",
  pages =        "296--304",
  month =        sep,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355791.355803",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Fullerton:1972:MIG}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Baker:1978:SAC,
  author =       "Christopher T. H. Baker and Malcolm S. Keech",
  title =        "Stability Analysis of Certain {Runge--Kutta}
                 Procedures for {Volterra} Integral Equations",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "305--315",
  month =        dec,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356502.356476",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65R20",
  MRnumber =     "80a:65264",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fairweather:1978:IRQ,
  author =       "Graeme Fairweather",
  title =        "An Investigation of {Romberg} Quadrature",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "316--322",
  month =        dec,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356502.356477",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Shampine:1978:SPA,
  author =       "Lawrence F. Shampine",
  title =        "Stability Properties of {Adams} Codes",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "323--329",
  month =        dec,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356502.356478",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05",
  MRnumber =     "80c:65157",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sherman:1978:ASG,
  author =       "Andrew H. Sherman",
  title =        "Algorithms for Sparse {Gaussian} Elimination with
                 Partial Pivoting",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "330--338",
  month =        dec,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356502.356494",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Tendler:1978:SSI,
  author =       "Joel M. Tendler and Theodore A. Bickart and Zdenek
                 Picel",
  title =        "A Stiffly Stable Integration Process Using Cyclic
                 Composite Methods",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "339--368",
  month =        dec,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356502.356495",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Miller:1978:SRA,
  author =       "Webb Miller and David Spooner",
  title =        "Software for Roundoff Analysis. {II}",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "369--387",
  month =        dec,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356502.356496",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G05 (65F99)",
  MRnumber =     "81i:65035",
  bibdate =      "Sat Aug 27 23:48:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "cs; rounding error; software",
}

@Article{Miller:1978:ASR,
  author =       "Webb Miller and David Spooner",
  title =        "{Algorithm 532}: Software for Roundoff Analysis
                 [{Z}]",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "388--390",
  month =        dec,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356502.356497",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:48:45 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sherman:1978:ANF,
  author =       "Andrew H. Sherman",
  title =        "{Algorithm 533}: {NSPIV}, {A Fortran} Subroutine for
                 Sparse {Gaussian} Elimination with Partial Pivoting
                 [{F4}]",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "391--398",
  month =        dec,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356502.356498",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:49:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Tendler:1978:ASS,
  author =       "Joel M. Tendler and Theodore A. Bickart and Zdenek
                 Picel",
  title =        "{Algorithm 534}: {STINT}: {STiff} (differential
                 equations) {INTegrator} [{D2}]",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "399--403",
  month =        dec,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356502.356499",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:50:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Garbow:1978:AQA,
  author =       "Burton S. Garbow",
  title =        "{Algorithm 535}: The {QZ} Algorithm to Solve the
                 Generalized Eigenvalue Problem for Complex Matrices
                 [{F2}]",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "404--410",
  month =        dec,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356502.356500",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:40:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Garbow:1982:RQA,Garbow:1984:RQA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Amos:1978:ECS,
  author =       "Donald E. Amos",
  title =        "Erratum: ``{Algorithm 511}: {CDC} 6600 Subroutines
                 {IBESS} and {JBESS} for {Bessel} Functions {$I_\nu(x)$}
                 and {$J_\nu(x)$}, {$x\ge0,\nu\ge0$} [{S18}]''",
  journal =      j-TOMS,
  volume =       "4",
  number =       "4",
  pages =        "411--411",
  month =        dec,
  year =         "1978",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356502.356501",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Amos:1977:ACS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Zave:1979:DAP,
  author =       "Pamela Zave and Werner C. Rheinboldt",
  title =        "Design of an Adaptive, Parallel Finite-Element
                 System",
  journal =      j-TOMS,
  volume =       "5",
  number =       "1",
  pages =        "1--17",
  month =        mar,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355815.355816",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65N30 (65-04)",
  MRnumber =     "80c:65213",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Duff:1979:SDF,
  author =       "I. S. Duff and J. K. Reid",
  title =        "Some Design Features of a Sparse Matrix Code",
  journal =      j-TOMS,
  volume =       "5",
  number =       "1",
  pages =        "18--35",
  month =        mar,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355815.355817",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Proskurowski:1979:NSH,
  author =       "Wlodzimierz Proskurowski",
  title =        "Numerical Solution of {Helmholtz}'s Equation by
                 Implicit Capacitance Matrix Methods",
  journal =      j-TOMS,
  volume =       "5",
  number =       "1",
  pages =        "36--49",
  month =        mar,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355815.355818",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65N20",
  MRnumber =     "80b:65129",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "John Crank",
}

@Article{Yohe:1979:SIA,
  author =       "J. M. Yohe",
  title =        "Software for Interval Arithmetic: a Reasonably
                 Portable Package",
  journal =      j-TOMS,
  volume =       "5",
  number =       "1",
  pages =        "50--63",
  month =        mar,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355815.355819",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:55:38 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "interval arithmetic; na; software",
}

@Article{More:1979:NSN,
  author =       "Jorge J. Mor{\'e} and Michel Y. Cosnard",
  title =        "Numerical Solution of Nonlinear Equations",
  journal =      j-TOMS,
  volume =       "5",
  number =       "1",
  pages =        "64--85",
  month =        mar,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355815.355820",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H05",
  MRnumber =     "80c:65110",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kahaner:1979:EAD,
  author =       "David K. Kahaner and Mark B. Wells",
  title =        "An Experimental Algorithm for ${N}$-Dimensional
                 Adaptive Quadrature",
  journal =      j-TOMS,
  volume =       "5",
  number =       "1",
  pages =        "86--96",
  month =        mar,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355815.355821",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:41:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Knoble:1979:EOW,
  author =       "H. D. Knoble and C. {Forney, Jr.} and F. S. Bader",
  title =        "An Efficient One-Way Enciphering Algorithm",
  journal =      j-TOMS,
  volume =       "5",
  number =       "1",
  pages =        "97--107",
  month =        mar,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355815.355822",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Knoble:1979:AEO,
  author =       "H. D. Knoble",
  title =        "{Algorithm 536}: An Efficient One-Way Enciphering
                 Algorithm [{Z}]",
  journal =      j-TOMS,
  volume =       "5",
  number =       "1",
  pages =        "108--111",
  month =        mar,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355815.355823",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:58:53 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Leeb:1979:ACV,
  author =       "Walter R. Leeb",
  title =        "{Algorithm 537}: Characteristic Values of {Mathieu}'s
                 Differential Equation",
  journal =      j-TOMS,
  volume =       "5",
  number =       "1",
  pages =        "112--117",
  month =        mar,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355815.355824",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Nikolai:1979:AEE,
  author =       "Paul J. Nikolai",
  title =        "{Algorithm 538}: Eigenvectors and Eigenvalues of Real
                 Generalized Symmetric Matrices by Simultaneous
                 Iteration [{F2}]",
  journal =      j-TOMS,
  volume =       "5",
  number =       "1",
  pages =        "118--125",
  month =        mar,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355815.355825",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Krogh:1979:AAP,
  author =       "Fred T. Krogh",
  title =        "{ACM} Algorithms Policy",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "129--131",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355826.355827",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:01:38 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Schrage:1979:MPF,
  author =       "Linus Schrage",
  title =        "A More Portable {Fortran} Random Number Generator",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "132--138",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355826.355828",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{George:1979:DUI,
  author =       "Alan George and Joseph W. H. Liu",
  title =        "The Design of a User Interface for a Sparse Matrix
                 Package",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "139--162",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355826.355829",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Payne:1979:CG,
  author =       "W. H. Payne and F. M. Ives",
  title =        "Combination Generators",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "163--172",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355826.355830",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 23:13:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{deBoor:1979:ECM,
  author =       "Carl {de Boor}",
  title =        "Efficient Computer Manipulation of Tensor Products",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "173--182",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355826.355831",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04",
  MRnumber =     "80d:65006a",
  bibdate =      "Thu Apr 29 15:18:18 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See corrigenda \cite{deBoor:1979:CCM}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cleary:1979:AAF,
  author =       "John Gerald Cleary",
  title =        "Analysis of an Algorithm for Finding Nearest Neighbors
                 in {Euclidean} Space",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "183--192",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355826.355832",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68H05 (68G10)",
  MRnumber =     "80e:68236",
  bibdate =      "Sun Aug 28 00:06:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Crowder:1979:RCE,
  author =       "Harlan Crowder and Ron S. Dembo and John M. Mulvey",
  title =        "On Reporting Computational Experiments with
                 Mathematical Software",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "193--203",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355826.355833",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:06:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Crary:1979:VPN,
  author =       "Fred D. Crary",
  title =        "A Versatile Precompiler for Nonstandard Arithmetics",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "204--217",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355826.355834",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:06:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Geddes:1979:SCP,
  author =       "K. O. Geddes",
  title =        "Symbolic Computation of {Pad{\'e}} Approximants",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "218--233",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355826.355835",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65F99 68C20)",
  MRnumber =     "80c:65005",
  bibdate =      "Sun Aug 28 00:06:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bogen:1979:ASI,
  author =       "Richard A. Bogen",
  title =        "Addendum to ``{Analytically} Solving Integral
                 Equations by Using Computer Algebra''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "234--237",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355826.355836",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65R20",
  MRnumber =     "80k:65102",
  bibdate =      "Sat Nov 19 13:07:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{elLozy:1979:RAS,
  author =       "Mohamed {el Lozy}",
  title =        "Remark on ``{Algorithm 395}: {Student}'s
                 $t$-Distribution'' and Remark on ``{Algorithm 396}:
                 {Student}'s Quantiles [{S14}]''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "238--239",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355826.355837",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 11:05:53 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Hill:1970:SD,Hill:1970:SQ,Hill:1981:RSD,Hill:1985:RCS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Geddes:1979:RCC,
  author =       "K. O. Geddes",
  title =        "Remark on ``{Algorithm 424}: {Clenshaw--Curtis}
                 Quadrature [{O1}]''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "240--240",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355826.355838",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Gentleman:1972:CCQ}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Anderson:1979:RBI,
  author =       "M. R. Anderson",
  title =        "Remark on ``{Algorithm 474}: Bivariate Interpolation
                 and Smooth Surface Fitting Based on Local
                 Procedures''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "241--241",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355826.355839",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Akima:1974:BIS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Akima:1979:RBI,
  author =       "Hiroshi Akima",
  title =        "Remark on ``{Algorithm} 526: Bivariate Interpolation
                 and Smooth Surface Fitting for Irregularly Distributed
                 Data Points [{E1}]''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "2",
  pages =        "242--243",
  month =        jun,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355826.355840",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Akima:1978:ABI,Preusser:1985:RBI}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Shampine:1979:SRR,
  author =       "L. F. Shampine",
  title =        "Storage Reduction for {Runge--Kutta} Codes",
  journal =      j-TOMS,
  volume =       "5",
  number =       "3",
  pages =        "245--250",
  month =        sep,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355841.355842",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:06:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ehrlich:1979:SBE,
  author =       "L. W. Ehrlich",
  title =        "Solving the Biharmonic Equation on Irregular Regions",
  journal =      j-TOMS,
  volume =       "5",
  number =       "3",
  pages =        "251--258",
  month =        sep,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355841.355843",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65N20",
  MRnumber =     "80e:65093",
  bibdate =      "Sun Aug 28 00:06:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gill:1979:DSF,
  author =       "Philip E. Gill and Walter Murray and Susan M. Picken
                 and Margaret H. Wright",
  title =        "The Design and Structure of a {Fortran} Program
                 Library for Optimization",
  journal =      j-TOMS,
  volume =       "5",
  number =       "3",
  pages =        "259--283",
  month =        sep,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355841.355844",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:06:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{George:1979:IPN,
  author =       "Alan George and Joseph W. H. Liu",
  title =        "An Implementation of a Pseudoperipheral Node Finder",
  journal =      j-TOMS,
  volume =       "5",
  number =       "3",
  pages =        "284--295",
  month =        sep,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355841.355845",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:06:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bennett:1979:SPE,
  author =       "James Michael Bennett and Robert Neff Bryan",
  title =        "A Single-Point Exchange Algorithm for Approximating
                 Functions of Two Variables",
  journal =      j-TOMS,
  volume =       "5",
  number =       "3",
  pages =        "296--307",
  month =        sep,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355841.355846",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15",
  MRnumber =     "80e:65020",
  bibdate =      "Sun Aug 28 00:06:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lawson:1979:BLA,
  author =       "C. L. Lawson and R. J. Hanson and D. R. Kincaid and F.
                 T. Krogh",
  title =        "{Basic Linear Algebra Subprograms} for {Fortran}
                 Usage",
  journal =      j-TOMS,
  volume =       "5",
  number =       "3",
  pages =        "308--323",
  month =        sep,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355841.355847",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 19:42:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "BLAS; nla; software",
}

@Article{Lawson:1979:ABL,
  author =       "C. L. Lawson and R. J. Hanson and D. R. Kincaid and F.
                 T. Krogh",
  title =        "{Algorithm 539}: {Basic Linear Algebra Subprograms}
                 for {Fortran} Usage [{F1}]",
  journal =      j-TOMS,
  volume =       "5",
  number =       "3",
  pages =        "324--325",
  month =        sep,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355841.355848",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu May 20 13:48:12 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also
                 \cite{Dodson:1982:RBL,Dodson:1983:CRB,Hanson:1987:ATA,Louter-Nool:1988:ATA,Hanson:2004:AAV,Hanson:2018:RAM}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Madsen:1979:APG,
  author =       "N. K. Madsen and R. F. Sincovec",
  title =        "{Algorithm 540}: {PDECOL}, General Collocation
                 Software for Partial Differential Equations [{D3}]",
  journal =      j-TOMS,
  volume =       "5",
  number =       "3",
  pages =        "326--351",
  month =        sep,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355841.355849",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 09:21:53 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Hopkins:1992:RPG}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Swartztrauber:1979:AEF,
  author =       "Paul N. Swartztrauber and Roland A. Sweet",
  title =        "{Algorithm 541}: Efficient {Fortran} Subprograms for
                 the Solution of Separable Elliptic Partial Differential
                 Equations [{D3}]",
  journal =      j-TOMS,
  volume =       "5",
  number =       "3",
  pages =        "352--364",
  month =        sep,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355841.355850",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 19:43:36 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/355841.355850;
                 http://www.acm.org/pubs/citations/journals/toms/1979-5-3/p352-swartztrauber/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Steuerwalt:1979:CEF,
  author =       "Michael Steuerwalt",
  title =        "Certification of ``{Algorithm} 541: Efficient
                 {Fortran} Subprograms for the Solution of Separable
                 Elliptic Partial Differential Equations [{D3}]''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "3",
  pages =        "365--371",
  month =        sep,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355841.355851",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Feb 24 09:58:08 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Larson:1979:ECE,
  author =       "John Larson",
  title =        "Errata: ``{Efficient} Calculation of the Effects of
                 Roundoff Errors''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "3",
  pages =        "372--372",
  month =        sep,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355841.355852",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "372. 65G05",
  MRnumber =     "80a:65092b",
  bibdate =      "Sat Nov 19 13:07:42 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Larson:1978:ECE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gear:1979:EN,
  author =       "C. W. Gear",
  title =        "{Editor}'s Note",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "373--373",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355854",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:32:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Enright:1979:APS,
  author =       "W. H. Enright and M. S. Kamel",
  title =        "Automatic Partitioning of Stiff Systems and Exploiting
                 the Resulting Structure",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "374--385",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355855",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:32:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gladwell:1979:IVR,
  author =       "Ian Gladwell",
  title =        "Initial Value Routines in the {NAG} Library",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "386--400",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355856",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:32:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Zlatev:1979:ASD,
  author =       "Zahari Zlatev and Per Grove Thomsen",
  title =        "Automatic Solution of Differential Equations Based on
                 the User of Linear Multistep Methods",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "401--414",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355857",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:32:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Stetter:1979:GEE,
  author =       "Hans J. Stetter",
  title =        "Global Error Estimation in {Adams PC}-Codes",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "415--430",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355858",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:32:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Houstis:1979:HOF,
  author =       "E. N. Houstis and T. S. Papatheodorou",
  title =        "High-Order Fast Elliptic Equation Solvers",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "431--441",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355859",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:32:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kaufman:1979:ADH,
  author =       "L. Kaufman",
  title =        "Application of Dense {Householder} Transformation to a
                 Sparse Matrix",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "442--450",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355860",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:38:08 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Householder transformation; nla; qrd; sparse",
}

@Article{Rayward-Smith:1979:CSN,
  author =       "V. J. Rayward-Smith",
  title =        "On Computing the {Smith} Normal Form of an Integer
                 Matrix",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "451--456",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355861",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:32:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Wampler:1979:SWL,
  author =       "Roy H. Wampler",
  title =        "Solutions to Weighted Least Squares Problems by
                 Modified {Gram--Schmidt} with Iterative Refinement",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "457--465",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355862",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 19:44:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Gram--Schmidt algorithm; iterative refinement; lsq;
                 nla; qrd; weights",
}

@Article{Gautschi:1979:CPI,
  author =       "Walter Gautschi",
  title =        "A Computational Procedure for Incomplete Gamma
                 Functions",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "466--481",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355863",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:32:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gautschi:1979:AIG,
  author =       "W. Gautschi",
  title =        "{Algorithm 542}: Incomplete Gamma Functions [{S14}]",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "482--489",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355864",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:39:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Houstis:1979:AFF,
  author =       "E. N. Houstis and T. S. Papatheodorou",
  title =        "{Algorithm 543}: {FFT9}, Fast Solution of
                 {Helmholtz}-Type Partial Differential Equations
                 [{D3}]",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "490--493",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355865",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:40:38 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Wampler:1979:ALL,
  author =       "Roy H. Wampler",
  title =        "{Algorithm 544}: {L2A} and {L2B}, Weighted Least
                 Squares Solutions by Modified {Gram--Schmidt} with
                 Iterative Refinement [{F4}]",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "494--499",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355866",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:04:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Gram--Schmidt algorithm; iterative refinement; lsq;
                 nla; qrd; weights",
}

@Article{Fraser:1979:AOM,
  author =       "D. Fraser",
  title =        "{Algorithm 545}: An Optimized Mass Storage {FFT}
                 [{C6}]",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "500--517",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355867",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Aug 28 00:41:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Brent:1979:RMF,
  author =       "R. P. Brent",
  title =        "Remark on ``{Algorithm} 524: {MP}, {A Fortran}
                 Multiple-Precision Arithmetic Package [{A1}]''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "518--519",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355868",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:35:42 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Brent:1978:AMF,Brent:1980:AIB,Smith:1998:AMP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Leathers:1979:RAS,
  author =       "Burton L. Leathers",
  title =        "Remark on ``{Algorithm} 513: Analysis of In-Situ
                 Transposition [{F1}]'' and Remark on ``{Algorithm} 467:
                 Matrix Transposition in Place''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "520--520",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355869",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Cate:1977:AAS,Brenner:1973:MTP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{vanSwieten:1979:RAV,
  author =       "A. C. M. {van Swieten} and J. Th. M. {de Hosson}",
  title =        "Remark on ``{Algorithm} 475: Visible Surface Plotting
                 Program''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "521--523",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355870",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Wright:1974:VSP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fox:1979:RFP,
  author =       "Phyllis Fox",
  title =        "Remark on ``{Algorithm} 528: Framework for a Portable
                 Library [{Z}]''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "524--524",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355871",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/gay-david-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  note =         "See \cite{Fox:1978:AFP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{deBoor:1979:CCM,
  author =       "Carl {de Boor}",
  title =        "Corrigenda: ``{Efficient} Computer Manipulation of
                 Tensor Products''",
  journal =      j-TOMS,
  volume =       "5",
  number =       "4",
  pages =        "525--525",
  month =        dec,
  year =         "1979",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355853.355872",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "525. 65-04",
  MRnumber =     "80d:65006b",
  bibdate =      "Sat Oct 24 15:50:17 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{deBoor:1979:ECM}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cheung:1980:CCE,
  author =       "To-Yat Cheung",
  title =        "Computational Comparison of Eight Methods for the
                 Maximum Network Flow Problem",
  journal =      j-TOMS,
  volume =       "6",
  number =       "1",
  pages =        "1--16",
  month =        mar,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355873.355874",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "90B10 (68E10)",
  MRnumber =     "80m:90046",
  bibdate =      "Mon Aug 29 08:58:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "breadth-first; computational comparison; depth-first;
                 Dinic; Karzanov; Kinariwala-Rao; maximum network flow",
}

@Article{Ho:1980:CST,
  author =       "James K. Ho and Etienne Loute",
  title =        "A Comparative Study of Two Methods for Staircase
                 Linear Problems",
  journal =      j-TOMS,
  volume =       "6",
  number =       "1",
  pages =        "17--30",
  month =        mar,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355873.355875",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 08:58:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "comparison of algorithms; decomposition;
                 factorization; large-scale systems; structured linear
                 programs",
}

@Article{Michaels:1980:MPG,
  author =       "William M. Michaels and Richard P. O'Neill",
  title =        "A Mathematical Program Generator {MPGENR}",
  journal =      j-TOMS,
  volume =       "6",
  number =       "1",
  pages =        "31--44",
  month =        mar,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355873.355876",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 08:58:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "large-scale optimization; linear and nonlinear
                 programming; software verification; test problem
                 generation",
}

@Article{Chung:1980:ACF,
  author =       "Won L. Chung",
  title =        "Automatic Curve Fittings Using an Adaptive Local
                 Algorithm",
  journal =      j-TOMS,
  volume =       "6",
  number =       "1",
  pages =        "45--57",
  month =        mar,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355873.355877",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 11:55:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "adaptive approximation; automatic curve fitting; data
                 compression; interactive display; modeling and
                 simulation systems; numerical stability; one-sided
                 algorithm; piecewise cubic polynomials; {$L_2$}
                 approximation with continuity constraints",
}

@Article{Clark:1980:REV,
  author =       "Gordon M. Clark",
  title =        "Recursive Estimation of the Variance of the Sample
                 Average",
  journal =      j-TOMS,
  volume =       "6",
  number =       "1",
  pages =        "58--67",
  month =        mar,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355873.355878",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68J05 (65C20)",
  MRnumber =     "80m:68086",
  bibdate =      "Mon Aug 29 08:58:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "recursive calculation; sample autocovariances;
                 simulation output analysis; variance estimation",
}

@Article{Power:1980:ISU,
  author =       "Leigh R. Power",
  title =        "Internal Sorting Using a Minimal Tree Merge Strategy",
  journal =      j-TOMS,
  volume =       "6",
  number =       "1",
  pages =        "68--79",
  month =        mar,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355873.355879",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68E05",
  MRnumber =     "80m:68056",
  bibdate =      "Mon Aug 29 08:58:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "internal sort; linked list; list processing; merge;
                 minimal tree; natural merge sort; sort; straight merge
                 sort",
}

@Article{deBoor:1980:SPS,
  author =       "Carl {de Boor} and Richard Weiss",
  title =        "{SOLVEBLOK}: a Package for Solving Almost Block
                 Diagonal Linear Systems",
  journal =      j-TOMS,
  volume =       "6",
  number =       "1",
  pages =        "80--87",
  month =        mar,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355873.355880",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 24 15:50:20 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "almost block diagonal systems; Gaussian elimination;
                 ordinary differential equations; spline approximation",
}

@Article{deBoor:1980:AS,
  author =       "Carl {de Boor} and Richard Weiss",
  title =        "{Algorithm 546}: {SOLVEBLOK} [{F4}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "1",
  pages =        "88--91",
  month =        mar,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355873.355881",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 24 15:50:24 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "almost block diagonal systems; Gaussian elimination;
                 ordinary differential equations; spline approximation",
}

@Article{Duris:1980:AFR,
  author =       "Charles S. Duris",
  title =        "{Algorithm 547}: {FORTRAN} Routines for Discrete Cubic
                 Spline Interpolation and Smoothing [{E1}], [{E3}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "1",
  pages =        "92--103",
  month =        mar,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355873.355882",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:29:10 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "discrete cubic splines; discrete natural splines;
                 discrete splines; interpolation; smoothing",
}

@Article{Carpaneto:1980:ASA,
  author =       "Giorgio Carpaneto and Paolo Toth",
  title =        "{Algorithm 548}: Solution of the Assignment Problem
                 [{H}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "1",
  pages =        "104--111",
  month =        mar,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355873.355883",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:29:23 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "assignment problem; Hungarian algorithm",
}

@Article{Eckhardt:1980:AWE,
  author =       "Ulrich Eckhardt",
  title =        "{Algorithm 549}: {Weierstrass}' Elliptic Functions
                 [{S21}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "1",
  pages =        "112--120",
  month =        mar,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355873.355884",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:31:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Weierstrass' elliptic functions",
}

@Article{Messner:1980:ASP,
  author =       "A. M. Messner and G. Q. Taylor",
  title =        "{Algorithm 550}: Solid Polyhedron Measure [{Z}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "1",
  pages =        "121--130",
  month =        mar,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355873.355885",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 14:44:11 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "graphics; numerical integration; polyhedron",
}

@Article{Anonymous:1980:AAD,
  author =       "{Anonymous}",
  title =        "{ACM Algorithms Distribution Service} Expanded",
  journal =      j-TOMS,
  volume =       "6",
  number =       "1",
  pages =        "131--132",
  month =        mar,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355873.355886",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 08:58:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Chan:1980:NLS,
  author =       "Tony F. Chan and William M. {Coughran, Jr.} and Eric
                 H. Grosse and Michael T. Heath",
  title =        "A Numerical Library and Its Support",
  journal =      j-TOMS,
  volume =       "6",
  number =       "2",
  pages =        "135--145",
  month =        jun,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355887.355888",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:33:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "library management and organization; mathematical
                 software; numerical analysis",
}

@Article{Brent:1980:AIB,
  author =       "Richard P. Brent and Judith A. Hooper and J. Michael
                 Yohe",
  title =        "An {AUGMENT} Interface for {Brent}'s Multiple
                 Precision Arithmetic Package",
  journal =      j-TOMS,
  volume =       "6",
  number =       "2",
  pages =        "146--149",
  month =        jun,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355887.355889",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:35:33 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Brent:1978:AMF,Brent:1979:RMF,Smith:1998:AMP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "arithmetic; AUGMENT interface; extended precision;
                 floating point; multiple precision; portable software;
                 precompiler interface; software package",
}

@Article{Kedem:1980:ADC,
  author =       "Gershon Kedem",
  title =        "Automatic Differentiation of Computer Programs",
  journal =      j-TOMS,
  volume =       "6",
  number =       "2",
  pages =        "150--165",
  month =        jun,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355887.355890",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68C20 (68F25)",
  MRnumber =     "81g:68058",
  bibdate =      "Mon Aug 29 10:33:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "automatic differentiation; factorable functions",
}

@Article{Rheinboldt:1980:DSA,
  author =       "Werner C. Rheinboldt and Charles K. Mesztenyi",
  title =        "On a Data Structure for Adaptive Finite Element Mesh
                 Refinements",
  journal =      j-TOMS,
  volume =       "6",
  number =       "2",
  pages =        "166--187",
  month =        jun,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355887.355891",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:33:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "access algorithms; finite elements; mesh refinements;
                 tree structure",
}

@Article{Verwer:1980:ICS,
  author =       "J. G. Verwer",
  title =        "An Implementation of a Class of Stabilized Explicit
                 Methods for the Time Integration of Parabolic
                 Equations",
  journal =      j-TOMS,
  volume =       "6",
  number =       "2",
  pages =        "188--205",
  month =        jun,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355887.355892",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:33:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "implementation of time integrators; numerical
                 analysis; parabolic partial differential equations;
                 semidiscretization",
}

@Article{Munksgaard:1980:SSS,
  author =       "N. Munksgaard",
  title =        "Solving Sparse Symmetric Sets of Linear Equations by
                 Preconditioned Conjugate Gradients",
  journal =      j-TOMS,
  volume =       "6",
  number =       "2",
  pages =        "206--219",
  month =        jun,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355887.355893",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:33:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "conjugate gradients; fixed space factorization; linear
                 equations; numerical drop tolerance modification;
                 positive definite; preconditioning; sparse",
}

@Article{Abdelmalek:1980:SOS,
  author =       "Nabih N. Abdelmalek",
  title =        "{$L_1$} Solution of Overdetermined Systems of Linear
                 Equations",
  journal =      j-TOMS,
  volume =       "6",
  number =       "2",
  pages =        "220--227",
  month =        jun,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355887.355894",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:33:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "discrete linear {$L_1$} approximation; dual simplex
                 algorithms; linear programming; overdetermined system
                 of linear equations; triangular decomposition",
}

@Article{Abdelmalek:1980:AFS,
  author =       "Nabih N. Abdelmalek",
  title =        "{Algorithm 551}: {A FORTRAN} Subroutine for the
                 {$L_1$} Solution of Overdetermined Systems of Linear
                 Equations [{F4}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "2",
  pages =        "228--230",
  month =        jun,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355887.355895",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:44:41 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "discrete linear {$L_1$} approximation; dual simplex
                 algorithms; linear programming; overdetermined system
                 of linear equations; triangular decomposition",
}

@Article{Barrodale:1980:ASC,
  author =       "I. Barrodale and F. D. K. Roberts",
  title =        "{Algorithm 552}: Solution of the Constrained $\ell_1$
                 Linear Approximation Problem [{F4}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "2",
  pages =        "231--235",
  month =        jun,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355887.355896",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:46:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "constrained $\ell_1$ approximation; linear
                 programming; simplex method",
}

@Article{Verwer:1980:AME,
  author =       "J. G. Verwer",
  title =        "{Algorithm 553}: {M3RK}, An Explicit Time Integrator
                 for Semidiscrete Parabolic Equations [{D3}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "2",
  pages =        "236--239",
  month =        jun,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355887.355897",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:49:22 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "explicit time integrator; parabolic partial
                 differential equations; semidiscretization",
}

@Article{More:1980:ABF,
  author =       "J. J. Mor{\'e} and M. Y. Cosnard",
  title =        "{Algorithm 554}: {BRENTM}, {A Fortran} Subroutine for
                 the Numerical Solution of Nonlinear Equations [{F5}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "2",
  pages =        "240--251",
  month =        jun,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355887.355898",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:49:42 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Brent's method; nonlinear equations; numerical
                 solution",
}

@Article{Watson:1980:ACY,
  author =       "L. T. Watson and D. Fenner",
  title =        "{Algorithm 555}: {Chow-Yorke} Algorithm for Fixed
                 Points or Zeros of ${C}^2$ Maps [{C5}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "2",
  pages =        "252--259",
  month =        jun,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355887.355899",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 10:17:11 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "continuation method; fixed point; fixed points of
                 nonlinear systems; homotopy method; nonlinear systems;
                 parameterized nonlinear system; zero; zero curve of a
                 homotopy map; zeros of nonlinear systems",
}

@Article{Gear:1980:RKS,
  author =       "C. W. Gear",
  title =        "{Runge--Kutta} Starters for Multistep Methods",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "263--279",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355901",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05",
  MRnumber =     "81m:65119",
  bibdate =      "Mon Aug 29 10:57:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "integration; multistep; ordinary differential
                 equations; Runge--Kutta",
  reviewer =     "J. Sprekels",
}

@Article{Barton:1980:TSS,
  author =       "David Barton",
  title =        "On {Taylor} Series and Stiff Equations",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "280--294",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355902",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05",
  MRnumber =     "82e:65078",
  bibdate =      "Mon Aug 29 10:57:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "stiff ordinary differential equations; Taylor series",
  reviewer =     "P. M. Dew",
}

@Article{Jackson:1980:AIV,
  author =       "K. R. Jackson and R. Sacks-Davis",
  title =        "An Alternative Implementation of Variable Step-Size
                 Multistep Formulas for Stiff {ODE}s",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "295--318",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355903",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05",
  MRnumber =     "81m:65120",
  bibdate =      "Mon Aug 29 10:57:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "backward differential formulas; stiff ODEs; variable
                 step-size methods",
  reviewer =     "Hans J. Stetter",
}

@Article{Gupta:1980:NAO,
  author =       "G. K. Gupta",
  title =        "A Note About Overhead Costs in {ODE} Solvers",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "319--326",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355904",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:57:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Adams methods; mathematical software; ordinary
                 differential equations; Runge--Kutta methods; software
                 evaluation",
}

@Article{Coleman:1980:SSI,
  author =       "David Coleman and Paul Holland and Neil Kaden and
                 Virginia Klema and Stephen C. Peters",
  title =        "A System of Subroutines for Iteratively Reweighted
                 Least Squares Computations",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "327--336",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355905",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:57:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "curve fitting; data analysis; least squares; linear
                 algebra; mathematical software; portability; robust
                 estimation; weight functions",
}

@Article{George:1980:FIM,
  author =       "Alan George and Joseph W. H. Liu",
  title =        "A Fast Implementation of the Minimum Degree Algorithm
                 Using Quotient Graphs",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "337--358",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355906",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05 (68E10)",
  MRnumber =     "82i:65022",
  bibdate =      "Mon Aug 29 10:57:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "graph algorithms; mathematical software; ordering
                 algorithms; quotient graphs; sparse linear equations",
  reviewer =     "Niels Munksgaard",
}

@Article{Bentley:1980:GSL,
  author =       "Jon Louis Bentley and James B. Saxe",
  title =        "Generating Sorted Lists of Random Numbers",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "359--364",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355907",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65C10 (68-01)",
  MRnumber =     "81k:65010",
  bibdate =      "Mon Aug 29 10:57:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "linear-time algorithm; probabilistic methods in
                 algorithm design; random number generation; sorting",
  reviewer =     "George Marsaglia",
}

@Article{Amos:1980:CEI,
  author =       "Donald E. Amos",
  title =        "Computation of Exponential Integrals",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "365--377",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355908",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30 (68-04)",
  MRnumber =     "82b:65011",
  bibdate =      "Mon Aug 29 10:57:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "exponential integral; Miller algorithm; recursion;
                 Taylor series",
  reviewer =     "M. M. Chawla",
}

@Article{Arthur:1980:PPA,
  author =       "Jeffrey L. Arthur and A. Ravindran",
  title =        "{PAGP}, a Partitioning Algorithm for (Linear) Goal
                 Programming Problems",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "378--386",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355909",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "90C05",
  MRnumber =     "81i:90122",
  bibdate =      "Mon Aug 29 10:57:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "constraint partitioning; goal program; multiple
                 objective optimization; simplex method",
}

@Article{Cheung:1980:MLP,
  author =       "To-Yat Cheung",
  title =        "Multifacility Location Problem with Rectilinear
                 Distance by the Minimum-Cut Approach",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "387--390",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355910",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 10:57:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "minimum cut; multifacility; optimal location;
                 rectilinear distance",
}

@Article{Betts:1980:CAC,
  author =       "J. T. Betts",
  title =        "A Compact Algorithm for Computing the Stationary Point
                 of a Quadratic Function Subject to Linear Constraints",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "391--397",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355911",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "90C20 (65K05)",
  MRnumber =     "81i:90162",
  bibdate =      "Mon Aug 29 10:57:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "orthogonal decomposition; quadratic programming",
}

@Article{Kaagstrom:1980:ANC,
  author =       "Bo K{\aa}gstr{\"o}m and Axel Ruhe",
  title =        "An Algorithm for Numerical Computation of the {Jordan}
                 Normal Form of a Complex Matrix",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "398--419",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355912",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F15 (15A21)",
  MRnumber =     "81m:65054",
  bibdate =      "Fri Aug 26 23:38:10 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "block diagonal form; canonical form; eig; eigenvalues;
                 eigenvectors; Jordan form; Jordan normal form; nla;
                 numerical multiple eigenvalues; principal vectors;
                 software",
  reviewer =     "Petr Liebl",
}

@Article{Amos:1980:AEI,
  author =       "Donald E. Amos",
  title =        "{Algorithm 556}: Exponential Integrals [{S13}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "420--428",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355913",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 11:13:05 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark in \cite{Amos:1983:REI}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "confluent hypergeometric functions; exponential
                 integrals; Miller algorithm",
}

@Article{Arthur:1980:APP,
  author =       "J. L. Arthur and A. Ravindran",
  title =        "{Algorithm 557}: {PAGP}, a Partitioning Algorithm
                 for (Linear) Goal Programming Problems [{H}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "429--429",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355914",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 11:13:53 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "constraint partitioning; goal program; multiple
                 objective optimization; simplex method",
}

@Article{Cheung:1980:APM,
  author =       "To-Yat Cheung",
  title =        "{Algorithm 558}: a Program for the Multifacility
                 Location Problem with Rectilinear Distance by the
                 Minimum-Cut Approach [{H}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "430--431",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355915",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 11:14:45 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "minimum cut; multifacility; optimal location;
                 rectilinear distance",
}

@Article{Betts:1980:ASP,
  author =       "J. T. Betts",
  title =        "{Algorithm 559}: The Stationary Point of a Quadratic
                 Function Subject to Linear Constraints [{E4}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "432--436",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355916",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 11:15:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "orthogonal decomposition; quadratic programming",
}

@Article{Kaagstroem:1980:AJA,
  author =       "Bo K{\aa{}}gstr{\"o}m and Axel Ruhe",
  title =        "{Algorithm 560}: {JNF}, An Algorithm for Numerical
                 Computation of the {Jordan} Normal Form of a Complex
                 Matrix [{F2}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "437--443",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355917",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 15:16:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "block diagonal form; canonical form; eig; eigenvalues;
                 eigenvectors; Jordan form; Jordan normal form; nla;
                 principal vectors; software",
}

@Article{Kahaner:1980:AFI,
  author =       "D. K. Kahaner",
  title =        "{Algorithm 561}: {FORTRAN} Implementation of Heap
                 Programs for Efficient Table Maintenance [{Z}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "444--449",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355918",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 11:17:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "heap; table maintenance",
}

@Article{Pape:1980:ASP,
  author =       "U. Pape",
  title =        "{Algorithm 562}: Shortest Path Lengths [{H}]",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "450--455",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355919",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 11:17:56 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Pape:1983:RSP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "shortest path; shortest route problem",
}

@Article{Harms:1980:RSM,
  author =       "U. Harms and H. Kollakowski and G. M{\"o}ller",
  title =        "Remark on ``{Algorithm} 408: a Sparse Matrix Package
                 (Part 1) [{F4}]''",
  journal =      j-TOMS,
  volume =       "6",
  number =       "3",
  pages =        "456--457",
  month =        sep,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355900.355920",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{McNamee:1971:SMP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Machura:1980:SSP,
  author =       "Marek Machura and Roland A. Sweet",
  title =        "A Survey of Software for Partial Differential
                 Equations",
  journal =      j-TOMS,
  volume =       "6",
  number =       "4",
  pages =        "461--488",
  month =        dec,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355921.355922",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65M99 (65-04 65N99)",
  MRnumber =     "81k:65106",
  bibdate =      "Mon Aug 29 11:23:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "partial differential equations; software; survey",
}

@Article{Kurator:1980:PIS,
  author =       "William G. Kurator and Richard P. O'Neill",
  title =        "{PERUSE}: An Interactive System for Mathematical
                 Programs",
  journal =      j-TOMS,
  volume =       "6",
  number =       "4",
  pages =        "489--509",
  month =        dec,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355921.355923",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 11:23:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "interactive mathematical programming; model auditing;
                 model debugging; model verification",
}

@Article{Brown:1980:EPB,
  author =       "W. S. Brown and S. I. Feldman",
  title =        "Environment Parameters and Basic Functions for
                 Floating-Point Computation",
  journal =      j-TOMS,
  volume =       "6",
  number =       "4",
  pages =        "510--523",
  month =        dec,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355921.355924",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 11:23:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "environment parameters; floating-point arithmetic;
                 software portability",
}

@Article{Luk:1980:CSV,
  author =       "Franklin T. Luk",
  title =        "Computing the Singular-Value Decomposition on the
                 {ILLIAC IV}",
  journal =      j-TOMS,
  volume =       "6",
  number =       "4",
  pages =        "524--539",
  month =        dec,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355921.355925",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F15",
  MRnumber =     "81k:65044",
  bibdate =      "Mon Aug 29 11:27:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Golub-Reinsch algorithm; Illiac; ILLIAC IV computer;
                 Jacobi-like method; nla; parallel matrix computations;
                 prll; singular-value decomposition; svd",
}

@Article{Sacks-Davis:1980:FLC,
  author =       "R. Sacks-Davis",
  title =        "Fixed Leading Coefficient Implementation of
                 {SD}-Formulas for Stiff {ODE}s",
  journal =      j-TOMS,
  volume =       "6",
  number =       "4",
  pages =        "540--562",
  month =        dec,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355921.355926",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05",
  MRnumber =     "81k:65084",
  bibdate =      "Mon Aug 29 11:23:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "ordinary differential equations; second-derivative
                 method",
}

@Article{Bentley:1980:OET,
  author =       "Jon Louis Bentley and Bruce W. Weide and Andrew C.
                 Yao",
  title =        "Optimal Expected-Time Algorithms for Closest Point
                 Problems",
  journal =      j-TOMS,
  volume =       "6",
  number =       "4",
  pages =        "563--580",
  month =        dec,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355921.355927",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68G10 (52-04 52A45 68E10 90C10)",
  MRnumber =     "82g:68084",
  bibdate =      "Mon Aug 29 11:23:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "closest point problems; computational geometry;
                 minimum spanning trees; nearest neighbor searching;
                 optimal algorithms; probabilistic analysis of
                 algorithms; Voronoi diagrams",
  reviewer =     "Wolfgang Boehm",
}

@Article{Campbell:1980:TAM,
  author =       "J. B. Campbell",
  title =        "On {Temme}'s Algorithm for the Modified {Bessel}
                 Function of the Third Kind",
  journal =      j-TOMS,
  volume =       "6",
  number =       "4",
  pages =        "581--586",
  month =        dec,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355921.355928",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "82d:65019",
  bibdate =      "Mon Aug 29 11:23:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "mathematical software; Miller's algorithm; modified
                 Bessel functions of the third kind",
}

@Article{Hoffman:1980:TPG,
  author =       "K. L. Hoffman and D. R. Shier",
  title =        "A Test Problem Generator for Discrete Linear {$L_1$}
                 Approximation Problems",
  journal =      j-TOMS,
  volume =       "6",
  number =       "4",
  pages =        "587--593",
  month =        dec,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355921.355929",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D99 (65K05)",
  MRnumber =     "81m:65042",
  bibdate =      "Mon Aug 29 11:23:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "least absolute deviation; problem generator; test
                 data; {$L_1$} approximation",
}

@Article{Bartels:1980:LCD,
  author =       "Richard H. Bartels and Andrew R. Conn",
  title =        "Linearly Constrained Discrete $\ell_1$ Problems",
  journal =      j-TOMS,
  volume =       "6",
  number =       "4",
  pages =        "594--608",
  month =        dec,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355921.355930",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "90C33 (65K05)",
  MRnumber =     "82a:90165",
  bibdate =      "Sat Aug 27 15:41:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "$\ell_1$ norm; data filling; discrete approximation;
                 l1 approximation; linearly constrained approximation;
                 nlop; software",
}

@Article{Bartels:1980:APL,
  author =       "Richard H. Bartels and Andrew R. Conn",
  title =        "{Algorithm 563}: a Program for Linearly Constrained
                 Discrete $\ell_1$ Problems",
  journal =      j-TOMS,
  volume =       "6",
  number =       "4",
  pages =        "609--614",
  month =        dec,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355921.355931",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:22:14 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Koenker:1996:RBC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "discrete $\ell_1$ approximation; l1 approximation;
                 linear constraints; nlop; numerical analysis;
                 overdetermined linear systems; software",
}

@Article{Hoffman:1980:ATP,
  author =       "K. L. Hoffman and D. R. Shier",
  title =        "{Algorithm 564}: a Test Problem Generator for Discrete
                 Linear {$L_1$} Approximation Problems",
  journal =      j-TOMS,
  volume =       "6",
  number =       "4",
  pages =        "615--617",
  month =        dec,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355921.355932",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "least absolute deviation; problem generator; test
                 data; {$L_1$} approximation",
}

@Article{Shanno:1980:RMU,
  author =       "D. F. Shanno and K. H. Phua",
  title =        "Remark on ``{Algorithm} 500: Minimization of
                 Unconstrained Multivariate Functions [{E4}]''",
  journal =      j-TOMS,
  volume =       "6",
  number =       "4",
  pages =        "618--622",
  month =        dec,
  year =         "1980",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355921.355933",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:07:08 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Shanno:1976:AMU}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hiebert:1981:EMS,
  author =       "K. L. Hiebert",
  title =        "An Evaluation of Mathematical Software that Solves
                 Nonlinear Least Squares Problems",
  journal =      j-TOMS,
  volume =       "7",
  number =       "1",
  pages =        "1--16",
  month =        mar,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355934.355935",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:46:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "augmented Gauss--Newton; Gauss--Newton;
                 Levenberg--Marquardt; lsq; nllsq; nlop; nonlinear data
                 fitting; nonlinear least squares; nonlinear regression;
                 quasi-Newton; software evaluation",
}

@Article{More:1981:TUO,
  author =       "Jorge J. Mor{\'e} and Burton S. Garbow and Kenneth E.
                 Hillstrom",
  title =        "Testing Unconstrained Optimization Software",
  journal =      j-TOMS,
  volume =       "7",
  number =       "1",
  pages =        "17--41",
  month =        mar,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355934.355936",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "90C30",
  MRnumber =     "83b:90144",
  bibdate =      "Mon Aug 29 22:02:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "nonlinear least squares; optimization software;
                 performance testing; systems of nonlinear equations;
                 unconstrained minimization",
}

@Article{Akl:1981:CCG,
  author =       "Selim G. Akl",
  title =        "A Comparison of Combination Generation Methods",
  journal =      j-TOMS,
  volume =       "7",
  number =       "1",
  pages =        "42--45",
  month =        mar,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355934.355937",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 22:02:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithm; combinations",
}

@Article{Fritsch:1981:DIU,
  author =       "F. N. Fritsch and D. K. Kahaner and J. N. Lyness",
  title =        "Double Integration Using One-Dimensional Adaptive
                 Quadrature Routines: a Software Interface Problem",
  journal =      j-TOMS,
  volume =       "7",
  number =       "1",
  pages =        "46--75",
  month =        mar,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355934.355938",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30",
  MRnumber =     "83c:65033a",
  bibdate =      "Sat Nov 19 13:07:46 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Fritsch:1981:CIU}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "adaptive integration; automatic quadrature routine;
                 double integration; quadrature; software interface",
}

@Article{Friedman:1981:NPP,
  author =       "Jerome H. Friedman and Margaret H. Wright",
  title =        "A Nested Partitioning Procedure for Numerical Multiple
                 Integration",
  journal =      j-TOMS,
  volume =       "7",
  number =       "1",
  pages =        "76--92",
  month =        mar,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355934.355939",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30",
  MRnumber =     "83d:65058",
  bibdate =      "Mon Aug 29 22:02:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "bounds-constrained optimization; numerical
                 integration; quadrature; recursive partitioning",
  reviewer =     "C. Dagnino",
}

@Article{Smith:1981:ERA,
  author =       "J. M. Smith and F. W. J. Olver and D. W. Lozier",
  title =        "Extended-Range Arithmetic and Normalized {Legendre}
                 Polynomials",
  journal =      j-TOMS,
  volume =       "7",
  number =       "1",
  pages =        "93--105",
  month =        mar,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355934.355940",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65G05)",
  MRnumber =     "83a:65017",
  bibdate =      "Mon Aug 29 22:02:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "angular momentum; extended-range arithmetic; Legendre
                 polynomials; overflow; underflow",
}

@Article{Melgaard:1981:GST,
  author =       "David K. Melgaard and Richard F. Sincovec",
  title =        "General Software for Two-Dimensional Nonlinear Partial
                 Differential Equations",
  journal =      j-TOMS,
  volume =       "7",
  number =       "1",
  pages =        "106--125",
  month =        mar,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355934.355941",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65M20",
  MRnumber =     "83a:65082",
  bibdate =      "Mon Aug 29 22:02:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "finite differences; method of lines; ordinary
                 differential equations; partial differential
                 equations",
}

@Article{Melgaard:1981:APS,
  author =       "David K. Melgaard and Richard F. Sincovec",
  title =        "{Algorithm 565}: {PDETWO}\slash {PSETM}\slash {GEARB}:
                 Solution of Systems of Two-Dimensional Nonlinear
                 Partial Differential Equations [{D3}]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "1",
  pages =        "126--135",
  month =        mar,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355934.355942",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 22:16:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "finite differences; method of lines; ordinary
                 differential equations; partial differential
                 equations",
}

@Article{More:1981:AFS,
  author =       "J. J. Mor{\'e} and B. S. Garbow and K. E. Hillstrom",
  title =        "{Algorithm 566}: {FORTRAN} Subroutines for Testing
                 Unconstrained Optimization Software [{C5} [{E4}]]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "1",
  pages =        "136--140",
  month =        mar,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355934.355943",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:13:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Averbukh:1994:RA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "nonlinear least squares; optimization software;
                 performance testing; systems of nonlinear equations;
                 unconstrained minimization",
}

@Article{Lozier:1981:AER,
  author =       "D. W. Lozier and J. M. Smith",
  title =        "{Algorithm 567}: Extended-Range Arithmetic and
                 Normalized {Legendre} Polynomials [{A1}], [{C1}]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "1",
  pages =        "141--146",
  month =        mar,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355934.355944",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 22:17:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "angular momentum; extended-range arithmetic; Legendre
                 polynomials; overflow; underflow",
}

@Article{Golub:1981:BLM,
  author =       "Gene H. Golub and Franklin T. Luk and Michael L.
                 Overton",
  title =        "A Block {L{\'a}nczos} Method for Computing the
                 Singular Values of Corresponding Singular Vectors of a
                 Matrix",
  journal =      j-TOMS,
  volume =       "7",
  number =       "2",
  pages =        "149--169",
  month =        jun,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355945.355946",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F50 (65F15)",
  MRnumber =     "84h:65045",
  bibdate =      "Fri Sep 30 01:47:15 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "block Lanczos method; Lanczos algorithm; large sparse
                 matrix; nla; singular values; singular vectors;
                 singular-value decomposition; svd; upper-triangular
                 band matrix",
}

@Article{Wang:1981:PMT,
  author =       "H. H. Wang",
  title =        "A Parallel Method for Tridiagonal Equations",
  journal =      j-TOMS,
  volume =       "7",
  number =       "2",
  pages =        "170--183",
  month =        jun,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355945.355947",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05",
  MRnumber =     "83d:65092",
  bibdate =      "Mon Aug 29 22:19:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "cyclic reduction method; parallel computers; partition
                 method; recursive doubling method; tridiagonal
                 equations; vectors computers",
}

@Article{Stewart:1981:SIA,
  author =       "William J. Stewart and Alan Jennings",
  title =        "A Simultaneous Iteration Algorithm for Real Matrices",
  journal =      j-TOMS,
  volume =       "7",
  number =       "2",
  pages =        "184--198",
  month =        jun,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355945.355948",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F15",
  MRnumber =     "83d:65118",
  bibdate =      "Mon Aug 29 22:19:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "eigenvalues; eigenvectors; large sparse matrices; real
                 unsymmetric matrices; simultaneous iteration",
}

@Article{Hill:1981:EIR,
  author =       "Geoffrey W. Hill",
  title =        "Evaluation and Inversion of the Ratios of Modified
                 {Bessel} Functions, {$I_1(x)/I_0(x)$} and
                 {$I_{1.5}(x)/I_{0.5}(x)$}",
  journal =      j-TOMS,
  volume =       "7",
  number =       "2",
  pages =        "199--208",
  month =        jun,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355945.355949",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "83d:65046",
  bibdate =      "Mon Aug 29 22:19:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "approximation; backward recursion; continued
                 fractions; Fisher distribution; function inversion;
                 modified Bessel function ratios; Newton--Raphson; von
                 Mises distribution",
}

@Article{Ascher:1981:CSB,
  author =       "U. Ascher and J. Christiansen and R. D. Russell",
  title =        "Collocation Software for Boundary Value {ODE}'s",
  journal =      j-TOMS,
  volume =       "7",
  number =       "2",
  pages =        "209--222",
  month =        jun,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355945.355950",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:48:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  annote =       "collocation",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "B-spline; boundary-value problems; collocation; damped
                 Newton's method; error estimates; general-purpose code;
                 mesh selection; ordinary differential equations",
}

@Article{Ascher:1981:ACC,
  author =       "U. Ascher and J. Christiansen and R. D. Russell",
  title =        "{Algorithm 569}: {COLSYS}: Collocation Software for
                 Boundary-Value {ODEs} [{D2}]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "2",
  pages =        "223--229",
  month =        jun,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355945.355951",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 22:26:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Hake:1986:RCC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "B-spline; boundary-value problems; collocation; damped
                 Newton's method; error estimates; general-purpose code;
                 mesh selection; ordinary differential equations",
}

@Article{Stewart:1981:ALS,
  author =       "William J. Stewart and Alan Jennings",
  title =        "{Algorithm 570}: {LOPSI}: a Simultaneous Iteration
                 Method for Real Matrices [{F2}]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "2",
  pages =        "230--232",
  month =        jun,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355945.355952",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 22:27:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "eigenvalues; eigenvectors; large sparse matrices; real
                 unsymmetric matrices; simultaneous iteration",
}

@Article{Hill:1981:ASM,
  author =       "Geoffrey W. Hill",
  title =        "{Algorithm 571}: Statistics for von {Mises}' and
                 {Fisher}'s Distributions of Directions:
                 {$I_1(x)/I_0(x)$}, {$I_{1.5}(x)/I_{0.5}(x)$} and Their
                 Inverses [{S14}]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "2",
  pages =        "233--238",
  month =        jun,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355945.355953",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 22:28:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "continued fraction; direction statistics; Fisher
                 distribution; function inversion; modified Bessel
                 function ratio; Newton--Raphson; von Mises
                 distribution",
}

@Article{OLeary:1981:ASH,
  author =       "Dianne P. O'Leary and Olof Widlund",
  title =        "{Algorithm 572}: Solution of the {Helmholtz} Equation
                 for the {Dirichlet} Problem on General Bounded
                 Three-Dimensional Regions [{D3}]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "2",
  pages =        "239--246",
  month =        jun,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355945.355954",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 22:31:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "capacitance matrix; conjugate gradients; fast Poisson
                 solvers; Helmholtz equation",
}

@Article{Hill:1981:RSD,
  author =       "G. W. Hill",
  title =        "Remark on ``{Algorithm} 395: {Student}'s
                 $t$-Distribution''",
  journal =      j-TOMS,
  volume =       "7",
  number =       "2",
  pages =        "247--249",
  month =        jun,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355945.355955",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Hill:1970:SD,Hill:1970:SQ,elLozy:1979:RAS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hill:1981:RSQ,
  author =       "G. W. Hill",
  title =        "Remark on ``{Algorithm} 396: {Student}'s
                 $t$-Quantiles''",
  journal =      j-TOMS,
  volume =       "7",
  number =       "2",
  pages =        "250--251",
  month =        jun,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355945.355956",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Hill:1970:SQ}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fritsch:1981:CIU,
  author =       "F. N. Fritsch",
  title =        "Corrigendum: ``{Double} Integration Using
                 One-Dimensional Adaptive Quadrature Routines: a
                 Software Interface Problem''",
  journal =      j-TOMS,
  volume =       "7",
  number =       "2",
  pages =        "252--252",
  month =        jun,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355945.355957",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "252. 65D30",
  MRnumber =     "83c:65033b",
  bibdate =      "Mon Aug 29 22:19:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Fritsch:1981:DIU}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ukkonen:1981:CER,
  author =       "Esko Ukkonen",
  title =        "On the Calculation of the Effects of Roundoff Errors",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "259--271",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355959",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G05",
  MRnumber =     "82i:65030",
  bibdate =      "Mon Aug 29 22:44:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "automatic roundoff analysis; numerical linear algebra;
                 numerical stability",
}

@Article{Linnainmaa:1981:SDP,
  author =       "Seppo Linnainmaa",
  title =        "Software for Doubled-Precision Floating-Point
                 Computations",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "272--283",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355960",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68B99 (65G99 68C05)",
  MRnumber =     "82h:68041",
  bibdate =      "Mon Aug 29 22:44:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accurate floating-point summation; exact
                 multiplication; floating-point arithmetic; rounding
                 errors; software portability",
}

@Article{Lii:1981:CBC,
  author =       "K. S. Lii and K. N. Helland",
  title =        "Cross-Bispectrum Computation and Variance Estimation",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "284--294",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355961",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "62M15",
  MRnumber =     "82m:62213",
  bibdate =      "Mon Aug 29 22:44:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "bispectra; time series analysis",
}

@Article{Dew:1981:SLR,
  author =       "P. M. Dew and J. E. Walsh",
  title =        "A Set of Library Routines for Solving Parabolic
                 Equations in One Space Variable",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "295--314",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355962",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 11:51:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  annote =       "parabolic equations",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "method of lines; parabolic equations",
}

@Article{Duff:1981:AOM,
  author =       "I. S. Duff",
  title =        "On Algorithms for Obtaining a Maximum Transversal",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "315--330",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355963",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 22:49:58 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "block-triangular form; maximum assignment; maximum
                 transversal; perm; sparse; sparse matrices; unsymmetric
                 permutations",
}

@Article{McAllister:1981:ACS,
  author =       "David F. McAllister and John A. Roulier",
  title =        "An Algorithm for Computing a Shape-Preserving
                 Osculatory Quadratic Spline",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "331--347",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355964",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D07",
  MRnumber =     "82h:65009",
  bibdate =      "Mon Aug 29 22:44:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Bernstein polynomial; convexity preserving; geometric
                 design; monotonicity preserving; osculation; parametric
                 curve; polynomial interpolation; shape preserving;
                 spline",
}

@Article{Dennis:1981:ANL,
  author =       "John E. {Dennis, Jr.} and David M. Gay and Roy E.
                 Welsch",
  title =        "An Adaptive Nonlinear Least-squares Algorithm",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "348--368",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355965",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:38:10 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "lsq; nllsq; nlop; nonlinear least squares; nonlinear
                 regression; quasi-Newton methods; secant methods;
                 unconstrained optimization",
}

@Article{Dennis:1981:ANE,
  author =       "John E. {Dennis, Jr.} and David M. Gay and Roy E.
                 Welsch",
  title =        "{Algorithm 573}: {NL2SOL}\emdash An Adaptive Nonlinear
                 Least-Squares Algorithm [{E4}]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "369--383",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355966",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 22:52:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Gay:1983:RNE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "lsq; nllsq; nlop; nonlinear least squares; nonlinear
                 regression; quasi-Newton methods; secant methods;
                 software; unconstrained optimization",
}

@Article{McAllister:1981:ASP,
  author =       "D. F. McAllister and J. A. Roulier",
  title =        "{Algorithm 574}: Shape-Preserving Osculatory Quadratic
                 Splines [{E1}, {E2}]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "384--386",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355967",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 22:55:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Bernstein polynomial; convexity preserving;
                 monotonicity preserving; osculation; polynomial
                 interpolation; shape preserving",
}

@Article{Duff:1981:APZ,
  author =       "I. S. Duff",
  title =        "{Algorithm 575}: Permutations for a Zero-Free Diagonal
                 [{F1}]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "387--390",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355968",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 22:56:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "block triangular form; maximum assignment; maximum
                 transversal; sparse matrices; unsymmetric
                 permutations",
}

@Article{Barrodale:1981:AFP,
  author =       "I. Barrodale and G. F. Stuart",
  title =        "{Algorithm 576}: {A FORTRAN} Program for Solving
                 {${\bf Ax} = {\bf b}$} [{F4}]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "391--397",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355969",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 22:57:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Gaussian elimination; linear equations; new pivoting
                 strategy",
}

@Article{Carlson:1981:AAI,
  author =       "B. C. Carlson and Elaine M. Notis",
  title =        "{Algorithm 577}: Algorithms for Incomplete Elliptic
                 Integrals [{S21}]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "398--403",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355970",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 22:58:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "$R$-functions; elliptic integrals; inverse circular
                 functions; inverse hyperbolic functions; logarithms",
}

@Article{Razaz:1981:RAF,
  author =       "M. Razaz and J. L. Schonfelder",
  title =        "Remark on ``{Algorithm} 498: {Airy} Functions Using
                 {Chebyshev} Series Approximations''",
  journal =      j-TOMS,
  volume =       "7",
  number =       "3",
  pages =        "404--405",
  month =        sep,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355958.355971",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Prince:1975:AAF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Shampine:1981:ETS,
  author =       "Lawrence F. Shampine",
  title =        "Evaluation of a Test Set for Stiff {ODE} Solvers",
  journal =      j-TOMS,
  volume =       "7",
  number =       "4",
  pages =        "409--420",
  month =        dec,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355972.355973",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05",
  MRnumber =     "83d:65215",
  bibdate =      "Mon Aug 29 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "stiff; test set; testing ODE codes",
}

@Article{Neves:1981:CIE,
  author =       "Kenneth W. Neves",
  title =        "Control of Interpolatory Error in Retarded
                 Differential Equations",
  journal =      j-TOMS,
  volume =       "7",
  number =       "4",
  pages =        "421--444",
  month =        dec,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355972.355974",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L99 (34K99)",
  MRnumber =     "83d:65243",
  bibdate =      "Mon Aug 29 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "automatic step-size reduction; delay differential
                 equations; derivative jump discontinuities; local error
                 control; Runge--Kutta methods",
}

@Article{Brown:1981:SRM,
  author =       "W. S. Brown",
  title =        "A Simple but Realistic Model of Floating-Point
                 Computation",
  journal =      j-TOMS,
  volume =       "7",
  number =       "4",
  pages =        "445--480",
  month =        dec,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355972.355975",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "computer arithmetic; environment parameters; error
                 analysis; Euclidean norm; floating-point arithmetic;
                 software portability",
}

@Article{Marsten:1981:DXL,
  author =       "Roy E. Marsten",
  title =        "The Design of the {XMP} Linear Programming Library",
  journal =      j-TOMS,
  volume =       "7",
  number =       "4",
  pages =        "481--497",
  month =        dec,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355972.355976",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "linear programming; mathematical programming;
                 optimization; software engineering; software
                 libraries",
}

@Article{Pallottino:1981:EAD,
  author =       "Stefano Pallottino and Tommaso Toffoli",
  title =        "An Efficient Algorithm for Determining the Length of
                 the Longest Dead Path in a ``{LIFO}'' Branch-and-Bound
                 Exploration Schema",
  journal =      j-TOMS,
  volume =       "7",
  number =       "4",
  pages =        "498--504",
  month =        dec,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355972.355977",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:08:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "branch-and-bound; length of longest dead path; LIFO
                 tree search",
}

@Article{Duff:1981:MSU,
  author =       "I. S. Duff",
  title =        "{ME28}: a Sparse Unsymmetric Linear Equation Solver
                 for Complex Equations",
  journal =      j-TOMS,
  volume =       "7",
  number =       "4",
  pages =        "505--511",
  month =        dec,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355972.355978",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "complex sparse linear equations; drop tolerances;
                 ME28; numerical software; real and complex arithmetic;
                 sparse matrix",
}

@Article{Fornberg:1981:NDA,
  author =       "Bengt Fornberg",
  title =        "Numerical Differentiation of Analytic Functions",
  journal =      j-TOMS,
  volume =       "7",
  number =       "4",
  pages =        "512--526",
  month =        dec,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355972.355979",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D25",
  MRnumber =     "83d:65056",
  bibdate =      "Mon Aug 29 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "analytic functions; numerical differentiation; Taylor
                 series coefficients",
}

@Article{DuCroz:1981:SLF,
  author =       "J. J. {Du Croz} and S. M. Nugent and J. K. Reid and D.
                 B. Taylor",
  title =        "Solving Large Full Sets of Linear Equations in a Paged
                 Virtual Store",
  journal =      j-TOMS,
  volume =       "7",
  number =       "4",
  pages =        "527--536",
  month =        dec,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355972.355980",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Gaussian elimination; paged virtual store",
}

@Article{DuCroz:1981:ASR,
  author =       "J. J. {Du Croz} and S. M. Nugent and J. K. Reid and D.
                 B. Taylor",
  title =        "{Algorithm 578}: Solution of Real Linear Equations in
                 a Paged Virtual Store [{F4}]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "4",
  pages =        "537--541",
  month =        dec,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355972.355981",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:12:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Gaussian elimination; paged virtual store",
}

@Article{Fornberg:1981:ACC,
  author =       "B. Fornberg",
  title =        "{Algorithm 579}: {CPSC}: Complex Power Series
                 Coefficients [{D4}]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "4",
  pages =        "542--547",
  month =        dec,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355972.355982",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:12:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "analytic functions; numerical differentiation; Taylor
                 series coefficients",
}

@Article{Buckley:1981:AQS,
  author =       "A. Buckley",
  title =        "{Algorithm 580}: {QRUP}: a Set of {FORTRAN} Routines
                 for Updating {QR} Factorizations [{F5}]",
  journal =      j-TOMS,
  volume =       "7",
  number =       "4",
  pages =        "548--549",
  month =        dec,
  year =         "1981",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355972.355983",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:13:39 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Buckley:1982:RQS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "matrix factorization; orthogonalization",
}

@Article{Krogh:1982:AAP,
  author =       "Fred T. Krogh",
  title =        "{ACM} Algorithms Policy",
  journal =      j-TOMS,
  volume =       "8",
  number =       "1",
  pages =        "1--4",
  month =        mar,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355984.355985",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:14:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hiebert:1982:EMS,
  author =       "K. L. Hiebert",
  title =        "An Evaluation of Mathematical Software That Solves
                 Systems of Nonlinear Equations",
  journal =      j-TOMS,
  volume =       "8",
  number =       "1",
  pages =        "5--20",
  month =        mar,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355984.355986",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:14:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; Brent's method; Brown's method;
                 performance; quasi-Newton Powell's hybrid method",
  subject =      "D.2.8 [Software Engineering]: Metrics\emdash
                 performance measures; G.1.5 [Numerical Analysis]:
                 Proofs of Nonlinear Equations\emdash systems of
                 equations; G.4 [Mathematics of Computing]: Mathematical
                 Software\emdash certification and testing",
}

@Article{Dunham:1982:CBC,
  author =       "Charles B. Dunham",
  title =        "Choice of Basis for {Chebyshev} Approximation",
  journal =      j-TOMS,
  volume =       "8",
  number =       "1",
  pages =        "21--25",
  month =        mar,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355984.355987",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "41A50 (65D15)",
  MRnumber =     "84i:41038",
  bibdate =      "Mon Aug 29 23:14:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; condition numbers; design;
                 Fraser--Hart--Remez algorithm; polynomials; rational
                 functions",
  subject =      "G.1.2 [Numerical Analysis]: Approximation\emdash
                 Chebyshev approximation and theory",
}

@Article{Deo:1982:AGF,
  author =       "Narsingh Deo and G. M. Prabhu and M. S.
                 Krishnamoorthy",
  title =        "Algorithms for Generating Fundamental Cycles in a
                 Graph",
  journal =      j-TOMS,
  volume =       "8",
  number =       "1",
  pages =        "26--42",
  month =        mar,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355984.355988",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68C05 (05C38 68E10)",
  MRnumber =     "83h:68041",
  bibdate =      "Mon Aug 29 23:14:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; fundamental-cycle set;
                 NP-complete; spanning tree",
  reviewer =     "Sukhamay Kundu",
  subject =      "F.2.2 [Analysis of Algorithms and Problem Complexity]:
                 Nonnumerical algorithms and problems\emdash
                 computations on discrete structures; G.2.2 [Discrete
                 Mathematics]: Graph Theory",
}

@Article{Paige:1982:LAS,
  author =       "Christopher C. Paige and Michael A. Saunders",
  title =        "{LSQR}: An Algorithm for Sparse Linear Equations and
                 Sparse Least Squares",
  journal =      j-TOMS,
  volume =       "8",
  number =       "1",
  pages =        "43--71",
  month =        mar,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355984.355989",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F10 (65F20)",
  MRnumber =     "83f:65048",
  bibdate =      "Fri Aug 26 23:38:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; analysis of variance; conjugate gradients;
                 Lanczos algorithm; lsq; nla",
}

@Article{Chan:1982:IAC,
  author =       "Tony F. Chan",
  title =        "An Improved Algorithm for Computing the Singular Value
                 Decomposition",
  journal =      j-TOMS,
  volume =       "8",
  number =       "1",
  pages =        "72--83",
  month =        mar,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355984.355990",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F30",
  MRnumber =     "83f:65058",
  bibdate =      "Mon Aug 29 23:23:48 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; Householder transformation; nla;
                 performance; singular values; software; svd",
}

@Article{Chan:1982:AIA,
  author =       "Tony F. Chan",
  title =        "{Algorithm 581}: An Improved Algorithm for Computing
                 the Singular Value Decomposition [{F1}]",
  journal =      j-TOMS,
  volume =       "8",
  number =       "1",
  pages =        "84--88",
  month =        mar,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355984.355991",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:38:11 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; nla; singular value decomposition;
                 software; svd",
}

@Article{Tracht:1982:RNR,
  author =       "Allen E. Tracht",
  title =        "Remark on ``{Algorithm} 334: Normal Random
                 Deviates''",
  journal =      j-TOMS,
  volume =       "8",
  number =       "1",
  pages =        "89--89",
  month =        mar,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355984.355992",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Bell:1968:NRD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Shampine:1982:IRM,
  author =       "L. F. Shampine",
  title =        "Implementation of {Rosenbrock} Methods",
  journal =      j-TOMS,
  volume =       "8",
  number =       "2",
  pages =        "93--113",
  month =        jun,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355993.355994",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05",
  MRnumber =     "83f:65115",
  bibdate =      "Mon Aug 29 23:27:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; FORTRAN Codes; Rosenbrock Methods;
                 theory",
}

@Article{Corliss:1982:SOD,
  author =       "George Corliss and Y. F. Chang",
  title =        "Solving Ordinary Differential Equations Using {Taylor}
                 Series",
  journal =      j-TOMS,
  volume =       "8",
  number =       "2",
  pages =        "114--144",
  month =        jun,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355993.355995",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05",
  MRnumber =     "83g:65072",
  bibdate =      "Mon Aug 29 23:27:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance; Taylor series method",
  reviewer =     "L. F. Shampine",
}

@Article{Hoaglin:1982:EDA,
  author =       "David C. Hoaglin and Virginia C. Klema and Stephen C.
                 Peters",
  title =        "Exploratory Data Analysis in a Study of the
                 Performance of Nonlinear Optimization Routines",
  journal =      j-TOMS,
  volume =       "8",
  number =       "2",
  pages =        "145--162",
  month =        jun,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355993.355996",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:27:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "experimentation; performance",
}

@Article{Ahrens:1982:CGP,
  author =       "J. H. Ahrens and U. Dieter",
  title =        "Computer Generation of {Poisson} Deviates from
                 Modified Normal Distributions",
  journal =      j-TOMS,
  volume =       "8",
  number =       "2",
  pages =        "163--179",
  month =        jun,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355993.355997",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65C10 (60-04 62E99)",
  MRnumber =     "84c:65016",
  bibdate =      "Mon Aug 29 23:31:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  country =      "USA",
  date =         "13/05/93",
  descriptors =  "RVG",
  enum =         "6930",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "acceptance-rejection method; algorithms; Poisson
                 distribution; theory",
  language =     "English",
  location =     "SEL: Wi",
  references =   "0",
  reviewer =     "James E. Gentle",
  revision =     "16/01/94",
}

@Article{Lewis:1982:IGP,
  author =       "John G. Lewis",
  title =        "Implementation of the {Gibbs-Poole-Stockmeyer} and
                 {Gibbs}-King Algorithms",
  journal =      j-TOMS,
  volume =       "8",
  number =       "2",
  pages =        "180--189",
  month =        jun,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355993.355998",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:27:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithms; banded matrix; Gibbs-King algorithms;
                 Gibbs-Poole-Stockmeyer algorithms; matrix bandwidth;
                 matrix profile; matrix wavefront",
}

@Article{Lewis:1982:AGP,
  author =       "John G. Lewis",
  title =        "{Algorithm 582}: The {Gibbs-Poole-Stockmeyer} and
                 {Gibbs-King} Algorithms for Reordering Sparse
                 Matrices",
  journal =      j-TOMS,
  volume =       "8",
  number =       "2",
  pages =        "190--194",
  month =        jun,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355993.355999",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:34:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithms; banded matrix; Gibbs-King algorithms;
                 Gibbs-Poole-Stockmeyer algorithms; matrix bandwidth;
                 matrix profile; matrix wavefront",
}

@Article{Paige:1982:ALS,
  author =       "Christopher C. Paige and Michael A. Saunders",
  title =        "{Algorithm 583}: {LSQR}: Sparse Linear Equations and
                 Least Squares Problems",
  journal =      j-TOMS,
  volume =       "8",
  number =       "2",
  pages =        "195--209",
  month =        jun,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355993.356000",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:38:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; analysis of variance; conjugate gradients;
                 conjugate-gradient method; Lanczos algorithm; least
                 squares; linear equations; lsq; nla; regression;
                 software; sparse matrix",
}

@Article{Laurie:1982:ACA,
  author =       "D. P. Laurie",
  title =        "{Algorithm 584}: {CUBTRI}: Automatic Cubature over a
                 Triangle",
  journal =      j-TOMS,
  volume =       "8",
  number =       "2",
  pages =        "210--218",
  month =        jun,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355993.356001",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:37:42 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Hanson:1986:RCA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithm; quadrature rule; theory",
}

@Article{Flamm:1982:RHE,
  author =       "David S. Flamm and Robert A. Walker",
  title =        "Remark on ``{Algorithm} 506: {HQR3} and {EXCHNG}:
                 {Fortran} Subroutines for Calculating and Ordering the
                 Eigenvalues of a Real Upper {Hessenberg} Matrix
                 [{F2}]''",
  journal =      j-TOMS,
  volume =       "8",
  number =       "2",
  pages =        "219--220",
  month =        jun,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355993.356002",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Stewart:1976:AHE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lewis:1982:RMB,
  author =       "John G. Lewis",
  title =        "Remark on ``{Algorithm}s 508 and 509: Matrix Bandwidth
                 and Profile Reduction [{F1}] and a Hybrid Profile
                 Reduction Algorithm [{F1}]''",
  journal =      j-TOMS,
  volume =       "8",
  number =       "2",
  pages =        "221--221",
  month =        jun,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/355993.356003",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Crane:1976:AMB,Gibbs:1976:AHP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ellison:1982:UUI,
  author =       "E. F. D. Ellison and Gautam Mitra",
  title =        "{UIMP}: User Interface for Mathematical Programming",
  journal =      j-TOMS,
  volume =       "8",
  number =       "3",
  pages =        "229--255",
  month =        sep,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356004.356005",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:27:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/356004.356005;
                 http://www.acm.org/pubs/citations/journals/toms/1982-8-3/p229-mitra/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "matrix generator; report writer; solution analysis",
}

@Article{Schreiber:1982:NIS,
  author =       "Robert Schreiber",
  title =        "A New Implementation of Sparse {Gaussian}
                 Elimination",
  journal =      j-TOMS,
  volume =       "8",
  number =       "3",
  pages =        "256--276",
  month =        sep,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356004.356006",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05",
  MRnumber =     "84d:65020",
  bibdate =      "Mon Aug 29 23:27:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; sparse matrix; sparse systems of linear
                 equations; theory",
}

@Article{Sasaki:1982:EGE,
  author =       "Tateaki Sasaki and Hirokazu Murao",
  title =        "Efficient {Gaussian} Elimination Method for Symbolic
                 Determinants and Linear Systems",
  journal =      j-TOMS,
  volume =       "8",
  number =       "3",
  pages =        "277--289",
  month =        sep,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356004.356007",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F40 (68Q40)",
  MRnumber =     "85b:65037",
  bibdate =      "Mon Aug 29 23:27:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; Cramer's method; expansion by minors;
                 Gaussian elimination; symbolic determinant; symbolic
                 linear systems",
  reviewer =     "E. Bareiss",
}

@Article{Brezinski:1982:ASG,
  author =       "C. Brezinski",
  title =        "{Algorithm 585}: a Subroutine for the General
                 Interpolation and Extrapolation Problems",
  journal =      j-TOMS,
  volume =       "8",
  number =       "3",
  pages =        "290--301",
  month =        sep,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356004.356008",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:49:19 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; convergence acceleration; extrapolation;
                 interpolation; least squares approximation;
                 Neville--Aitken scheme",
}

@Article{Kincaid:1982:AIF,
  author =       "David R. Kincaid and John R. Respess and David M.
                 Young and Roger G. Grimes",
  title =        "{Algorithm 586}: {ITPACK 2C}: {A FORTRAN} Package for
                 Solving Large Sparse Linear Systems by Adaptive
                 Accelerated Iterative Methods",
  journal =      j-TOMS,
  volume =       "8",
  number =       "3",
  pages =        "302--322",
  month =        sep,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356004.356009",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 23:49:22 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; documentation; iterative methods;
                 numerical software; sparse matrix",
}

@Article{Hanson:1982:ATA,
  author =       "Richard J. Hanson and Karen H. Haskell",
  title =        "{Algorithm 587}: Two Algorithms for the Linearly
                 Constrained Least Squares Problem",
  journal =      j-TOMS,
  volume =       "8",
  number =       "3",
  pages =        "323--333",
  month =        sep,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356004.356010",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 20:52:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Dadurkevicius:1989:RA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; covariance matrix; equality constraints;
                 inconsistent constraints; inequality constraints;
                 linear least squares solution",
}

@Article{Hanson:1982:RPQ,
  author =       "R. J. Hanson",
  title =        "Remark on ``{Algorithm} 507: Procedures for Quintic
                 Natural Spline Interpolation [{E1}]''",
  journal =      j-TOMS,
  volume =       "8",
  number =       "3",
  pages =        "334--334",
  month =        sep,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356004.356011",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Herriot:1976:APQ}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Wolfe:1982:CCG,
  author =       "Philip Wolfe",
  title =        "Checking the Calculation of Gradients",
  journal =      j-TOMS,
  volume =       "8",
  number =       "4",
  pages =        "337--343",
  month =        dec,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356012.356013",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:02:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "nonlinearity; optimization",
}

@Article{Anderson:1982:FHT,
  author =       "Walter L. Anderson",
  title =        "Fast {Hankel} Transforms Using Related and Lagged
                 Convolutions",
  journal =      j-TOMS,
  volume =       "8",
  number =       "4",
  pages =        "344--368",
  month =        dec,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356012.356014",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:02:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Bessel functions of the first kind; convolution
                 integrals; Hankel transforms of integer order; linear
                 digital filters",
}

@Article{Anderson:1982:AFH,
  author =       "Walter L. Anderson",
  title =        "{Algorithm 588}: Fast {Hankel} Transforms Using
                 Related and Lagged Convolutions",
  journal =      j-TOMS,
  volume =       "8",
  number =       "4",
  pages =        "369--370",
  month =        dec,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356012.356015",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:05:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Bessel functions of the first kind; convolution
                 integrals; Hankel transforms of integer order; linear
                 digital filters",
}

@Article{Dongarra:1982:ASF,
  author =       "Jack J. Dongarra",
  title =        "{Algorithm 589}: {SICEDR}: {A FORTRAN} Subroutine for
                 Improving the Accuracy of Computed Matrix Eigenvalues",
  journal =      j-TOMS,
  volume =       "8",
  number =       "4",
  pages =        "371--375",
  month =        dec,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356012.356016",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:05:58 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; eigensystems improvement; iterative
                 method; matrix eigensystems",
}

@Article{VanDooren:1982:ADE,
  author =       "P. {Van Dooren}",
  title =        "{Algorithm 590}: {DSUBSP} and {EXCHQZ}: {FORTRAN}
                 Subroutines for Computing Deflating Subspaces with
                 Specified Spectrum",
  journal =      j-TOMS,
  volume =       "8",
  number =       "4",
  pages =        "376--382",
  month =        dec,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356012.356017",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:17:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Petkov:1984:RDE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithm; generalized eigenvalue; QZ algorithm",
}

@Article{Hemmerle:1982:ACM,
  author =       "William J. Hemmerle",
  title =        "{Algorithm 591}: a Comprehensive Matrix-Free Algorithm
                 for Analysis of Variance",
  journal =      j-TOMS,
  volume =       "8",
  number =       "4",
  pages =        "383--401",
  month =        dec,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356012.356018",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:08:00 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algebraic-model specification; algorithms; analysis of
                 variance; balanced data operators; G-inverse solution;
                 hypothesis testing; iterative improvement; linear
                 models; missing cells; rank computations;
                 storage-efficient algorithm; unbalanced data",
}

@Article{Garbow:1982:RQA,
  author =       "B. S. Garbow",
  title =        "Remark on ``{Algorithm} 535: The {QZ} Algorithm to
                 Solve the Generalized Eigenvalue Problem for Complex
                 Matrices [{F2}]''",
  journal =      j-TOMS,
  volume =       "8",
  number =       "4",
  pages =        "402--402",
  month =        dec,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356012.356019",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Garbow:1978:AQA,Garbow:1984:RQA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Dodson:1982:RBL,
  author =       "David S. Dodson and Roger G. Grimes",
  title =        "Remark on ``{Algorithm} 539: {Basic Linear Algebra
                 Subprograms} for {Fortran} Usage [{F1}]''",
  journal =      j-TOMS,
  volume =       "8",
  number =       "4",
  pages =        "403--404",
  month =        dec,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356012.356020",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 21:11:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Lawson:1979:ABL,Dodson:1983:CRB,Hanson:1987:ATA,Louter-Nool:1988:ATA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Buckley:1982:RQS,
  author =       "A. Buckley",
  title =        "Remark on ``{Algorithm} 580: {QRUP}: a Set of
                 {FORTRAN} Routines for Updating {QR} Factorizations
                 [{F5}]''",
  journal =      j-TOMS,
  volume =       "8",
  number =       "4",
  pages =        "405--405",
  month =        dec,
  year =         "1982",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356012.356021",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:08 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Buckley:1981:AQS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Morgan:1983:MCA,
  author =       "Alexander P. Morgan",
  title =        "A Method for Computing All Solutions to Systems of
                 Polynomials Equations",
  journal =      j-TOMS,
  volume =       "9",
  number =       "1",
  pages =        "1--17",
  month =        mar,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356022.356023",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H10",
  MRnumber =     "85f:65051",
  bibdate =      "Sun Sep 04 19:32:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Eugene Allgower",
}

@Article{Greenberg:1983:FDA,
  author =       "Harvey Greenberg",
  title =        "A Functional Description of {ANALYZE}: a
                 Computer-Assisted Analysis System for Linear
                 Programming Models",
  journal =      j-TOMS,
  volume =       "9",
  number =       "1",
  pages =        "18--56",
  month =        mar,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356022.356024",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 19:32:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Beck:1983:RGA,
  author =       "P. Beck and L. Lasdon and M. Engquist",
  title =        "A Reduced Gradient Algorithm for Nonlinear Network
                 Problems",
  journal =      j-TOMS,
  volume =       "9",
  number =       "1",
  pages =        "57--70",
  month =        mar,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356022.356025",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65K10",
  MRnumber =     "84m:65077",
  bibdate =      "Sun Sep 04 19:32:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Kailash C. Kapur",
}

@Article{Hanson:1983:CDE,
  author =       "P. M. Hanson and W. H. Enright",
  title =        "Controlling the defect in existing variable-order
                 {Adams} codes for initial-value problems",
  journal =      j-TOMS,
  volume =       "9",
  number =       "1",
  pages =        "71--97",
  month =        mar,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356022.356026",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05 (65L07)",
  MRnumber =     "85i:65086",
  bibdate =      "Sat Aug 13 17:16:02 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; reliability; theory",
  review =       "ACM CR 40497",
  reviewer =     "Syvert P. N{\o}rsett",
  subject =      "G.1.4 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Quadrature and Numerical Differentiation, Error
                 analysis \\ G.1.7 Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Error
                 analysis \\ G.1.7 Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems",
}

@Article{Gaffney:1983:AFS,
  author =       "Patrick W. Gaffney",
  title =        "{Algorithm 592}: {A FORTRAN} Subroutine for Computing
                 the Optimal Estimate of {$f(x)$}",
  journal =      j-TOMS,
  volume =       "9",
  number =       "1",
  pages =        "98--116",
  month =        mar,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356022.356027",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Proskurowski:1983:APH,
  author =       "Wlodzimierz Proskurowski",
  title =        "{Algorithm 593}: a Package for the {Helmholtz}
                 Equation in Nonrectangular Planar Regions",
  journal =      j-TOMS,
  volume =       "9",
  number =       "1",
  pages =        "117--124",
  month =        mar,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356022.356028",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Larson:1983:ASR,
  author =       "John L. Larson and Mary E. Pasternak and John A.
                 Wisniewski",
  title =        "{Algorithm 594}: Software for Relative Error
                 Analysis",
  journal =      j-TOMS,
  volume =       "9",
  number =       "1",
  pages =        "125--130",
  month =        mar,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356022.356029",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Martello:1983:AEA,
  author =       "Silvano Martello",
  title =        "{Algorithm 595}: An Enumerative Algorithm for Finding
                 {Hamiltonian} Circuits in a Directed Graph",
  journal =      j-TOMS,
  volume =       "9",
  number =       "1",
  pages =        "131--138",
  month =        mar,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356022.356030",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gay:1983:RNE,
  author =       "David M. Gay",
  title =        "Remark on ``{Algorithm} 573: {NL2SOL}\emdash An
                 Adaptive Nonlinear Least-Squares Algorithm''",
  journal =      j-TOMS,
  volume =       "9",
  number =       "1",
  pages =        "139--139",
  month =        mar,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356022.356031",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 19:32:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Dennis:1981:ANE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "lsq; nllsq; nlop; software",
}

@Article{Dodson:1983:CRB,
  author =       "David S. Dodson",
  title =        "Corrigendum: Remark on ``{Algorithm} 539: {Basic
                 Linear Algebra Subroutines} for {FORTRAN} Usage''",
  journal =      j-TOMS,
  volume =       "9",
  number =       "1",
  pages =        "140--140",
  month =        mar,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356022.356032",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 21:11:39 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Lawson:1979:ABL,Dodson:1982:RBL,Hanson:1987:ATA,Louter-Nool:1988:ATA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fourer:1983:MLV,
  author =       "Robert Fourer",
  title =        "Modeling Languages Versus Matrix Generators for Linear
                 Programming",
  journal =      j-TOMS,
  volume =       "9",
  number =       "2",
  pages =        "143--183",
  month =        jun,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/357456.357457",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 19:43:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Armstrong:1983:CSM,
  author =       "R. D. Armstrong and D. S. Kung and P. Sinha and A. A.
                 Zoltners",
  title =        "A Computational Study of a Multiple-Choice Knapsack
                 Algorithm",
  journal =      j-TOMS,
  volume =       "9",
  number =       "2",
  pages =        "184--198",
  month =        jun,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/357456.357458",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "90C10",
  MRnumber =     "85a:90163",
  bibdate =      "Sun Sep 04 19:43:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cryer:1983:ESL,
  author =       "C. W. Cryer",
  title =        "The Efficient Solution of Linear Complementarity
                 Problems for Tridiagonal {Minkowski} Matrices",
  journal =      j-TOMS,
  volume =       "9",
  number =       "2",
  pages =        "199--214",
  month =        jun,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/357456.357459",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "90C33 (65F10)",
  MRnumber =     "84j:90088",
  bibdate =      "Sun Sep 04 19:43:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rheinboldt:1983:LPC,
  author =       "Werner C. Rheinboldt and John V. Burkardt",
  title =        "A Locally Parametrized Continuation Process",
  journal =      j-TOMS,
  volume =       "9",
  number =       "2",
  pages =        "215--235",
  month =        jun,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/357456.357460",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H10",
  MRnumber =     "85f:65052",
  bibdate =      "Sun Sep 04 19:43:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Dietrich Braess",
}

@Article{Rheinboldt:1983:APL,
  author =       "Werner C. Rheinboldt and John V. Burkardt",
  title =        "{Algorithm 596}: a Program for a Locally Parametrized
                 Continuation Process",
  journal =      j-TOMS,
  volume =       "9",
  number =       "2",
  pages =        "236--241",
  month =        jun,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/357456.357461",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 29 12:18:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cody:1983:ASM,
  author =       "W. J. Cody",
  title =        "{Algorithm 597}: Sequence of Modified {Bessel}
                 Functions of the First Kind",
  journal =      j-TOMS,
  volume =       "9",
  number =       "2",
  pages =        "242--245",
  month =        jun,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/357456.357462",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 6 22:16:30 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation G
                 Mathematics of Computing, MISCELLANEOUS",
}

@Article{Davis:1983:AAC,
  author =       "George J. Davis",
  title =        "{Algorithm 598}: An Algorithm to Compute Solvents of
                 the Matrix Equation {$AX^2 + BX + C = 0$}",
  journal =      j-TOMS,
  volume =       "9",
  number =       "2",
  pages =        "246--254",
  month =        jun,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/357456.357463",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ahrens:1983:ASG,
  author =       "J. H. Ahrens and K. D. Kohrt and U. Dieter",
  title =        "{Algorithm 599}: Sampling from {Gamma} and {Poisson}
                 Distributions",
  journal =      j-TOMS,
  volume =       "9",
  number =       "2",
  pages =        "255--257",
  month =        jun,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/357456.357464",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 16:10:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  country =      "USA",
  date =         "13/05/93",
  descriptors =  "RVG",
  enum =         "6932",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  language =     "English",
  location =     "SEL: Wi",
  references =   "0",
  revision =     "16/01/94",
}

@Article{Herriott:1983:ATA,
  author =       "John G. Herriott and Christian H. Reinsch",
  title =        "{Algorithm 600}: Translation of {Algorithm} 507:
                 {Procedures} for Quintic Natural Spline Interpolation",
  journal =      j-TOMS,
  volume =       "9",
  number =       "2",
  pages =        "258--259",
  month =        jun,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/357456.357465",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 5 23:07:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pape:1983:RSP,
  author =       "U. Pape",
  title =        "Remark on ``{Algorithm} 562: Shortest Path Lengths''",
  journal =      j-TOMS,
  volume =       "9",
  number =       "2",
  pages =        "260--260",
  month =        jun,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/357456.357466",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 19:43:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Pape:1980:ASP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Krogh:1983:AAP,
  author =       "Fred T. Krogh",
  title =        "{ACM} Algorithms Policy",
  journal =      j-TOMS,
  volume =       "9",
  number =       "2",
  pages =        "261--264",
  month =        jun,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/357456.357467",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 19:43:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Zave:1983:QEF,
  author =       "Pamela Zave and George E. {Cole, Jr.}",
  title =        "A Quantitative Evaluation of the Feasibility of, and
                 Suitable Hardware Architectures for, an Adaptive,
                 Parallel Finite-Element System",
  journal =      j-TOMS,
  volume =       "9",
  number =       "3",
  pages =        "271--292",
  month =        sep,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356044.356045",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65W05 (65N30)",
  MRnumber =     "86g:65244",
  bibdate =      "Sun Sep 04 19:50:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Beny Neta",
}

@Article{Watkins:1983:NSS,
  author =       "David S. Watkins and Ralph W. HansonSmith",
  title =        "The Numerical Solution of Separably Stiff Systems by
                 Precise Partitioning",
  journal =      j-TOMS,
  volume =       "9",
  number =       "3",
  pages =        "293--301",
  month =        sep,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356044.356046",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05 (65-04)",
  MRnumber =     "86g:65136",
  bibdate =      "Sun Sep 04 19:51:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; experimentation; measurement;
                 performance",
  review =       "ACM CR 8406-0468",
  subject =      "G.1.7 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Ordinary Differential Equations, Initial value problems
                 \\ G.1.7 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Ordinary Differential Equations, Stiff equations",
}

@Article{Duff:1983:MSI,
  author =       "I. S. Duff and J. K. Reid",
  title =        "The Multifrontal Solution of Indefinite Sparse
                 Symmetric Linear Systems",
  journal =      j-TOMS,
  volume =       "9",
  number =       "3",
  pages =        "302--325",
  month =        sep,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356044.356047",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F50 (65W05)",
  MRnumber =     "86k:65030",
  bibdate =      "Fri Aug 26 23:38:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "indefinite system; nla; sparse; symmetric matrix",
  reviewer =     "Stephen W. Brady",
}

@Article{Tarjan:1983:SEI,
  author =       "Robert E. Tarjan",
  title =        "Space-Efficient Implementations of Graph Search
                 Methods",
  journal =      j-TOMS,
  volume =       "9",
  number =       "3",
  pages =        "326--339",
  month =        sep,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356044.356048",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68P10",
  MRnumber =     "86m:68023",
  bibdate =      "Sun Sep 04 19:50:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{McNamee:1983:SMP,
  author =       "J. M. McNamee",
  title =        "A Sparse Matrix Package\emdash {Part II}: Special
                 Cases",
  journal =      j-TOMS,
  volume =       "9",
  number =       "3",
  pages =        "340--343",
  month =        sep,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356044.356049",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 19:50:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{McNamee:1983:ASM,
  author =       "J. M. McNamee",
  title =        "{Algorithm 601}: a Sparse-Matrix Package\emdash {Part
                 II}: Special Cases",
  journal =      j-TOMS,
  volume =       "9",
  number =       "3",
  pages =        "344--345",
  month =        sep,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356044.356050",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fessler:1983:HAA,
  author =       "Theodore Fessler and William F. Ford and David A.
                 Smith",
  title =        "{HURRY}: An Acceleration Algorithm for Scalar
                 Sequences and Series",
  journal =      j-TOMS,
  volume =       "9",
  number =       "3",
  pages =        "346--354",
  month =        sep,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356044.356051",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65B10",
  MRnumber =     "791 970",
  bibdate =      "Sun Sep 04 19:50:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fessler:1983:AHA,
  author =       "Theodore Fessler and William F. Ford and David A.
                 Smith",
  title =        "{Algorithm 602}: {HURRY}: An Acceleration Algorithm
                 for Scalar Sequences and Series",
  journal =      j-TOMS,
  volume =       "9",
  number =       "3",
  pages =        "355--357",
  month =        sep,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356044.356052",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65B10",
  MRnumber =     "791 971",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Diaz:1983:FPS,
  author =       "J. C. D{\'i}az and G. Fairweather and P. Keast",
  title =        "{FORTRAN} Packages for Solving Certain Almost Block
                 Diagonal Linear Systems by Modified Alternate Row and
                 Column Elimination",
  journal =      j-TOMS,
  volume =       "9",
  number =       "3",
  pages =        "358--375",
  month =        sep,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356044.356053",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05 (65-04)",
  MRnumber =     "791 972",
  bibdate =      "Sun Sep 04 19:50:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Diaz:1983:ACA,
  author =       "J. C. D{\'i}az and G. Fairweather and P. Keast",
  title =        "{Algorithm 603}: {COLROW} and {ARCECO}: {FORTRAN}
                 Packages for Solving Certain Almost Block Diagonal
                 Linear Systems by Modified Alternate Row and Column
                 Elimination",
  journal =      j-TOMS,
  volume =       "9",
  number =       "3",
  pages =        "376--380",
  month =        sep,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356044.356054",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05 (65-04)",
  MRnumber =     "791 973",
  bibdate =      "Sun Sep 4 22:04:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Diaz:1988:RCA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sauer:1983:AFP,
  author =       "Frederick W. Sauer",
  title =        "{Algorithm 604}: a {FORTRAN} Program for the
                 Calculation of an Extremal Polynomial",
  journal =      j-TOMS,
  volume =       "9",
  number =       "3",
  pages =        "381--383",
  month =        sep,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356044.356055",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65F10 65K10)",
  MRnumber =     "86g:65007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hopkins:1983:APV,
  author =       "T. R. Hopkins",
  title =        "{Algorithm 605}: {PBASIC}: a Verifier Program for
                 {American National Standard Minimal BASIC}",
  journal =      j-TOMS,
  volume =       "9",
  number =       "4",
  pages =        "391--394",
  month =        dec,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356056.356057",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gaffney:1983:NIT,
  author =       "P. W. Gaffney and J. W. Wooten and K. A. Kessel and W.
                 R. McKinney",
  title =        "{NITPACK}: An Interactive Tree Package",
  journal =      j-TOMS,
  volume =       "9",
  number =       "4",
  pages =        "395--417",
  month =        dec,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356056.356058",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 19:56:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gaffney:1983:ANI,
  author =       "P. W. Gaffney and J. W. Wooten and K. A. Kessel and W.
                 R. McKinney",
  title =        "{Algorithm 606}: {NITPACK}: An Interactive Tree
                 Package",
  journal =      j-TOMS,
  volume =       "9",
  number =       "4",
  pages =        "418--426",
  month =        dec,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356056.356059",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Snyder:1983:ATE,
  author =       "W. V. Snyder and R. J. Hanson",
  title =        "{Algorithm 607}: Text Exchange System: a Transportable
                 System for Management and Exchange of Programs and
                 other Text",
  journal =      j-TOMS,
  volume =       "9",
  number =       "4",
  pages =        "427--440",
  month =        dec,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356056.356060",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Horn:1983:CLE,
  author =       "B. K. P. Horn",
  title =        "The Curve of Least Energy",
  journal =      j-TOMS,
  volume =       "9",
  number =       "4",
  pages =        "441--460",
  month =        dec,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356056.356061",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D07 (65D10)",
  MRnumber =     "87c:65009",
  bibdate =      "Sun Sep 04 19:58:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "G. P. Bhattacharjee",
}

@Article{West:1983:AAS,
  author =       "David H. West",
  title =        "{Algorithm 608}: Approximate Solution of the Quadratic
                 Assignment Problem",
  journal =      j-TOMS,
  volume =       "9",
  number =       "4",
  pages =        "461--466",
  month =        dec,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356056.356062",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65K05 (90C10)",
  MRnumber =     "791 976",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Amos:1983:UAE,
  author =       "D. E. Amos",
  title =        "Uniform Asymptotic Expansions for Exponential
                 Integrals ${E}_n(x)$ and {Bickley} Functions
                 $\hbox{Ki}_n(x)$",
  journal =      j-TOMS,
  volume =       "9",
  number =       "4",
  pages =        "467--479",
  month =        dec,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356056.356063",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (33A70)",
  MRnumber =     "87a:65043",
  bibdate =      "Sun Sep 04 19:56:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Marietta J. Tretter",
}

@Article{Amos:1983:APFa,
  author =       "D. E. Amos",
  title =        "{Algorithm 609}: a Portable {FORTRAN} Subroutine for
                 the {Bickley} Functions {$\hbox{Ki}_n(x)$}",
  journal =      j-TOMS,
  volume =       "9",
  number =       "4",
  pages =        "480--493",
  month =        dec,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356056.356064",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (33A70 65-04)",
  MRnumber =     "87a:65044",
  bibdate =      "Sun Sep 4 20:00:39 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Marietta J. Tretter",
}

@Article{Amos:1983:APFb,
  author =       "D. E. Amos",
  title =        "{Algorithm 610}: a Portable {FORTRAN} Subroutine for
                 Derivatives of the Psi Function",
  journal =      j-TOMS,
  volume =       "9",
  number =       "4",
  pages =        "494--502",
  month =        dec,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356056.356065",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "791 979",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  catcode =      "G.1.0; G.1; G; D.3.2",
  CRclass =      "G.1.0 General; G.1.0 Numerical algorithms; G.1.m
                 Miscellaneous; D.3.2 Language Classifications; D.3.2
                 FORTRAN",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms; Mathematics of Computing,
                 NUMERICAL ANALYSIS, Miscellaneous; Mathematics of
                 Computing, MISCELLANEOUS; Software, PROGRAMMING
                 LANGUAGES, Language Classifications, FORTRAN",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  genterm =      "ALGORITHMS",
  guideno =      "02212",
  journal-URL =  "https://dl.acm.org/loi/toms",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.m MISCELLANEOUS; D.
                 Software; D.3 PROGRAMMING LANGUAGES",
}

@Article{Gay:1983:ASU,
  author =       "David M. Gay",
  title =        "{Algorithm 611}: Subroutines for Unconstrained
                 Minimization Using a Model\slash Trust-Region
                 Approach",
  journal =      j-TOMS,
  volume =       "9",
  number =       "4",
  pages =        "503--524",
  month =        dec,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356056.356066",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65K10 (65-04 90C30)",
  MRnumber =     "86f:65111",
  bibdate =      "Fri Aug 26 23:38:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "lsq; nllsq; nlop",
}

@Article{Amos:1983:REI,
  author =       "Donald E. Amos",
  title =        "Remark on ``{Algorithm} 556: Exponential Integrals''",
  journal =      j-TOMS,
  volume =       "9",
  number =       "4",
  pages =        "525--525",
  month =        dec,
  year =         "1983",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356056.356067",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 30 00:28:08 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Amos:1980:AEI}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{deDoncker:1984:AAI,
  author =       "Elise {de Doncker} and Ian Robinson",
  title =        "An Algorithm for Automatic Integration Over a Triangle
                 Using Nonlinear Extrapolation",
  journal =      j-TOMS,
  volume =       "10",
  number =       "1",
  pages =        "1--16",
  month =        mar,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356068.356069",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30 (65V05)",
  MRnumber =     "86e:65035a",
  bibdate =      "Fri Mar 28 11:00:07 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{deDoncker:1984:ATI,
  author =       "Elise {de Doncker} and Ian Robinson",
  title =        "{Algorithm 612}: {TRIEX}: Integration Over a
                 {TRIangle} Using Nonlinear {EXtrapolation}",
  journal =      j-TOMS,
  volume =       "10",
  number =       "1",
  pages =        "17--22",
  month =        mar,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356068.356070",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30 (65V05)",
  MRnumber =     "86e:65035b",
  bibdate =      "Sat Oct 24 15:51:01 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/356068.356070;
                 http://www.acm.org/pubs/citations/journals/toms/1984-10-1/p17-doncker/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gear:1984:SOD,
  author =       "C. W. Gear and O. {\O}sterby",
  title =        "Solving Ordinary Differential Equations with
                 Discontinuities",
  journal =      j-TOMS,
  volume =       "10",
  number =       "1",
  pages =        "23--44",
  month =        mar,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356068.356071",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05",
  MRnumber =     "86h:65097",
  bibdate =      "Sun Sep 04 20:02:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "W. C. Rheinboldt",
}

@Article{Krogh:1984:ARI,
  author =       "Fred T. Krogh and Kris Stewart",
  title =        "Asymptotic ($h\rightarrow\infty$) Absolute Stability
                 for {BDFs} Applied to Stiff Differential Equations",
  journal =      j-TOMS,
  volume =       "10",
  number =       "1",
  pages =        "45--57",
  month =        mar,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356068.356072",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L20 (65-04)",
  MRnumber =     "86j:65103",
  bibdate =      "Sun Sep 04 20:02:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Gh. Adam",
}

@Article{Gaffney:1984:PES,
  author =       "Patrick W. Gaffney",
  title =        "A Performance Evaluation of Some {FORTRAN} Subroutines
                 for the Solution of Stiff Oscillatory Ordinary
                 Differential Equations",
  journal =      j-TOMS,
  volume =       "10",
  number =       "1",
  pages =        "58--72",
  month =        mar,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356068.356073",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05 (65-04)",
  MRnumber =     "86f:65117",
  bibdate =      "Sun Sep 04 20:02:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kaufman:1984:BES,
  author =       "Linda Kaufman",
  title =        "Banded Eigenvalue Solvers on Vector Machines",
  journal =      j-TOMS,
  volume =       "10",
  number =       "1",
  pages =        "73--85",
  month =        mar,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356068.356074",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65W05 (65F15)",
  MRnumber =     "86f:65223",
  bibdate =      "Fri Sep 30 01:11:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lenard:1984:RGT,
  author =       "Melanie L. Lenard and Michael Minkoff",
  title =        "Randomly Generated Test Problems for Positive Definite
                 Quadratic Programming",
  journal =      j-TOMS,
  volume =       "10",
  number =       "1",
  pages =        "86--96",
  month =        mar,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356068.356075",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65K10 (90C20)",
  MRnumber =     "86e:65088",
  bibdate =      "Sun Sep 04 20:02:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Jones:1984:SRM,
  author =       "Christopher B. Jones",
  title =        "A Significance Rule for Multiple-Precision
                 Arithmetic",
  journal =      j-TOMS,
  volume =       "10",
  number =       "1",
  pages =        "97--107",
  month =        mar,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356068.356076",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G05 (65G10)",
  MRnumber =     "86e:65063",
  bibdate =      "Sun Sep 04 20:02:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Multiple-precision arithmetic overcomes the round-off
                 error incurred in conventional floating-point
                 arithmetic, at the cost of increased processing
                 overhead. Significance arithmetic takes into account
                 the inexactness of the operands of a calculation, but
                 can lead to loss of significant digits after a long
                 series of operations. A new technique is described
                 which alleviates the overhead of multiple-precision
                 arithmetic by allowing nonsignificant digits to be
                 discarded, while limiting the significance loss per
                 operation to a controllable and acceptable rate. The
                 technique is based on storing an inexact number
                 interval, using a criterion of significance to
                 determine the precision with which the limits of
                 interval should be stored. A procedure referred to as a
                 significance rule uses this criterion to remove some of
                 the nonsignificant digits from the limits of an
                 interval prior to storage. A certain number of
                 nonsignificant digits are retained as guard digits.
                 Calculations are performed using exact interval
                 arithmetic and the significance-rule procedure is
                 invoked after each operation to remove superfluous
                 digits. Round-off in the procedure causes a slight
                 increase in the interval width on each operation. This
                 results in a cumulative loss of significance at a rate
                 related to the number of guard digits.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Haymond:1984:AMS,
  author =       "R. E. Haymond and J. P. Jarvis and D. R. Shier",
  title =        "{Algorithm 613}: Minimum Spanning Tree for Moderate
                 Integer Weights",
  journal =      j-TOMS,
  volume =       "10",
  number =       "1",
  pages =        "108--111",
  month =        mar,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/356068.356077",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Shapiro:1984:IRG,
  author =       "Henry D. Shapiro",
  title =        "Increasing Robustness in Global Adaptive Quadrature
                 Through Interval Selection Heuristics",
  journal =      j-TOMS,
  volume =       "10",
  number =       "2",
  pages =        "117--139",
  month =        jun,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/399.400",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D32 (65V05)",
  MRnumber =     "87a:65053",
  bibdate =      "Sun Sep 04 20:09:42 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sikorski:1984:OQS,
  author =       "K. Sikorski and F. Stenger",
  title =        "Optimal Quadratures in {$H_p$} Spaces",
  journal =      j-TOMS,
  volume =       "10",
  number =       "2",
  pages =        "140--151",
  month =        jun,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/399.448",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D32",
  MRnumber =     "87a:65054a",
  bibdate =      "Sun Sep 04 20:09:42 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "J. B. Butler, Jr.",
}

@Article{Sikorski:1984:AFS,
  author =       "K. Sikorski and F. Stenger and J. Schwing",
  title =        "{Algorithm 614}: {A FORTRAN} Subroutine for Numerical
                 Integration in {$H_p$}",
  journal =      j-TOMS,
  volume =       "10",
  number =       "2",
  pages =        "152--160",
  month =        jun,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/399.449",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D32 (65-04)",
  MRnumber =     "87a:65054b",
  bibdate =      "Sun Sep 4 20:11:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "J. B. Butler, Jr.",
}

@Article{Rall:1984:DPS,
  author =       "L. B. Rall",
  title =        "Differentiation in {Pascal-SC}: Type {GRADIENT}",
  journal =      j-TOMS,
  volume =       "10",
  number =       "2",
  pages =        "161--184",
  month =        jun,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/399.418",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D25 (65-04 65H05)",
  MRnumber =     "86j:65025",
  bibdate =      "Sun Sep 04 20:09:42 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Stephen W. Brady",
}

@Article{Lawrie:1984:CCC,
  author =       "D. H. Lawrie and A. H. Sameh",
  title =        "The Computation and Communication Complexity of a
                 Parallel Banded System Solver",
  journal =      j-TOMS,
  volume =       "10",
  number =       "2",
  pages =        "185--195",
  month =        jun,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/399.401",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65W05 (65F05 68Q25)",
  MRnumber =     "86k:65138",
  bibdate =      "Sat Nov 19 13:08:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Lawrie:1985:CCC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "D. Bini",
}

@Article{Reid:1984:SAB,
  author =       "J. K. Reid and A. Jennings",
  title =        "On Solving Almost Block Diagonal (Staircase) Linear
                 Systems",
  journal =      j-TOMS,
  volume =       "10",
  number =       "2",
  pages =        "196--201",
  month =        jun,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/399.450",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05 (65F50 65L10)",
  MRnumber =     "86g:65063",
  bibdate =      "Sun Sep 04 20:09:42 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Armstrong:1984:ABS,
  author =       "R. D. Armstrong and P. O. Beck and M. T. Kung",
  title =        "{Algorithm 615}: The Best Subset of Parameters in
                 Least Absolute Value Regression",
  journal =      j-TOMS,
  volume =       "10",
  number =       "2",
  pages =        "202--206",
  month =        jun,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/399.319410",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D10 (65K05)",
  MRnumber =     "791 987",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Petkov:1984:RDE,
  author =       "P. {Hr.} Petkov and N. D. Christov and M. M.
                 Konstantinov",
  title =        "Remark on ``{Algorithm} 590: {DSUBSP} and {EXCHQZ}:
                 {FORTRAN} Subroutines for Computing Deflating Subspaces
                 with Specified Spectrum''",
  journal =      j-TOMS,
  volume =       "10",
  number =       "2",
  pages =        "207--207",
  month =        jun,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/399.319411",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 24 15:51:05 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{VanDooren:1982:ADE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Krogh:1984:AAP,
  author =       "Fred T. Krogh",
  title =        "{ACM} Algorithms Policy",
  journal =      j-TOMS,
  volume =       "10",
  number =       "2",
  pages =        "208--211",
  month =        jun,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/399.319412",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:09:42 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Dongarra:1984:SMA,
  author =       "Jack J. Dongarra and Stanley C. Eisenstat",
  title =        "Squeezing the Most out of an Algorithm in {CRAY}
                 {FORTRAN}",
  journal =      j-TOMS,
  volume =       "10",
  number =       "3",
  pages =        "219--230",
  month =        sep,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1271.319413",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F99",
  MRnumber =     "791 988",
  bibdate =      "Fri Aug 26 23:38:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "cray; fortran; nla; vect",
}

@Article{Molchanov:1984:PCS,
  author =       "I. N. Molchanov and V. S. Zubatenko and L. D.
                 Nikolenko and M. F. Yakovlev",
  title =        "A Program Complex for Solving Systems of Linear
                 Algebraic Equations",
  journal =      j-TOMS,
  volume =       "10",
  number =       "3",
  pages =        "231--241",
  month =        sep,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1271.1273",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05 (65F10 65V05)",
  MRnumber =     "86f:65061",
  bibdate =      "Sun Sep 04 20:18:56 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rivara:1984:DDS,
  author =       "Mar{\'i}a-Cecilia Rivara",
  title =        "Design and Data Structure of Fully Adaptive Multigrid,
                 Finite-Element Software",
  journal =      j-TOMS,
  volume =       "10",
  number =       "3",
  pages =        "242--264",
  month =        sep,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1271.1274",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65N50 (65F50 65N30)",
  MRnumber =     "86f:65207",
  bibdate =      "Sat Aug 27 19:10:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Monahan:1984:AFC,
  author =       "John F. Monahan",
  title =        "{Algorithm 616}: Fast Computation of the
                 {Hodges-Lehman} Location Estimator",
  journal =      j-TOMS,
  volume =       "10",
  number =       "3",
  pages =        "265--270",
  month =        sep,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1271.319414",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65U05 (62-04 62G05)",
  MRnumber =     "791 991",
  bibdate =      "Sun Sep 4 20:21:15 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "This paper reduces the previous complexity bound for
                 the {Hodges-Lehman} location estimator from
                 ${O}(n^2\log{n})$ to ${O}(n\log{n})$.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kronmal:1984:ACA,
  author =       "Richard A. Kronmal and Arthur V. {Peterson, Jr.}",
  title =        "An Acceptance-Complement Analogue of the
                 Mixture-plus-Acceptance-Rejection Method for Generating
                 Random Variables",
  journal =      j-TOMS,
  volume =       "10",
  number =       "3",
  pages =        "271--281",
  month =        sep,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1271.1272",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65C10 (65U05)",
  MRnumber =     "86f:65027",
  bibdate =      "Wed Aug 24 22:43:47 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  country =      "USA",
  date =         "13/05/93",
  descriptors =  "RVG",
  enum =         "7548",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  language =     "English",
  location =     "SEL: Wi",
  references =   "0",
  revision =     "16/01/94",
}

@Article{Gill:1984:POP,
  author =       "Philip E. Gill and Walter Murray and Michael A.
                 Saunders and Margaret H. Wright",
  title =        "Procedures for Optimization Problems with a Mixture of
                 Bounds and General Linear Constraints",
  journal =      j-TOMS,
  volume =       "10",
  number =       "3",
  pages =        "282--298",
  month =        sep,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1271.1276",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65K10 (65F30 90C30)",
  MRnumber =     "86h:65091",
  bibdate =      "Sun Sep 04 20:18:56 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Aluffi-Pentini:1984:DEA,
  author =       "Filippo Aluffi-Pentini and Valerio Parisi and
                 Francesco Zirilli",
  title =        "A Differential-Equations Algorithm for Nonlinear
                 Equations",
  journal =      j-TOMS,
  volume =       "10",
  number =       "3",
  pages =        "299--316",
  month =        sep,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1271.1631",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H10 (65L05)",
  MRnumber =     "87a:65085",
  bibdate =      "Sun Sep 04 20:18:56 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Hj. Wacker",
}

@Article{Aluffi-Pentini:1984:ADD,
  author =       "Filippo Aluffi-Pentini and Valerio Parisi and
                 Francesco Zirilli",
  title =        "{Algorithm 617}: {DAFNE}: a Differential-Equations
                 Algorithm for Nonlinear Equations",
  journal =      j-TOMS,
  volume =       "10",
  number =       "3",
  pages =        "317--324",
  month =        sep,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1271.1632",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H10 (65-04 65L05)",
  MRnumber =     "87a:65086",
  bibdate =      "Sun Sep 04 20:18:56 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "Hj. Wacker",
}

@Article{Regener:1984:MID,
  author =       "Eric Regener",
  title =        "Multiprecision Integer Division Examples Using
                 Arbitrary Radix",
  journal =      j-TOMS,
  volume =       "10",
  number =       "3",
  pages =        "325--328",
  month =        sep,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1271.2738",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65V05",
  MRnumber =     "86g:65241",
  bibdate =      "Sun Sep 04 20:18:56 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{BrinchHansen:1994:MLD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Coleman:1984:SES,
  author =       "Thomas F. Coleman and Burton S. Garbow and Jorge J.
                 Mor{\'e}",
  title =        "Software for Estimating Sparse {Jacobian} Matrices",
  journal =      j-TOMS,
  volume =       "10",
  number =       "3",
  pages =        "329--345",
  month =        sep,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1271.1610",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F50 (65H10)",
  MRnumber =     "86f:65086a",
  bibdate =      "Mon Sep 05 09:48:14 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Coleman:1984:AFS,
  author =       "Thomas F. Coleman and Burton S. Garbow and Jorge J.
                 Mor{\'e}",
  title =        "{Algorithm 618}: {Fortran} Subroutines for Estimating
                 Sparse {Jacobian} Matrices",
  journal =      j-TOMS,
  volume =       "10",
  number =       "3",
  pages =        "346--347",
  month =        sep,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1271.319415",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F50 (65-04 65H10)",
  MRnumber =     "86f:65086b",
  bibdate =      "Sun Sep 04 20:28:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Piessens:1984:AAN,
  author =       "Robert Piessens and Rudi Huysmans",
  title =        "{Algorithm 619}: Automatic Numerical Inversion of the
                 {Laplace} Transform [{D5}]",
  journal =      j-TOMS,
  volume =       "10",
  number =       "3",
  pages =        "348--353",
  month =        sep,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1271.319416",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65R10",
  MRnumber =     "791 999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Piessens:1984:RNI,
  author =       "Robert Piessens",
  title =        "Remark on ``{Algorithm} 486: Numerical Inversion of
                 {Laplace} Transform''",
  journal =      j-TOMS,
  volume =       "10",
  number =       "3",
  pages =        "354--354",
  month =        sep,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1271.319417",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:18:56 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Veillon:1977:RNI,Koppelaar:1976:RNI}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rice:1984:ARK,
  author =       "John R. Rice and Richard J. Hanson",
  title =        "{Algorithm 620}: References and Keywords for {\em
                 {Collected Algorithms} of the {ACM}}",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "359--360",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.356100",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 11:00:44 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Hamilton:1985:RRK,Hopkins:1990:RRK}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Black:1984:NIS,
  author =       "Cheryl M. Black and Robert P. Burton and Thomas H.
                 Miller",
  title =        "The Need for an Industry Standard of Accuracy for
                 Elementary-Function Programs",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "361--366",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.356101",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "792 000",
  bibdate =      "Sun Sep 04 20:32:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Eiger:1984:BMS,
  author =       "A. Eiger and K. Sikorski and F. Stenger",
  title =        "A Bisection Method for Systems of Nonlinear
                 Equations",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "367--377",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.2705",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H10",
  MRnumber =     "86g:65102",
  bibdate =      "Sun Sep 04 20:32:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sommeijer:1984:ASL,
  author =       "B. P. Sommeijer and P. J. {van der Houwen}",
  title =        "{Algorithm 621}: Software with Low Storage
                 Requirements for Two-Dimensional, Nonlinear, Parabolic
                 Differential Equations",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "378--396",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.356103",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65M20",
  MRnumber =     "792 002",
  bibdate =      "Sat Oct 24 15:50:58 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bundy:1984:GIP,
  author =       "Alan Bundy",
  title =        "A Generalized Interval Package and Its Use for
                 Semantic Checking",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "397--409",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.2702",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G10",
  MRnumber =     "86g:65088",
  bibdate =      "Sun Sep 04 20:32:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rice:1984:ASM,
  author =       "John R. Rice and Calvin Ribbens and William A. Ward",
  title =        "{Algorithm 622}: a Simple Macroprocessor",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "410--416",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.356105",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:17:12 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Levin:1998:RAS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Renka:1984:IDS,
  author =       "Robert J. Renka",
  title =        "Interpolation of Data on the Surface of a Sphere",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "417--436",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.2703",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D05 (65-04)",
  MRnumber =     "86k:65013a",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  review =       "ACM CR 8511-1051",
  reviewer =     "G. P. Bhattacharjee",
  subject =      "G.1 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation",
}

@Article{Renka:1984:AIS,
  author =       "Robert J. Renka",
  title =        "{Algorithm 623}: Interpolation on the Surface of a
                 Sphere",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "437--439",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.356107",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D05 (65-04)",
  MRnumber =     "86k:65013b",
  bibdate =      "Fri Mar 28 11:02:10 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "G. P. Bhattacharjee",
}

@Article{Renka:1984:ATI,
  author =       "Robert J. Renka",
  title =        "{Algorithm 624}: Triangulation and Interpolation at
                 Arbitrarily Distributed Points in the Plane",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "440--442",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.356108",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D05 (65V05)",
  MRnumber =     "792 006",
  bibdate =      "Fri Mar 28 11:02:31 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rice:1984:NCG,
  author =       "John R. Rice",
  title =        "Numerical Computation with General Two-Dimensional
                 Domains",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "443--452",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.356109",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65N50",
  MRnumber =     "792 007",
  bibdate =      "Sun Sep 04 20:32:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rice:1984:ATD,
  author =       "John R. Rice",
  title =        "{Algorithm 625}: a Two-Dimensional Domain Processor",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "453--462",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.356110",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65N50",
  MRnumber =     "792 008",
  bibdate =      "Fri Mar 28 11:03:12 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Preusser:1984:CCS,
  author =       "Albrecht Preusser",
  title =        "Computing Contours by Successive Solution of Quintic
                 Polynomial Equations",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "463--472",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.2770",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D05",
  MRnumber =     "792 009",
  bibdate =      "Sun Sep 04 20:32:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Preusser:1984:ATE,
  author =       "Albrecht Preusser",
  title =        "{Algorithm 626}: {TRICP}\emdash a Contour Plot
                 Program for Triangular Meshes",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "473--475",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.2772",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D05 (65N50)",
  MRnumber =     "792 010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Garbow:1984:RQA,
  author =       "B. S. Garbow",
  title =        "Remark on ``{Algorithm} 535: The {QZ} Algorithm to
                 Solve the Generalized Eigenvalue Problem for Complex
                 Matrices [{F2}]''",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "476--476",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.356113",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:32:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Garbow:1978:AQA,Garbow:1982:RQA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Celis:1984:RCE,
  author =       "Pedro Celis",
  title =        "Remark: Corrections and Errors in {John Ivie}'s Some
                 {MACSYMA} Programs for Solving Recurrence Relations",
  journal =      j-TOMS,
  volume =       "10",
  number =       "4",
  pages =        "477--478",
  month =        dec,
  year =         "1984",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2701.356114",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:32:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Ivie:1978:SMP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Tomlin:1985:IPS,
  author =       "J. A. Tomlin and J. S. Welch",
  title =        "Integration of a Primal Simplex Network Algorithm with
                 a Large-Scale Mathematical Programming System",
  journal =      j-TOMS,
  volume =       "11",
  number =       "1",
  pages =        "1--11",
  month =        mar,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3147.3163",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65K05 (90C05)",
  MRnumber =     "86h:65087",
  bibdate =      "Sun Sep 04 20:43:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-1/p1-tomlin/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Linear programming.",
}

@Article{Davidon:1985:ESD,
  author =       "William C. Davidon and Jorge Nocedal",
  title =        "Evaluation of Step Directions in Optimization
                 Algorithms",
  journal =      j-TOMS,
  volume =       "11",
  number =       "1",
  pages =        "12--19",
  month =        mar,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3147.3164",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65K10 (90C30)",
  MRnumber =     "86h:65089",
  bibdate =      "Sun Sep 04 20:43:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-1/p12-davidon/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Gradient methods.",
}

@Article{Cuyt:1985:CIM,
  author =       "Annie A. M. Cuyt and L. B. Rall",
  title =        "Computational Implementation of the Multivariate
                 {Halley} Method for Solving Nonlinear Systems of
                 Equations",
  journal =      j-TOMS,
  volume =       "11",
  number =       "1",
  pages =        "20--36",
  month =        mar,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3147.3162",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H05 (65-04)",
  MRnumber =     "86g:65092",
  bibdate =      "Sun Sep 04 20:43:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-1/p20-cuyt/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; languages",
  subject =      "{\bf G.1.5}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Iterative
                 methods. {\bf G.1.5}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Roots of Nonlinear Equations,
                 Systems of equations. {\bf G.1.m}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Miscellaneous. {\bf
                 I.1.m}: Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Miscellaneous.",
}

@Article{Vitter:1985:RSR,
  author =       "Jeffrey Scott Vitter",
  title =        "Random Sampling with a Reservoir",
  journal =      j-TOMS,
  volume =       "11",
  number =       "1",
  pages =        "37--57",
  month =        mar,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3147.3165",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65C10 (62-04)",
  MRnumber =     "87b:65007",
  bibdate =      "Sun Sep 04 20:43:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-1/p37-vitter/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; performance; theory;
                 verification",
  reviewer =     "Brian Conolly",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Probabilistic algorithms (including Monte
                 Carlo). {\bf G.3}: Mathematics of Computing,
                 PROBABILITY AND STATISTICS, Random number generation.
                 {\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Statistical software. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis. {\bf D.4.3}: Software, OPERATING
                 SYSTEMS, File Systems Management, Access methods.",
}

@Article{Bownds:1985:AFS,
  author =       "John M. Bownds and Lee Appelbaum",
  title =        "{Algorithm 627}: a {FORTRAN} Subroutine for Solving
                 {Volterra} Integral Equations",
  journal =      j-TOMS,
  volume =       "11",
  number =       "1",
  pages =        "58--65",
  month =        mar,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3147.214314",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65R20",
  MRnumber =     "793 057",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-1/p58-bownds/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "documentation; economics; performance",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Chebyshev approximation and
                 theory. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Portability.",
}

@Article{Winkler:1985:AAC,
  author =       "F. Winkler and B. Buchberger and F. Lichtenberger and
                 H. Rolletschek",
  title =        "{Algorithm 628}: An Algorithm for Constructing
                 Canonical Bases of Polynomial Ideals",
  journal =      j-TOMS,
  volume =       "11",
  number =       "1",
  pages =        "66--78",
  month =        mar,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3147.214316",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68Q40 (13-04)",
  MRnumber =     "793 058",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-1/p66-winkler/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE. {\bf I.1.1}: Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Expressions and Their
                 Representation. {\bf I.1.2}: Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf J.2}: Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING.",
}

@Article{Atkinson:1985:AIE,
  author =       "Kendall E. Atkinson",
  title =        "{Algorithm 629}: An Integral Equation Program for
                 {Laplace}'s Equation in Three Dimensions",
  journal =      j-TOMS,
  volume =       "11",
  number =       "2",
  pages =        "85--96",
  month =        jun,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214392.214393",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65N30 (65R20)",
  MRnumber =     "86m:65137",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p85-atkinson/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  reviewer =     "H. Kersten",
  subject =      "{\bf G.1.9}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Integral Equations. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Dembo:1985:TPG,
  author =       "R. S. Dembo and T. Steihaug",
  title =        "A Test Problem Generator for Large-Scale Unconstrained
                 Optimization",
  journal =      j-TOMS,
  volume =       "11",
  number =       "2",
  pages =        "97--102",
  month =        jun,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214392.214394",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65K10 (90C30)",
  MRnumber =     "86h:65090",
  bibdate =      "Sun Sep 04 20:43:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p97-dembo/",
  abstract =     "A test problem generator for large-scale unconstrained
                 optimization is described. It permits the generation of
                 a poorly or well-conditioned problems of arbitrary
                 size, derived from nonlinear network flow models. An
                 eigenvalue analysis provides bounds on the condition
                 number of the Hessian of the objective function and an
                 example of an efficient preconditioner, using these
                 bounds, is outlined.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; experimentation; measurement",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Nonlinear programming. {\bf
                 G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Numerical algorithms. {\bf G.4}: Mathematics
                 of Computing, MATHEMATICAL SOFTWARE, Certification and
                 testing. {\bf D.2.5}: Software, SOFTWARE ENGINEERING,
                 Testing and Debugging, Test data generators.",
}

@Article{Buckley:1985:ABE,
  author =       "A. Buckley and A. LeNir",
  title =        "{Algorithm 630}: {BBVSCG}\emdash a Variable Storage
                 Algorithm for Function Minimization",
  journal =      j-TOMS,
  volume =       "11",
  number =       "2",
  pages =        "103--119",
  month =        jun,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214392.214395;
                 http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p103-buckley/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Buckley:1989:RA}.",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS. {\bf G.1.6}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Optimization. {\bf G.1.6}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Gradient methods.",
}

@Article{Norton:1985:AFB,
  author =       "Victor Norton",
  title =        "{Algorithm 631}: Finding a Bracketed Zero by
                 {Larkin}'s Method of Rational Interpolation",
  journal =      j-TOMS,
  volume =       "11",
  number =       "2",
  pages =        "120--134",
  month =        jun,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214392.214396",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H05 (65D05)",
  MRnumber =     "797 616",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Norton:1986:RFB}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p120-norton/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.5}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Iterative
                 methods. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.1.1}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation.",
}

@Article{Martello:1985:APM,
  author =       "Silvano Martello and Paolo Toth",
  title =        "{Algorithm 632}: a Program for the $0-1$ Multiple
                 Knapsack Problem",
  journal =      j-TOMS,
  volume =       "11",
  number =       "2",
  pages =        "135--140",
  month =        jun,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214392.214397",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:12:05 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p135-martello/",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.2.1}: Mathematics of Computing, DISCRETE
                 MATHEMATICS, Combinatorics, Combinatorial algorithms.
                 {\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization.",
}

@Article{Liu:1985:MMD,
  author =       "Joseph W. H. Liu",
  title =        "Modification of the Minimum-Degree Algorithm by
                 Multiple Elimination",
  journal =      j-TOMS,
  volume =       "11",
  number =       "2",
  pages =        "141--153",
  month =        jun,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214392.214398",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F50 (65F05)",
  MRnumber =     "86m:65040",
  bibdate =      "Sun Sep 04 20:43:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p141-liu/",
  abstract =     "The most widely used ordering scheme to reduce fills
                 and operations in sparse matrix computation is the
                 minimum-degree algorithm. The notion of {\em multiple
                 elimination} is introduced here as a modification to
                 the conventional scheme. The motivation is discussed
                 using the $k$-by-$k$ grid model problem. Experimental
                 results indicate that the modified version retains the
                 fill-reducing property of (and is often better than)
                 the original ordering algorithm and yet requires less
                 computer time. The reduction in ordering time is
                 problem dependent, and for some problems the modified
                 algorithm can run a few times faster than existing
                 implementations of the minimum-degree algorithm. The
                 use of {\em external degree} in the algorithm is also
                 introduced.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  reviewer =     "David R. Kincaid",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Sparse and very
                 large systems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis.",
}

@Article{Gan:1985:NCG,
  author =       "C. T. Gan",
  title =        "A Note on Combination Generators",
  journal =      j-TOMS,
  volume =       "11",
  number =       "2",
  pages =        "154--156",
  month =        jun,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214392.214401",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:43:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p154-gan/",
  abstract =     "A recent study by Akl indicates that Mifsud's
                 algorithm, which involves unnecessary searching
                 operations, is the fastest existing combination
                 generator. A modified Page and Wilson's algorithm,
                 which is essentially similar to Mifsud's algorithm, is
                 presented. A theoretical analysis of the modified
                 algorithm is also given.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.2.1}: Mathematics of Computing, DISCRETE
                 MATHEMATICS, Combinatorics, Combinatorial algorithms.
                 {\bf F.2.2}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Computations on discrete
                 structures.",
}

@Article{Ahrens:1985:SRS,
  author =       "J. H. Ahrens and U. Dieter",
  title =        "Sequential Random Sampling",
  journal =      j-TOMS,
  volume =       "11",
  number =       "2",
  pages =        "157--169",
  month =        jun,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214392.214402",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:43:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p157-ahrens/",
  abstract =     "Fast algorithms for selecting a random set of exactly
                 $k$ records from a file of $n$ records are constructed.
                 Selection is sequential: the sample records are chosen
                 in the same order in which they occur in the file. All
                 procedures run in $O(k)$ time. The ``geometric'' method
                 has two versions: with or without $O(k)$ auxiliary
                 space. A further procedure uses hashing techniques and
                 requires $O(k)$ space.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Random number generation. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@Article{Ward:1985:AAL,
  author =       "R. C. Ward and G. J. Davis and V. E. Kane",
  title =        "{Algorithm 633}: An Algorithm for Linear Dependency
                 Analysis of Multivariate Data",
  journal =      j-TOMS,
  volume =       "11",
  number =       "2",
  pages =        "170--182",
  month =        jun,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214392.214403",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65U05 (62-04)",
  MRnumber =     "86j:65187",
  bibdate =      "Fri Sep 30 01:12:58 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p170-ward/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "measurement; performance",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra. {\bf G.3}:
                 Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing.",
}

@Article{Novotny:1985:RNS,
  author =       "Milan Novotny",
  title =        "Remark on ``{Algorithm} 30: Numerical Solution of the
                 Polynomial Equation''",
  journal =      j-TOMS,
  volume =       "11",
  number =       "2",
  pages =        "183--184",
  month =        jun,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214392.214404",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:43:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Ellenberger:1960:NSP}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p183-novotny/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE.",
}

@Article{Hill:1985:RCS,
  author =       "I. D. Hill and M. C. Pike",
  title =        "Remark on ``{Algorithm} 299: Chi-Squared Integral''",
  journal =      j-TOMS,
  volume =       "11",
  number =       "2",
  pages =        "185--185",
  month =        jun,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214392.214405;
                 http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p185-hill/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 29 15:20:54 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Hill:1967:CSI,elLozy:1976:RAC,elLozy:1979:RAS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE.",
}

@Article{Preusser:1985:RBI,
  author =       "Albrect Preusser",
  title =        "Remark on ``{Algorithm} 526: Bivariate Interpolation
                 and Smooth Surface Fitting for Irregularly Distributed
                 Data Points [{E1}]''",
  journal =      j-TOMS,
  volume =       "11",
  number =       "2",
  pages =        "186--187",
  month =        jun,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214392.214407",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:43:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Akima:1978:ABI,Akima:1979:RBI}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-2/p186-preusser/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE.",
}

@Article{Lawrie:1985:CCC,
  author =       "D. H. Lawrie and A. H. Sameh",
  title =        "Corrections to ``{The} Computation and Communication
                 Complexity of a Parallel Banded System Solver''",
  journal =      j-TOMS,
  volume =       "11",
  number =       "2",
  pages =        "188--188",
  month =        jun,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214392.356133",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:43:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Lawrie:1984:CCC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Krogh:1985:AAP,
  author =       "Fred T. Krogh",
  title =        "{ACM} Algorithms Policy",
  journal =      j-TOMS,
  volume =       "11",
  number =       "2",
  pages =        "193--196",
  month =        jun,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214392.356134",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:43:27 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bartels:1985:LSF,
  author =       "Richard H. Bartels and John J. Jezioranski",
  title =        "Least-Squares Fitting Using Orthogonal Multinomials",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "201--217",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214408.214410",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D10",
  MRnumber =     "87f:65016",
  bibdate =      "Sun Sep 04 20:57:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p201-bartels/",
  abstract =     "Forsythe has given a method for generating basis
                 polynomials in a single variable that are orthogonal
                 with respect to a given inner product. Weisfeld later
                 demonstrated that Forsythe's approach could be extended
                 to polynomials in an arbitrary number of variables. In
                 this paper we sharpen Weisfeld's results and present a
                 method for computing weighted, multinomial,
                 least-squares approximations to given data.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  reviewer =     "Wolfgang Boehm",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Least squares methods. {\bf
                 F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
}

@Article{Bartels:1985:ACE,
  author =       "Richard H. Bartels and John J. Jezioranski",
  title =        "{Algorithm 634}: {CONSTR} and {EVAL}: Routines for
                 Fitting Multinomials in a Least-Squares Sense",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "218--228",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214408.214412",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D10",
  MRnumber =     "87f:65017",
  bibdate =      "Sun Sep 4 20:58:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p218-bartels/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  reviewer =     "Wolfgang Boehm",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Least squares methods. {\bf
                 F.1.2}: Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Modes of Computation.",
}

@Article{Hull:1985:PRV,
  author =       "T. E. Hull and A. Abrham",
  title =        "Properly Rounded Variable Precision Square Root",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "229--237",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214408.214413",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15 (65G05)",
  MRnumber =     "87a:65041",
  bibdate =      "Fri Nov 8 18:01:57 MST 2002",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p229-hull/;
                 http://www.acm.org/pubs/toc/Abstracts/toms/214413.html",
  abstract =     "The square root function presented here returns a
                 properly rounded approximation to the square root of
                 its argument, or it raises an error condition if the
                 argument is negative. {\em Properly rounded} means
                 rounded to the nearest, or to nearest even in case of a
                 tie. It is {\em variable precision} in that it is
                 designed to return a $p$-digit approximation to a
                 $p$-digit argument, for any $ p > 0 $. (Precision $p$
                 means $p$ decimal digits.) The program and the analysis
                 are valid for all $ p > 0 $, but current
                 implementations place some restrictions on $p$.",
  acknowledgement = ack-nhfb,
  catcode =      "G.4; G.4; G.1.0; G.1.2; G.4; G.1.0",
  CRclass =      "G.4 Algorithm analysis; G.4 Verification; G.1.0
                 General; G.1.0 Numerical algorithms; G.1.2
                 Approximation; G.1.2 Elementary function approximation;
                 G.4 Certification and testing; G.1.0 General; G.1.0
                 Error analysis",
  descriptor =   "Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis; Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Verification; Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation; Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing; Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Error
                 analysis",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  genterm =      "algorithms; verification",
  guideno =      "02789",
  journal-URL =  "https://dl.acm.org/loi/toms",
  jrldate =      "Sept. 1985",
  keywords =     "algorithms; decimal floating-point arithmetic;
                 verification",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Verification. {\bf
                 G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Error analysis. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms.",
}

@Article{Stewart:1985:NCD,
  author =       "G. W. Stewart",
  title =        "A Note on Complex Division",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "238--241",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214408.214414",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:38:15 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See corrigendum \cite{Stewart:1986:CNC} and the faster
                 and more robust algorithm in \cite{Priest:2004:ESC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p238-stewart/",
  abstract =     "An algorithm for computing the quotient of two complex
                 numbers is modified to make it more robust in the
                 presence of underflows.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; complex arithmetic; computer arithmetic;
                 na",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness.",
}

@Article{Streit:1985:AAS,
  author =       "Roy L. Streit",
  title =        "{Algorithm 635}: An Algorithm for the Solution of
                 Systems of Complex Linear Equations in the ${L}_\infty$
                 Norm with Constraints on the Unknowns",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "242--249",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214408.214415",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:59:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p242-streit/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Minimax approximation and
                 algorithms. {\bf G.1.3}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear
                 systems (direct and iterative methods). {\bf G.1.6}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming.",
}

@Article{Le:1985:EDF,
  author =       "D. Le",
  title =        "An Efficient Derivative-Free Method for Solving
                 Nonlinear Equations",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "250--262",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214408.214416",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H05",
  MRnumber =     "87d:65057",
  bibdate =      "Sat Nov 19 13:08:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Le:1989:CED}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p250-le/",
  abstract =     "An algorithm is presented for finding a root of a real
                 function. The algorithm combines bisection with second
                 and third order methods using derivatives estimated
                 from objective function values. Global convergence is
                 ensured and the number of function evaluations is
                 bounded by four times the number needed by bisection.
                 Numerical comparisons with existing algorithms indicate
                 the superiority of the new algorithm in all classes of
                 problems.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  reviewer =     "T. Feagin",
  subject =      "{\bf G.1.5}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Convergence.",
}

@Article{Tischer:1985:ESN,
  author =       "P. E. Tischer and G. K. Gupta",
  title =        "An Evaluation of Some New Cyclic Linear Multistep
                 Formulas for Stiff {ODEs}",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "263--270",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214408.214417",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05 (65-04)",
  MRnumber =     "87d:65078",
  bibdate =      "Sun Sep 04 20:57:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p263-tischer/",
  abstract =     "We evaluate several sets of cyclic linear multistep
                 formulas (CLMFs). One of these sets was derived by
                 Tischer and Sacks-Davis. Three new sets of formulas
                 have been derived and we present their
                 characteristics.\par

                 The formulas have been evaluated by comparing the
                 performance of four versions of a code which implements
                 CLMFs. The four versions are very similar and each
                 version implements one of the sets of CLMFs being
                 studied. We compare the performance of these codes with
                 that of a widely used code, LSODE. One of the new sets
                 of CLMFs is not only much more efficient in solving
                 stiff problems that have a Jacobian with eigenvalues
                 close to the imaginary axis but is almost as efficient
                 as LSODE in solving other problems. This is a
                 significant improvement over the only other CLMF code
                 available, STINT from Tendler, Bickart, and Picel.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  reviewer =     "W. H. Enright",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations.",
}

@Article{Johnsson:1985:SNB,
  author =       "S. Lennart Johnsson",
  title =        "Solving Narrow Banded Systems on Ensemble
                 Architectures",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "271--288",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214408.214418",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65W05 (65F05)",
  MRnumber =     "86m:65170",
  bibdate =      "Sun Sep 04 21:01:13 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p271-johnsson/",
  abstract =     "We present concurrent algorithms for the solution of
                 narrow banded systems on ensemble architectures, and
                 analyze the communication and arithmetic complexities
                 of the algorithms. The algorithms consist of three
                 phases. In phase 1, a block tridiagonal system of
                 reduced size is produced through largely local
                 operations. Diagonal dominance is preserved. If the
                 original system is positive, definite, and symmetric,
                 so is the reduced system. It is solved in a second
                 phase, and the remaining variables obtained through
                 local back substitution in a third phase. With a
                 sufficient number of processing elements, there is no
                 first and third phase. We investigate the arithmetic
                 and communication complexity of Gaussian elimination
                 and block cyclic reduction for the solution of the
                 reduced system on boolean cubes, perfect shuffle and
                 shuffle-exchange networks, binary trees, and linear
                 arrays.\par

                 With an optimum number of processors, the minimum
                 solution time on a linear array is of an order that
                 ranges from $O(m^{2}Nm)$ to $O(m^{3} +
                 m^{3}\log_{2}(N/m))$ depending on the bandwidth, the
                 dimension of the problem, and the times for
                 communication and arithmetic. For boolean cubes,
                 cube-connected cycles, prefect shuffle and
                 shuffle-exchange networks, and binary trees, the
                 minimum time is $O(m^{3}+m^{3}\log_2(N/m))$ including
                 the communication complexity",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; band matrix; linear system; nla;
                 performance; prll",
  subject =      "{\bf C.1.2}: Computer Systems Organization, PROCESSOR
                 ARCHITECTURES, Multiple Data Stream Architectures
                 (Multiprocessors), Multiple-instruction-stream,
                 multiple-data-stream processors (MIMD). {\bf F.2.1}:
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices. {\bf G.1.3}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative methods).
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Algorithm analysis. {\bf I.1.2}: Computing
                 Methodologies, ALGEBRAIC MANIPULATION, Algorithms,
                 Analysis of algorithms.",
}

@Article{Hall:1985:ESR,
  author =       "George Hall",
  title =        "Equilibrium States of {Runge Kutta} Schemes",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "289--301",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214408.214424",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05",
  MRnumber =     "87c:65082",
  bibdate =      "Sun Sep 04 20:57:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p289-hall/",
  abstract =     "Understanding the behavior of Runge--Kutta codes when
                 stability considerations restrict the stepsize provides
                 useful information for stiffness detection and other
                 implementation details. Analysis of equilibrium states
                 on test problems is presented which provides
                 predictions and insights into this behavior. The
                 implications for global error are also discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  reviewer =     "Henning Esser",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems. {\bf G.1.7}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Single step methods. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.",
}

@Article{Ericksen:1985:IPT,
  author =       "Wilhelm S. Ericksen",
  title =        "Inverse Pairs of Test Matrices",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "302--304",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214408.214425",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "15A09 (65F35)",
  MRnumber =     "87f:15002",
  bibdate =      "Sun Sep 04 20:57:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p302-ericksen/",
  abstract =     "Algorithms that are readily programmable are provided
                 for constructing inverse pairs of matrices with
                 elements in a field, a division ring, or a ring.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  reviewer =     "R. Kala",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Condition (and ill-condition). {\bf
                 G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Numerical algorithms. {\bf G.1.3}: Mathematics
                 of Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Conditioning. {\bf G.1.3}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Matrix inversion.",
}

@Article{Hamilton:1985:RRK,
  author =       "Dennis E. Hamilton",
  title =        "Remark on ``{Algorithm} 620: References and Keywords
                 for {\em {Collected Algorithms} of the {ACM}}''",
  journal =      j-TOMS,
  volume =       "11",
  number =       "3",
  pages =        "305--307",
  month =        sep,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/214408.214426",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:57:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Rice:1984:ARK,Hopkins:1990:RRK}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-3/p305-hamilton/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE.",
}

@Article{Boisvert:1985:GFM,
  author =       "Ronald F. Boisvert and Sally E. Howe and David K.
                 Kahaner",
  title =        "{GAMS}: a Framework for the Management of Scientific
                 Software",
  journal =      j-TOMS,
  volume =       "11",
  number =       "4",
  pages =        "313--355",
  month =        dec,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6187.6188",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:06:30 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-4/p313-boisvert/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "documentation; human factors; management",
  review =       "ACM CR 8702-0100",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, GAMS. {\bf G.3}: Mathematics of Computing,
                 PROBABILITY AND STATISTICS, Statistical software. {\bf
                 H.3.5}: Information Systems, INFORMATION STORAGE AND
                 RETRIEVAL, Online Information Services. {\bf D.2.7}:
                 Software, SOFTWARE ENGINEERING, Distribution and
                 Maintenance, Documentation.",
}

@Article{Davenport:1985:PRA,
  author =       "J. H. Davenport and B. M. Trager",
  title =        "On the Parallel {Risch} Algorithm ({II})",
  journal =      j-TOMS,
  volume =       "11",
  number =       "4",
  pages =        "356--362",
  month =        dec,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6187.6189",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "12H05 (68Q40)",
  MRnumber =     "87d:12010",
  bibdate =      "Sun Sep 04 21:06:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-4/p356-davenport/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory; verification",
  reviewer =     "Michael F. Singer",
  subject =      "{\bf I.1.2}: Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms.",
}

@Article{Coleman:1985:SES,
  author =       "Thomas F. Coleman and Burton S. Garbow and Jorge J.
                 Mor{\'e}",
  title =        "Software for Estimating Sparse {Hessian} Matrices",
  journal =      j-TOMS,
  volume =       "11",
  number =       "4",
  pages =        "363--377",
  month =        dec,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6187.6190",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F50 (65K10)",
  MRnumber =     "828 562",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-4/p363-coleman/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  review =       "ACM CR 8710-0876",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Sparse and very
                 large systems. {\bf G.1.6}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Optimization, Nonlinear
                 programming. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE.",
}

@Article{Coleman:1985:AFS,
  author =       "Thomas F. Coleman and Burton S. Garbow and Jorge J.
                 Mor{\'e}",
  title =        "{Algorithm 636}: {FORTRAN} subroutines for estimating
                 sparse {Hessian} matrices",
  journal =      j-TOMS,
  volume =       "11",
  number =       "4",
  pages =        "378--378",
  month =        dec,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6187.6193",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "378. 65F50 (65-04)",
  MRnumber =     "828 563",
  bibdate =      "Sat Aug 27 14:55:36 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "The title of this paper incorrectly said Algorithm
                 649; it should be {Algorithm 636}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-4/p378-coleman/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf E.1}: Data, DATA STRUCTURES, Graphs. {\bf E.2}:
                 Data, DATA STORAGE REPRESENTATIONS, Linked
                 representations. {\bf G.1.3}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf
                 G.m}: Mathematics of Computing, MISCELLANEOUS. {\bf
                 D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN.",
}

@Article{Houstis:1985:CSS,
  author =       "E. N. Houstis and W. F. Mitchell and J. R. Rice",
  title =        "Collocation Software for Second-Order Elliptic Partial
                 Differential Equations",
  journal =      j-TOMS,
  volume =       "11",
  number =       "4",
  pages =        "379--412",
  month =        dec,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6187.6191",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65N35 (65-04)",
  MRnumber =     "87e:65081a",
  bibdate =      "Sun Sep 04 21:07:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-4/p379-houstis/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; measurement; performance",
  review =       "ACM CR 8702-0097",
  reviewer =     "John Stephenson",
  subject =      "{\bf G.1.8}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations, Elliptic
                 equations. {\bf G.1.8}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Partial Differential Equations,
                 Finite element methods.",
}

@Article{Houstis:1985:AGC,
  author =       "E. N. Houstis and W. F. Mitchell and J. R. Rice",
  title =        "{Algorithm 637}: {GENCOL}: Collocation of General
                 Domains with Bicubic {Hermite} Polynomials",
  journal =      j-TOMS,
  volume =       "11",
  number =       "4",
  pages =        "413--415",
  month =        dec,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6187.6194",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65N35 (65-04)",
  MRnumber =     "87e:65081b",
  bibdate =      "Sat Aug 27 14:56:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-4/p413-houstis/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "John Stephenson",
  subject =      "G.1.8 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Partial Differential Equations, Elliptic equations \\
                 G.1.8 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Partial Differential Equations, Finite element methods
                 \\ G.m Mathematics of Computing, MISCELLANEOUS \\ D.3.2
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN",
}

@Article{Houstis:1985:AIH,
  author =       "E. N. Houstis and W. F. Mitchell and J. R. Rice",
  title =        "{Algorithm 638}: {INTCOL} and {HERMCOL}: Collocation
                 on Rectangular Domains with Bicubic {Hermite}
                 Polynomials",
  journal =      j-TOMS,
  volume =       "11",
  number =       "4",
  pages =        "416--418",
  month =        dec,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6187.6195",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65N35 (65-04)",
  MRnumber =     "87e:65081c",
  bibdate =      "Sun Sep 04 21:08:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-4/p416-houstis/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  reviewer =     "John Stephenson",
  subject =      "{\bf G.1.8}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations, Elliptic
                 equations. {\bf G.1.8}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Partial Differential Equations,
                 Finite element methods. {\bf G.m}: Mathematics of
                 Computing, MISCELLANEOUS. {\bf D.3.2}: Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 FORTRAN.",
}

@Article{Schnabel:1985:MSA,
  author =       "Robert B. Schnabel and John E. Koontz and Barry E.
                 Weiss",
  title =        "A Modular System of Algorithms for Unconstrained
                 Minimization",
  journal =      j-TOMS,
  volume =       "11",
  number =       "4",
  pages =        "419--440",
  month =        dec,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6187.6192",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65K10 (65-04 90-04 90C30)",
  MRnumber =     "828 567",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1985-11-4/p419-schnabel/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  review =       "ACM CR 8702-0093",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Unconstrained optimization.
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, UNCMIN.",
}

@Article{Er:1985:RG,
  author =       "M. C. Er",
  title =        "Remark on ``{Algorithm} 246: {Graycode} [{Z}]''",
  journal =      j-TOMS,
  volume =       "11",
  number =       "4",
  pages =        "441--443",
  month =        dec,
  year =         "1985",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6187.356154",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 20:42:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Boothroyd:1964:G,Misra:1975:RG}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Shampine:1986:FVV,
  author =       "L. F. Shampine and L. S. Baca",
  title =        "Fixed versus Variable Order {Runge--Kutta}",
  journal =      j-TOMS,
  volume =       "12",
  number =       "1",
  pages =        "1--23",
  month =        mar,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/5960.5964",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:09:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p1-shampine/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance",
  review =       "ACM CR 8702-0096",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems. {\bf G.1.7}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Single step methods. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@Article{Lyness:1986:AIS,
  author =       "James Lyness and Gwendolen Hines",
  title =        "{Algorithm 639}: To Integrate Some Infinite
                 Oscillating Tails",
  journal =      j-TOMS,
  volume =       "12",
  number =       "1",
  pages =        "24--25",
  month =        mar,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/5960.214318",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30 (65D32)",
  MRnumber =     "868 093",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p24-lyness/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.",
}

@Article{Laub:1986:AEC,
  author =       "Alan J. Laub",
  title =        "{Algorithm 640}: Efficient Calculation of Frequency
                 Response Matrices from State Space Models",
  journal =      j-TOMS,
  volume =       "12",
  number =       "1",
  pages =        "26--33",
  month =        mar,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/5960.214319",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p26-laub/",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications. {\bf G.1.3}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear
                 systems (direct and iterative methods). {\bf G.1.3}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Matrix inversion. {\bf J.2}: Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Engineering.",
}

@Article{Deak:1986:EMG,
  author =       "I. Deak",
  title =        "The Economical Method for Generating Random Samples
                 from Discrete Distributions",
  journal =      j-TOMS,
  volume =       "12",
  number =       "1",
  pages =        "34--36",
  month =        mar,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/5960.214321",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:11:10 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p34-deak/",
  abstract =     "The idea of the economical method is applied for
                 generating samples from any discrete distribution. In
                 the resulting procedure, the expected number of
                 uniformly distributed random numbers is less than in
                 the alias method (practically 1). A refinement gives a
                 version where in limit just one uniformly distributed
                 number is required at the expense of some storage
                 space.",
  acknowledgement = ack-nhfb,
  country =      "USA",
  date =         "13/05/93",
  descriptors =  "RVG",
  enum =         "7183",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  language =     "English",
  location =     "SEL: Wi",
  references =   "0",
  revision =     "16/01/94",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS. {\bf I.6.1}: Computing Methodologies,
                 SIMULATION AND MODELING, Simulation Theory.",
}

@Article{Law:1986:NAM,
  author =       "Kincho H. Law and Steven J. Fenives",
  title =        "A Node-Addition Model for Symbolic Factorization",
  journal =      j-TOMS,
  volume =       "12",
  number =       "1",
  pages =        "37--50",
  month =        mar,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/5960.5963",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F30",
  MRnumber =     "87m:65068",
  bibdate =      "Sun Sep 04 21:11:23 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p37-law/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance; theory;
                 verification",
  review =       "ACM CR 8704-0290",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf G.2.2}:
                 Mathematics of Computing, DISCRETE MATHEMATICS, Graph
                 Theory, Graph algorithms. {\bf E.1}: Data, DATA
                 STRUCTURES.",
}

@Article{Springer:1986:ESG,
  author =       "J{\"o}rn Springer",
  title =        "Exact Solution of General Integer Systems of Linear
                 Equations",
  journal =      j-TOMS,
  volume =       "12",
  number =       "1",
  pages =        "51--61",
  month =        mar,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/5960.5961",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F20",
  MRnumber =     "868 095",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p51-springer/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  review =       "ACM CR 8703-0190",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Least squares approximation. {\bf
                 F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations in finite fields.",
}

@Article{Jansen:1986:HAA,
  author =       "Paul Jansen and Peter Weidner",
  title =        "High-Accuracy Arithmetic Software --- Some Tests of
                 the {ACRITH} Problem-Solving Routines",
  journal =      j-TOMS,
  volume =       "12",
  number =       "1",
  pages =        "62--70",
  month =        mar,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/5960.5962",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65Dxx",
  MRnumber =     "868 096",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-1/p62-jansen/",
  abstract =     "The program package ACRITH (High-Accuracy Arithmetic
                 Subroutine Library) provides FORTRAN subroutines for
                 the solution of several standard mathematical problems.
                 The routines use floating point operations with
                 extended precision and interval arithmetic and are
                 designated especially for the solution of
                 ill-conditioned problems. Test results for most of the
                 routines are presented with emphasis on the practical
                 usability of the package. It turns out that not all
                 routines are of equal high quality and reliability; in
                 the documentation, hints to the implemented numerical
                 algorithms are completely missing, and the error
                 messages are not always concise. Some possible
                 alternatives like symbolic algebra systems or multiple
                 precision packages are mentioned.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  review =       "ACM CR 8612-1110",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, ACRITH. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms. {\bf I.1.3}: Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Languages and Systems, REDUCE.
                 {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Reliability and
                 robustness.",
}

@Article{Hanson:1986:RCA,
  author =       "Richard J. Hanson",
  title =        "Remark on ``{Algorithm} 584: {CUBTRI}: Automatic
                 Cubature over a Triangle''",
  journal =      j-TOMS,
  volume =       "12",
  number =       "1",
  pages =        "71--71",
  month =        mar,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/5960.356162",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 20:57:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Laurie:1982:ACA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Norton:1986:RFB,
  author =       "Victor Norton",
  title =        "Remark on ``{Algorithm} 631: Finding a Bracketed Zero
                 by {Larkin}'s Method of Rational Interpolation''",
  journal =      j-TOMS,
  volume =       "12",
  number =       "1",
  pages =        "72--72",
  month =        mar,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/5960.356163",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "72. 65H05 (65D05)",
  MRnumber =     "868 097",
  bibdate =      "Mon Sep 05 20:41:38 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Norton:1985:AFB}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hull:1986:VPE,
  author =       "T. E. Hull and A. Abrham",
  title =        "Variable Precision Exponential Function",
  journal =      j-TOMS,
  volume =       "12",
  number =       "2",
  pages =        "79--91",
  month =        jun,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6497.6498",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15 (65D20)",
  MRnumber =     "863 786",
  bibdate =      "Sun Sep 04 21:17:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p79-hull/",
  abstract =     "The exponential function presented here returns a
                 result which differs from $e^x$ by less than one unit
                 in the last place, for any representable value of $x$
                 which is not too close to values for which $e^x$ would
                 overflow or underflow. (For values of $x$ which are not
                 within this range, an error condition is raised.) It is
                 a ``variable precision'' function in that it returns a
                 $p$-digit approximation for a $p$-digit argument, for
                 any $p > 0$ ($p$-digit means $p$-decimal-digit). The
                 program and analysis are valid for all $p > 0$, but
                 current implementations place a restriction on $p$. The
                 program is presented in a Pascal-like programming
                 language called Numerical Turing which has special
                 facilities for scientific computing, including
                 precision control, directed roundings, and built-in
                 functions for getting and setting exponents.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; decimal floating-point arithmetic; theory;
                 verification",
  review =       "ACM CR 8702-0091",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Verification.",
}

@Article{Dolk:1986:GMM,
  author =       "Daniel R. Dolk",
  title =        "A Generalized Model Management System for Mathematical
                 Programming",
  journal =      j-TOMS,
  volume =       "12",
  number =       "2",
  pages =        "92--126",
  month =        jun,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6497.6501",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:18:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p92-dolk/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "human factors; languages; management",
  review =       "ACM CR 8705-0407",
  subject =      "{\bf H.4.2}: Information Systems, INFORMATION SYSTEMS
                 APPLICATIONS, Types of Systems, Decision support. {\bf
                 D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Applicative languages. {\bf D.3.2}:
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Nonprocedural languages. {\bf G.1.6}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming. {\bf G.1.6}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Nonlinear programming. {\bf G.1.6}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Integer programming. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE, XMP.
                 {\bf H.2.3}: Information Systems, DATABASE MANAGEMENT,
                 Languages, Query languages. {\bf H.2.4}: Information
                 Systems, DATABASE MANAGEMENT, Systems, Query
                 processing. {\bf D.2.2}: Software, SOFTWARE
                 ENGINEERING, Tools and Techniques, User interfaces.
                 {\bf I.2.1}: Computing Methodologies, ARTIFICIAL
                 INTELLIGENCE, Applications and Expert Systems, GXMP.
                 {\bf I.2.4}: Computing Methodologies, ARTIFICIAL
                 INTELLIGENCE, Knowledge Representation Formalisms and
                 Methods.",
}

@Article{Liu:1986:CRS,
  author =       "Joseph W. H. Liu",
  title =        "A Compact Row Storage Scheme for {Cholesky} Factors
                 Using Elimination Trees",
  journal =      j-TOMS,
  volume =       "12",
  number =       "2",
  pages =        "127--148",
  month =        jun,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6497.6499",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05 (65F50)",
  MRnumber =     "863 787",
  bibdate =      "Sun Sep 04 21:18:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p127-liu/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; experimentation; measurement; performance;
                 theory; verification",
  review =       "ACM CR 8703-0191",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Sparse and very
                 large systems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.2.2}:
                 Mathematics of Computing, DISCRETE MATHEMATICS, Graph
                 Theory.",
}

@Article{Springer:1986:AES,
  author =       "J{\"o}rn Springer",
  title =        "{Algorithm 641}: Exact Solution of General Systems of
                 Linear Equations",
  journal =      j-TOMS,
  volume =       "12",
  number =       "2",
  pages =        "149--149",
  month =        jun,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6497.356167",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 4 21:19:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hutchinson:1986:AFP,
  author =       "M. F. Hutchinson",
  title =        "{Algorithm 642}: a Fast Procedure for Calculating
                 Minimum Cross-Validation Cubic Smoothing Splines",
  journal =      j-TOMS,
  volume =       "12",
  number =       "2",
  pages =        "150--153",
  month =        jun,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6497.214322",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D10 (65D07)",
  MRnumber =     "863 788",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p150-hutchinson/",
  abstract =     "The procedure CUBGCV is an implementation of a
                 recently developed algorithm for fast $O(n)$
                 calculation of a cubic smoothing spline fitted to $n$
                 noisy data points, with the degree of smoothing chosen
                 to minimize the expected mean square error at the data
                 points when the variance of the error associated with
                 the data is known, or, to minimize the generalized
                 cross validation (GCV) when the variance of the error
                 associated with the data is unknown. The data may be
                 unequally spaced and nonuniformly weighted. The
                 algorithm exploits the banded structure of the matrices
                 associated with the cubic smoothing spline problem.
                 Bayesian point error estimates are also calculated in
                 $O(n)$ operations.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Smoothing. {\bf G.1.1}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Spline and piecewise polynomial
                 interpolation. {\bf G.1.2}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Spline and piecewise
                 polynomial approximation. {\bf G.3}: Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Statistical
                 software.",
}

@Article{Mehta:1986:AFF,
  author =       "Cyrus R. Mehta and Nitin R. Patel",
  title =        "{Algorithm 643}: {FEXACT}: {A FORTRAN} Subroutine for
                 {Fisher}'s Exact Test on Unordered $r\times c$
                 Contingency Tables",
  journal =      j-TOMS,
  volume =       "12",
  number =       "2",
  pages =        "154--161",
  month =        jun,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6497.214326",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65U05",
  MRnumber =     "863 789",
  bibdate =      "Tue Mar 9 10:27:54 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Clarkson:1993:RAF}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p154-mehta/",
  abstract =     "The computer code for Mehta and Patel's (1983) network
                 algorithm for Fisher's exact test on unordered $r\times
                 c$ contingency tables is provided. The code is written
                 in double precision FORTRAN 77. This code provides the
                 fastest currently available method for executing
                 Fisher's exact test, and is shown to be orders of
                 magnitude superior to any other available algorithm.
                 Many important details of data structures and
                 implementation that have contributed crucially to the
                 success of the network algorithm are recorded here.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Nonlinear programming. {\bf
                 G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Statistical computing. {\bf G.3}:
                 Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical software.",
}

@Article{McKeown:1986:IIU,
  author =       "G. P. McKeown",
  title =        "Iterated Interpolation Using a Systolic Array",
  journal =      j-TOMS,
  volume =       "12",
  number =       "2",
  pages =        "162--170",
  month =        jun,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6497.6500",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-2/p162-mckeown/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design",
  review =       "ACM CR 8703-0161",
  subject =      "{\bf B.6.1}: Hardware, LOGIC DESIGN, Design Styles,
                 Cellular arrays and automata. {\bf G.1.0}: Mathematics
                 of Computing, NUMERICAL ANALYSIS, General, Parallel
                 algorithms. {\bf G.1.1}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Interpolation.",
}

@Article{Krogh:1986:AAP,
  author =       "Fred T. Krogh",
  title =        "{ACM} Algorithms Policy",
  journal =      j-TOMS,
  volume =       "12",
  number =       "2",
  pages =        "171--174",
  month =        jun,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/6497.356171",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:20:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hall:1986:ESR,
  author =       "George Hall",
  title =        "Equilibrium States of {Runge--Kutta} Schemes: {Part
                 II}",
  journal =      j-TOMS,
  volume =       "12",
  number =       "3",
  pages =        "183--192",
  month =        sep,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/7921.7922",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05",
  MRnumber =     "88e:65087",
  bibdate =      "Sun Sep 04 21:21:39 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p183-hall/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  reviewer =     "Henning Esser",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems. {\bf G.1.7}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Single step methods. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.",
}

@Article{Enright:1986:IRK,
  author =       "W. H. Enright and K. R. Jackson and S. P. N{\o}rsett
                 and P. G. Thomsen",
  title =        "Interpolants for {Runge--Kutta} Formulas",
  journal =      j-TOMS,
  volume =       "12",
  number =       "3",
  pages =        "193--218",
  month =        sep,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/7921.7923",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D07 (65L05)",
  MRnumber =     "889 066",
  bibdate =      "Sun Sep 04 21:21:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p193-enright/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  review =       "ACM CR 8707-0591",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Single step
                 methods. {\bf G.1.7}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Error analysis. {\bf G.1.7}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Initial value problems. {\bf G.1.1}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Interpolation,
                 Interpolation formulas.",
}

@Article{Kallay:1986:PCM,
  author =       "Michael Kallay",
  title =        "Plane Curves of Minimal Energy",
  journal =      j-TOMS,
  volume =       "12",
  number =       "3",
  pages =        "219--222",
  month =        sep,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/7921.7924",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "53A04 (58E10 73K05)",
  MRnumber =     "89c:53002",
  bibdate =      "Sun Sep 04 21:22:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p219-kallay/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  review =       "ACM CR 8706-0499",
  subject =      "{\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Spline and piecewise
                 polynomial interpolation. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Spline
                 and piecewise polynomial approximation. {\bf G.1.6}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Constrained optimization. {\bf I.3.5}:
                 Computing Methodologies, COMPUTER GRAPHICS,
                 Computational Geometry and Object Modeling, Curve,
                 surface, solid, and object representations.",
}

@Article{Skeel:1986:NBL,
  author =       "Robert D. Skeel and Thu V. Vu",
  title =        "Note on Blended Linear Multistep Formulas",
  journal =      j-TOMS,
  volume =       "12",
  number =       "3",
  pages =        "223--224",
  month =        sep,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/7921.7925",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p223-skeel/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems. {\bf G.1.7}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Stiff equations. {\bf G.1.7}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Single step methods.",
}

@Article{Sagie:1986:CAM,
  author =       "Ike Sagie",
  title =        "Computer-Aided Modeling and Planning ({CAMP})",
  journal =      j-TOMS,
  volume =       "12",
  number =       "3",
  pages =        "225--248",
  month =        sep,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/7921.15667",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p225-sagie/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "economics; languages; management",
  review =       "ACM CR 8710-0893",
  subject =      "{\bf J.6}: Computer Applications, COMPUTER-AIDED
                 ENGINEERING, Computer-aided design (CAD). {\bf H.2.3}:
                 Information Systems, DATABASE MANAGEMENT, Languages.
                 {\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Linear programming. {\bf
                 H.1.2}: Information Systems, MODELS AND PRINCIPLES,
                 User/Machine Systems, Human factors. {\bf I.6.2}:
                 Computing Methodologies, SIMULATION AND MODELING,
                 Simulation Languages. {\bf I.2.7}: Computing
                 Methodologies, ARTIFICIAL INTELLIGENCE, Natural
                 Language Processing.",
}

@Article{Liu:1986:SRC,
  author =       "Joseph W. H. Liu",
  title =        "On the Storage Requirement in the Out-of-Core
                 Multifrontal Method for Sparse Factorization",
  journal =      j-TOMS,
  volume =       "12",
  number =       "3",
  pages =        "249--264",
  month =        sep,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/7921.11325",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F50",
  MRnumber =     "889 068",
  bibdate =      "Sun Sep 04 21:23:42 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p249-liu/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  review =       "ACM CR 8709-0776",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Sparse and very
                 large systems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis.",
}

@Article{Amos:1986:APP,
  author =       "D. E. Amos",
  title =        "{Algorithm 644}: a Portable Package for {Bessel}
                 Functions of a Complex Argument and Nonnegative Order",
  journal =      j-TOMS,
  volume =       "12",
  number =       "3",
  pages =        "265--273",
  month =        sep,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/7921.214331",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "889 069",
  bibdate =      "Tue Mar 09 10:26:27 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also
                 \cite{Amos:1990:RPP,Amos:1995:RAP,Kodama:2007:RA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p265-amos/",
  abstract =     "This algorithm is a package of subroutines for
                 Computing Bessel functions $H_{v}^{(1)}(z)$,
                 $H_{v}^{(2)}(z)$, $I_{v}(z)$, $J_{v}(z)$, $K_{v}(z)$,
                 $Y_{v}(z)$ and Airy functions $\mbox{Ai}(z)$,
                 $\mbox{Ai}'(z)$, $\mbox{Bi}(z)$, $\mbox{Bi}'(z)$ for
                 orders $v \geq 0$ and complex $z$ in $-\pi< \mbox{arg}
                 z \leq \pi$. Eight callable subroutines and their
                 double-precision counterparts are provided. Exponential
                 scaling and sequence generation are auxiliary
                 options.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.m}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Miscellaneous. {\bf G.m}: Mathematics of Computing,
                 MISCELLANEOUS.",
}

@Article{Nash:1986:AST,
  author =       "J. C. Nash and R. L. C. Wang",
  title =        "{Algorithm 645}: Subroutines for Testing Programs that
                 Compute the Generalized Inverse of a Matrix",
  journal =      j-TOMS,
  volume =       "12",
  number =       "3",
  pages =        "274--277",
  month =        sep,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/7921.214334",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F20",
  MRnumber =     "889 070",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p274-nash/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods).",
}

@Article{Crawford:1986:APR,
  author =       "Charles R. Crawford",
  title =        "{Algorithm 646}: {PDFIND}: a Routine to Find a
                 Positive Definite Linear Combination of Two Real
                 Symmetric Matrices",
  journal =      j-TOMS,
  volume =       "12",
  number =       "3",
  pages =        "278--282",
  month =        sep,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/7921.214335",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F30",
  MRnumber =     "889 071",
  bibdate =      "Sun Sep 04 21:24:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p278-crawford/",
  abstract =     "PDFIND is a FORTRAN-77 implementation of an algorithm
                 that finds a positive definite linear combination of
                 two symmetric matrices, or determines that such a
                 combination does not exist. The algorithm is designed
                 to be independent of the data structures used to store
                 the matrices. The user must provide a subroutine,
                 CHLSKY, which acts as an interface between PDFIND and
                 the matrix data structures. CHLSKY also provides the
                 user control over the number of iterations of the
                 algorithm. Implementations of CHLSKY are included which
                 call LINPAC routines for full matrices as well as
                 symmetric banded matrices.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; geig; nla; symmetric matrix",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra.",
}

@Article{Hake:1986:RCC,
  author =       "J.-Fr. Hake",
  title =        "Remark on ``{Algorithm} 569: {COLSYS}: Collocation
                 Software for Boundary-Value {ODEs} [{D2}]''",
  journal =      j-TOMS,
  volume =       "12",
  number =       "3",
  pages =        "283--284",
  month =        sep,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/7921.356181",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:16:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Ascher:1981:ACC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Stewart:1986:CNC,
  author =       "G. W. Stewart",
  title =        "Corrigendum: ``{A} Note on Complex Division''",
  journal =      j-TOMS,
  volume =       "12",
  number =       "3",
  pages =        "285--285",
  month =        sep,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/7921.356182",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:17:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Stewart:1985:NCD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Milovanovic:1986:CEI,
  author =       "G. V. Milovanovi{\'c} and M. S. Petkovi{\'c}",
  title =        "On Computational Efficiency of the Iterative Methods
                 for the Simultaneous Approximation of Polynomial
                 Zeros",
  journal =      j-TOMS,
  volume =       "12",
  number =       "4",
  pages =        "295--306",
  month =        dec,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/22721.8932",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:39:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-3/p274-milovanovic/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "measurement; performance",
  review =       "ACM CR 8707-0590",
  subject =      "{\bf G.1.5}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Iterative
                 methods.",
}

@Article{Nazareth:1986:IAO,
  author =       "J. L. Nazareth",
  title =        "Implementation Aids for Optimization Algorithms that
                 Solve Sequences of Linear Programs",
  journal =      j-TOMS,
  volume =       "12",
  number =       "4",
  pages =        "307--323",
  month =        dec,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/22721.22959",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:29:30 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-4/p307-nazareth/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; experimentation; languages",
  review =       "ACM CR 8708-0686",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Linear programming. {\bf
                 G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Constrained optimization. {\bf G.1.6}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Nonlinear programming. {\bf D.2.2}:
                 Software, SOFTWARE ENGINEERING, Tools and Techniques,
                 Modules and interfaces. {\bf D.2.2}: Software, SOFTWARE
                 ENGINEERING, Tools and Techniques, Software libraries.
                 {\bf D.3.3}: Software, PROGRAMMING LANGUAGES, Language
                 Constructs and Features, Modules, packages.",
}

@Article{Cowell:1986:TFD,
  author =       "Wayne R. Cowell and Christopher P. Thompson",
  title =        "Transforming {Fortran DO} Loops to Improve Performance
                 on Vector Architectures",
  journal =      j-TOMS,
  volume =       "12",
  number =       "4",
  pages =        "324--353",
  month =        dec,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/22721.24035",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:30:12 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-4/p324-cowell/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; languages; performance",
  review =       "ACM CR 8712-0989",
  subject =      "{\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and
                 Techniques. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE. {\bf G.1.3}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra. {\bf C.1.2}: Computer Systems Organization,
                 PROCESSOR ARCHITECTURES, Multiple Data Stream
                 Architectures (Multiprocessors), Array and vector
                 processors.",
}

@Article{Ostermann:1986:SCP,
  author =       "A. Ostermann and P. Kaps and T. D. Bui",
  title =        "The Solution of a Combustion Problem with {Rosenbrock}
                 Methods",
  journal =      j-TOMS,
  volume =       "12",
  number =       "4",
  pages =        "354--361",
  month =        dec,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/22721.22722",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:30:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-4/p354-ostermann/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "performance",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems. {\bf G.1.7}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Stiff equations. {\bf G.1.8}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Partial Differential Equations,
                 Method of lines.",
}

@Article{Fox:1986:AIR,
  author =       "Bennett L. Fox",
  title =        "{Algorithm 647}: Implementation and Relative
                 Efficiency of Quasirandom Sequence Generators",
  journal =      j-TOMS,
  volume =       "12",
  number =       "4",
  pages =        "362--376",
  month =        dec,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/22721.356187",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 10:43:26 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{DiDonato:1986:CIG,
  author =       "Armido R. DiDonato and Alfred H. {Morris, Jr.}",
  title =        "Computation of the Incomplete Gamma Function Ratios
                 and Their Inverse",
  journal =      j-TOMS,
  volume =       "12",
  number =       "4",
  pages =        "377--393",
  month =        dec,
  year =         "1986",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/22721.23109",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:31:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1986-12-4/p377-didonato/",
  abstract =     "An algorithm is given for computing the incomplete
                 gamma function ratios $ P(a, x) $ and $ Q(a, x) $ for $
                 a \geq 0 $, $ x \geq 0 $, $ a + x \neq 0 $. Temme's
                 uniform asymptotic expansions are used. The algorithm
                 is robust; results accurate to 14 significant digits
                 can be obtained. An extensive set of coefficients for
                 the Temme expansions is included.\par

                 An algorithm, employing third-order Schr{\"o}der
                 iteration supported by Newton-Raphson iteration, is
                 provided for computing $x$ when $a$, $ P(a, x) $, and $
                 Q(a, x) $ are given. Three iterations at most are
                 required to obtain 10 significant digit accuracy for
                 $x$.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  review =       "ACM CR 8709-0775",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation.",
}

@Article{Enright:1987:TFP,
  author =       "W. H. Enright and J. D. Pryce",
  title =        "Two {FORTRAN} Packages for Assessing Initial Value
                 Methods",
  journal =      j-TOMS,
  volume =       "13",
  number =       "1",
  pages =        "1--27",
  month =        mar,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/23002.27645",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:08:36 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Enright:1989:CFP}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-1/p1-enright/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance; reliability",
  review =       "ACM CR 8803-0208",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing.",
}

@Article{Enright:1987:ANS,
  author =       "W. H. Enright and J. D. Pryce",
  title =        "{Algorithm 648}: {NSDTST} and {STDTST}: Routines for
                 Assessing the Performance of {IV} Solvers",
  journal =      j-TOMS,
  volume =       "13",
  number =       "1",
  pages =        "28--34",
  month =        mar,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/23002.214338",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 4 21:32:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-1/p28-enright/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance; reliability",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing.",
}

@Article{Alagar:1987:FLS,
  author =       "Vangalur S. Alagar and David K. Probst",
  title =        "A Fast, Low-Space Algorithm for Multiplying Dense
                 Multivariate Polynomials",
  journal =      j-TOMS,
  volume =       "13",
  number =       "1",
  pages =        "35--57",
  month =        mar,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/23002.27646",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:32:38 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-1/p35-alagar/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design",
  review =       "ACM CR 8802-0114",
  subject =      "{\bf I.1.2}: Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms, Algebraic algorithms. {\bf
                 I.1.2}: Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms, Analysis of algorithms.",
}

@Article{Vitter:1987:EAS,
  author =       "Jeffrey Scott Vitter",
  title =        "An Efficient Algorithm for Sequential Random
                 Sampling",
  journal =      j-TOMS,
  volume =       "13",
  number =       "1",
  pages =        "58--67",
  month =        mar,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/23002.23003",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:32:58 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-1/p58-vitter/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; performance",
  review =       "ACM CR 8808-0614",
  subject =      "{\bf F.2.m}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Miscellaneous. {\bf
                 G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Statistical software.",
}

@Article{Foley:1987:IIP,
  author =       "Thomas A. Foley",
  title =        "Interpolation with Interval and Point Tension Controls
                 Using Cubic Weighted $v$-Splines",
  journal =      j-TOMS,
  volume =       "13",
  number =       "1",
  pages =        "68--96",
  month =        mar,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/23002.23004",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D07 (65D05 65D10)",
  MRnumber =     "88h:65023",
  bibdate =      "Sat Nov 19 13:08:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Foley:1988:CIP}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-1/p68-foley/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  review =       "ACM CR 8802-0098",
  reviewer =     "K. Jetter",
  subject =      "{\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Spline and piecewise
                 polynomial interpolation. {\bf G.1.6}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization,
                 Constrained optimization. {\bf I.3.5}: Computing
                 Methodologies, COMPUTER GRAPHICS, Computational
                 Geometry and Object Modeling, Curve, surface, solid,
                 and object representations.",
}

@Article{Giunta:1987:APC,
  author =       "G. Giunta and A. Murli",
  title =        "{Algorithm 649}: a Package for Computing Trigonometric
                 {Fourier} Coefficients Based on {Lyness}'s Algorithm",
  journal =      j-TOMS,
  volume =       "13",
  number =       "1",
  pages =        "97--107",
  month =        mar,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/23002.214339",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-1/p97-giunta/",
  abstract =     "We present a package that allows the computation of
                 the trigonometric Fourier coefficients of a smooth
                 function. The function can be provided as a subprogram
                 or as a data list of function values at equally spaced
                 points.\par

                 The computational cost of the algorithm does not depend
                 on the required number of Fourier coefficients.
                 Numerical results of comparative tests with a standard
                 integrator for oscillatory functions are also
                 reported.",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.",
}

@Article{Dyksen:1987:IEI,
  author =       "Wayne R. Dyksen and Calvin J. Ribbens",
  title =        "Interactive {ELLPACK}: An Interactive Problem-Solving
                 Environment for Elliptic Partial Differential
                 Equations",
  journal =      j-TOMS,
  volume =       "13",
  number =       "2",
  pages =        "113--132",
  month =        jun,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/328512.328515",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65N99 (65V05)",
  MRnumber =     "88g:65127",
  bibdate =      "Sun Sep 04 21:35:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "W. C. Rheinboldt",
}

@Article{Pardalos:1987:GLS,
  author =       "Panos M. Pardalos",
  title =        "Generation of Large-Scale Quadratic Programs for Use
                 as Global Optimization Test Problems",
  journal =      j-TOMS,
  volume =       "13",
  number =       "2",
  pages =        "133--137",
  month =        jun,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/328512.328516",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "49D40 (90C30 93A15)",
  MRnumber =     "88h:49057",
  bibdate =      "Sun Sep 04 21:35:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "G. Di Pillo",
}

@Article{Johnson:1987:AES,
  author =       "Kenneth C. Johnson",
  title =        "{Algorithm 650}: Efficient Square Root Implementation
                 on the 68000",
  journal =      j-TOMS,
  volume =       "13",
  number =       "2",
  pages =        "138--151",
  month =        jun,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/328512.328520",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15",
  MRnumber =     "898 489",
  bibdate =      "Sun Sep 4 21:36:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Johnson:1987:CES}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Morgan:1987:BBS,
  author =       "Alexander Morgan and Vadim Shapiro",
  title =        "Box-Bisection for Solving Second-Degree Systems and
                 the Problem of Clustering",
  journal =      j-TOMS,
  volume =       "13",
  number =       "2",
  pages =        "152--167",
  month =        jun,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/328512.328521",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H10",
  MRnumber =     "88e:65063",
  bibdate =      "Sat Nov 19 13:08:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Morgan:1987:CBS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Monahan:1987:AGC,
  author =       "John F. Monahan",
  title =        "An Algorithm for Generating Chi Random Variables",
  journal =      j-TOMS,
  volume =       "13",
  number =       "2",
  pages =        "168--172",
  month =        jun,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/328512.328522",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65C10",
  MRnumber =     "88d:65013",
  bibdate =      "Sat Nov 19 13:08:24 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Johnson:1987:CES,Monahan:1988:CAG}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Liu:1987:PPS,
  author =       "Joseph W. H. Liu",
  title =        "A Partial Pivoting Strategy for Sparse Symmetric
                 Matrix Decomposition",
  journal =      j-TOMS,
  volume =       "13",
  number =       "2",
  pages =        "173--182",
  month =        jun,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/328512.328525",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05 (65F50)",
  MRnumber =     "88f:65046",
  bibdate =      "Sun Sep 04 21:35:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  reviewer =     "R. P. Tewarson",
}

@Article{Krogh:1987:AAP,
  author =       "Fred T. Krogh",
  title =        "{ACM} Algorithms Policy",
  journal =      j-TOMS,
  volume =       "13",
  number =       "2",
  pages =        "183--186",
  month =        jun,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/328512.328526",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:35:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kearfott:1987:STG,
  author =       "R. Baker Kearfott",
  title =        "Some Tests of Generalized Bisection",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "197--220",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.29862",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H10",
  MRnumber =     "88m:65081",
  bibdate =      "Sat Nov 19 13:08:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Kearfott:1988:CTG}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p197-kearfott/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance; theory",
  subject =      "{\bf G.1.5}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Systems of
                 equations. {\bf G.1.5}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Roots of Nonlinear Equations,
                 Polynomials, methods for.",
}

@Article{Boisvert:1987:FOA,
  author =       "Ronald F. Boisvert",
  title =        "A Fourth-Order-Accurate {Fourier} Method for the
                 {Helmholtz} Equation in Three Dimensions",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "221--234",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.29863",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65N05",
  MRnumber =     "88m:65149",
  bibdate =      "Sun Sep 04 21:39:43 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p221-boisvert/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory; verification",
  review =       "ACM CR 8808-0622",
  reviewer =     "Ian Gladwell",
  subject =      "G.1.8 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Partial Differential Equations, Elliptic equations \\
                 G.4 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis",
}

@Article{Boisvert:1987:AAH,
  author =       "Ronald F. Boisvert",
  title =        "{Algorithm 651}: Algorithm {HFFT}\emdash High-Order
                 Fast-Direct Solution of the {Helmholtz} Equation",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "235--249",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.214342",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65V05",
  MRnumber =     "918 578",
  bibdate =      "Sun Sep 4 21:40:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Johnson:1987:CES}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p235-boisvert/",
  abstract =     "HFFT is a software package for solving the Helmholtz
                 equation on bounded two- and three-dimensional
                 rectangular domains with Dirichlet, Neumann, or
                 periodic boundary conditions. The software is the
                 result of combining new fourth-order accurate compact
                 finite difference (HODIE) discretizations and a
                 fast-direct solution technique (the Fourier method). In
                 this paper we briefly describe the user interface to
                 HFFT and present an example of its usage and several
                 details of its implementation.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory; verification",
  subject =      "{\bf G.1.8}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations, Elliptic
                 equations. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis.",
}

@Article{Liu:1987:TPM,
  author =       "Joseph W. H. Liu",
  title =        "On Threshold Pivoting in the Multifrontal Method for
                 Sparse Indefinite Systems",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "250--261",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.31331",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F50 (65F05)",
  MRnumber =     "88j:65089",
  bibdate =      "Sun Sep 04 21:40:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p250-liu/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance; theory",
  review =       "ACM CR 8804-0281",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Sparse and very
                 large systems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis.",
}

@Article{Corana:1987:MMF,
  author =       "A. Corana and M. Marchesi and C. Martini and S.
                 Ridella",
  title =        "Minimizing Multimodal Functions of Continuous
                 Variables with the {``Simulated Annealing''}
                 Algorithm",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "262--280",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.29864",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "90C30 (65K05)",
  MRnumber =     "88m:90121",
  bibdate =      "Sat Nov 19 13:08:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Corana:1989:CMF}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p262-corana/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  review =       "ACM CR 8804-0282",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Nonlinear programming. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing. {\bf G.3}: Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Probabilistic
                 algorithms (including Monte Carlo). {\bf F.2.2}: Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Sorting and searching.",
}

@Article{Watson:1987:AHS,
  author =       "Layne T. Watson and Stephen C. Billups and Alexander
                 P. Morgan",
  title =        "{Algorithm 652}: {HOMPACK}: a Suite of Codes for
                 Globally Convergent Homotopy Algorithms",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "281--310",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.214343",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65V05 (58C30 65H10 90C30)",
  MRnumber =     "918 581",
  bibdate =      "Sun Sep 4 21:41:46 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p281-watson/",
  abstract =     "There are algorithms for finding zeros or fixed points
                 of nonlinear systems of equations that are globally
                 convergent for almost all starting points, i.e., with
                 probability one. The essence of all such algorithms is
                 the construction of an appropriate homotopy map and
                 then tracking some smooth curve in the zero set of this
                 homotopy map. HOMPACK provides three qualitatively
                 different algorithms for tracking the homotopy zero
                 curve: ordinary differential equation-based, normal
                 flow, and augmented Jacobian matrix. Separate routines
                 are also provided for dense and sparse Jacobian
                 matrices. A high-level driver is included for the
                 special case of polynomial systems.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.5}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Systems of
                 equations. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE.",
}

@Article{Hanson:1987:ATA,
  author =       "R. J. Hanson and F. T. Krogh",
  title =        "{Algorithm 653}: Translation of {Algorithm} 539:
                 {PC-BLAS Basic Linear Algebra Subprograms} for
                 {FORTRAN} Usage with the {INTEL} 8087, 80287 Numeric
                 Data Processor",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "311--317",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.214346",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 23:07:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Lawson:1979:ABL,Dodson:1982:RBL,Dodson:1983:CRB,Louter-Nool:1988:ATA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-3/p311-hanson/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{DiDonato:1987:AFS,
  author =       "Armido R. DiDonato and Alfred H. {Morris, Jr.}",
  title =        "{Algorithm 654}: {FORTRAN} Subroutines for Computing
                 the Incomplete Gamma Function Ratios and their
                 Inverse",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "318--319",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.214348",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 4 21:43:08 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran2.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/pdf/10.1145/29380.214348",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation. {\bf G.m}: Mathematics of
                 Computing, MISCELLANEOUS.",
}

@Article{Johnson:1987:CES,
  author =       "Kenneth C. Johnson",
  title =        "Corrigendum: {``Algorithm 650: efficient square root
                 implementation on the 68000'' [{ACM} Trans. Math.
                 Software {\bf 13} (1987), no. 2, 138--151]}",
  journal =      j-TOMS,
  volume =       "13",
  number =       "3",
  pages =        "320--320",
  month =        sep,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/29380.356210",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "320. 65D15",
  MRnumber =     "918 582",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Johnson:1987:AES,Monahan:1987:AGC,Boisvert:1987:AAH}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bar-On:1987:PPA,
  author =       "Ilan Bar-On",
  title =        "A Practical Parallel Algorithm for Solving Band
                 Symmetric Positive Definite Systems of Linear
                 Equations",
  journal =      j-TOMS,
  volume =       "13",
  number =       "4",
  pages =        "323--332",
  month =        dec,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/35078.35079",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05 (65W05)",
  MRnumber =     "88m:65048",
  bibdate =      "Sun Sep 04 21:45:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-4/p323-bar-on/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance; theory",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Parallel algorithms. {\bf G.1.3}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Linear systems (direct and iterative
                 methods). {\bf G.1.3}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix
                 inversion.",
}

@Article{Schoenauer:1987:SCB,
  author =       "Willi Sch{\"o}nauer and Eric Schnepf",
  title =        "Software Considerations for the ``Black Box'' Solver
                 {FIDISOL} for Partial Differential Equations",
  journal =      j-TOMS,
  volume =       "13",
  number =       "4",
  pages =        "333--349",
  month =        dec,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/35078.35080",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:08:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-4/p333-schonauer/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design",
  review =       "ACM CR 8809-0699",
  subject =      "{\bf G.1.8}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations, Difference
                 methods. {\bf G.1.8}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Partial Differential Equations,
                 Elliptic equations. {\bf G.1.8}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Partial Differential
                 Equations, Parabolic equations. {\bf G.4}: Mathematics
                 of Computing, MATHEMATICAL SOFTWARE, FIDOSOL.",
}

@Article{Ahlfeld:1987:NPG,
  author =       "David P. Ahlfeld and John M. Mulvey and Ron S. Dembo
                 and Stavros A. Zenios",
  title =        "Nonlinear Programming on Generalized Networks",
  journal =      j-TOMS,
  volume =       "13",
  number =       "4",
  pages =        "350--367",
  month =        dec,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/35078.42181",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "90C35 (90C30)",
  MRnumber =     "89b:90218",
  bibdate =      "Sun Sep 04 21:47:23 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-4/p350-ahlfeld/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  review =       "ACM CR 8810-0796",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Constrained optimization. {\bf
                 G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Gradient methods. {\bf G.1.6}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Nonlinear programming. {\bf G.2.2}:
                 Mathematics of Computing, DISCRETE MATHEMATICS, Graph
                 Theory, Network problems.",
}

@Article{Haas:1987:MPR,
  author =       "Alexander Haas",
  title =        "The Multiple Prime Random Number Generator",
  journal =      j-TOMS,
  volume =       "13",
  number =       "4",
  pages =        "368--381",
  month =        dec,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/35078.214349",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65C10",
  MRnumber =     "89h:65018",
  bibdate =      "Sun Sep 04 21:45:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-4/p368-haas/",
  abstract =     "A new pseudorandom number generator, the Multiple
                 Prime Random Number Generator, has been developed; it
                 is efficient, conceptually simple, flexible, and easy
                 to program. The generator utilizes cycles around prime
                 numbers to guarantee the length of the period, which
                 can easily be programmed to surpass the maximum period
                 of any other presently available random number
                 generator. There are minimum limits placed on the seed
                 values of the variables because the period of the
                 generator is not a function of the initial values of
                 the variables. The generator passes thirteen standard
                 random number generator tests. It requires only about
                 fifteen lines of FORTRAN code to program and utilizes
                 programming language constructs found in most major
                 languages. Finally, it compares very favorably to the
                 fastest of the other available generators.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; economics; experimentation; performance;
                 reliability",
  reviewer =     "Brian Conolly",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Probabilistic algorithms (including Monte
                 Carlo). {\bf G.3}: Mathematics of Computing,
                 PROBABILITY AND STATISTICS, Random number generation.
                 {\bf I.6.3}: Computing Methodologies, SIMULATION AND
                 MODELING, Applications. {\bf I.6.4}: Computing
                 Methodologies, SIMULATION AND MODELING, Model
                 Validation and Analysis. {\bf J.2}: Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Mathematics and statistics. {\bf J.4}: Computer
                 Applications, SOCIAL AND BEHAVIORAL SCIENCES,
                 Economics. {\bf J.4}: Computer Applications, SOCIAL AND
                 BEHAVIORAL SCIENCES, Sociology.",
}

@Article{Schneider:1987:EEA,
  author =       "Michael H. Schneider",
  title =        "The Expanding Equilibrium Algorithm",
  journal =      j-TOMS,
  volume =       "13",
  number =       "4",
  pages =        "382--398",
  month =        dec,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/35078.42322",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:48:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-4/p382-schneider/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; economics; performance",
  review =       "ACM CR 8812-0937",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Nonlinear programming. {\bf
                 J.4}: Computer Applications, SOCIAL AND BEHAVIORAL
                 SCIENCES, Economics.",
}

@Article{Elhay:1987:AIF,
  author =       "Sylvan Elhay and Jaroslav Kautsky",
  title =        "{Algorithm 655}: {IQPACK}: {FORTRAN} Subroutines for
                 the Weights of Interpolatory Quadratures",
  journal =      j-TOMS,
  volume =       "13",
  number =       "4",
  pages =        "399--415",
  month =        dec,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/35078.214351",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 4 21:49:00 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1987-13-4/p399-elhay/",
  abstract =     "We present FORTRAN subroutines that implement the
                 method described in [3] for the stable evaluation of
                 the weights of interpolatory quadratures with
                 prescribed simple or multiple knots. Given a set of
                 knots and their multiplicities, the package generates
                 the weights by using the zeroth moment $\mu_{0}$ of
                 $w$, the weight function in the integrand, and the
                 (symmetric tridiagonal) Jacobi matrix $J$ associated
                 with the polynomials orthogonal on $(a, b)$ with
                 respect to $w$. There are utility routines that
                 generate $\mu_{0}$ and $J$ for classical weight
                 functions, but quadratures can be generated for any
                 $\mu_{0}$ and $J$ supplied by the user. Utility
                 routines are also provided that (1) evaluate a computed
                 quadrature, applied to a user-supplied integrand, (2)
                 check the polynomial order of precision of a quadrature
                 formula, and (3) compute the knots and weights of
                 simple Gaussian quadrature formula.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.4}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Quadrature and Numerical Differentiation, Gaussian
                 quadrature.",
}

@Article{Morgan:1987:CBS,
  author =       "Alexander Morgan and Vadim Shapiro",
  title =        "Corrigendum: ``{Box-Bisection} for Solving
                 Second-Degree Systems and the Problem of Clustering''",
  journal =      j-TOMS,
  volume =       "13",
  number =       "4",
  pages =        "416--416",
  month =        dec,
  year =         "1987",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/35078.356217",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H10",
  MRnumber =     "89a:65088, 88e:65063",
  bibdate =      "Sun Sep 04 21:45:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Morgan:1987:BBS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Dongarra:1988:ESF,
  author =       "Jack J. Dongarra and Jeremy {Du Croz} and Sven
                 Hammarling and Richard J. Hanson",
  title =        "An Extended Set of {FORTRAN Basic Linear Algebra
                 Subprograms}",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "1--17",
  month =        mar,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/42288.42291",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:08:30 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Dongarra:1988:CES}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p1-dongarra/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; standardization",
  review =       "ACM CR 8812-0940",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Portability. {\bf G.1.3}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra.",
}

@Article{Dongarra:1988:AES,
  author =       "Jack J. Dongarra and Jeremy {Du Croz} and Sven
                 Hammarling and Richard J. Hanson",
  title =        "{Algorithm 656}: An Extended Set of {Basic Linear
                 Algebra Subprograms}: Model Implementation and Test
                 Programs",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "18--32",
  month =        mar,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/42288.42292",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:52:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p18-dongarra/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; BLAS; nla; software; theory; vect",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@Article{Sewell:1988:PCS,
  author =       "Granville Sewell",
  title =        "Plotting Contour Surfaces of a Function of Three
                 Variables",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "33--41",
  month =        mar,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/42288.42289",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65S05",
  MRnumber =     "89c:65140",
  bibdate =      "Sun Sep 04 21:53:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p33-sewell/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design",
  review =       "ACM CR 8810-0795",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf F.2.1}:
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems.
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE.",
}

@Article{Sewell:1988:ASP,
  author =       "Granville Sewell",
  title =        "{Algorithm 657}: Software for Plotting Contour
                 Surfaces of a Function of Three Variables",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "42--44",
  month =        mar,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/42288.42290",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 15:08:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Sewell:1990:RSP}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p42-sewell/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf F.2.1}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms. {\bf G.1.3}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative methods).
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE.",
}

@Article{Leis:1988:SSS,
  author =       "Jorge R. Leis and Mark A. Kramer",
  title =        "The Simultaneous Solution and Sensitivity Analysis of
                 Systems Described by Ordinary Differential Equations",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "45--60",
  month =        mar,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/42288.46156",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05 (65V05)",
  MRnumber =     "89b:65176",
  bibdate =      "Sun Sep 04 21:54:22 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p45-leis/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; experimentation; performance; reliability;
                 theory",
  review =       "ACM CR 8903-0152",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf I.6.4}:
                 Computing Methodologies, SIMULATION AND MODELING, Model
                 Validation and Analysis. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Efficiency.",
}

@Article{Leis:1988:AOO,
  author =       "Jorge R. Leis and Mark A. Kramer",
  title =        "{Algorithm 658}: {ODESSA}: An Ordinary Differential
                 Equation Solver with Explicit Simultaneous Sensitivity
                 Analysis",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "61--67",
  month =        mar,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/42288.214371",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p61-leis/",
  abstract =     "ODESSA is a package of FORTRAN routines for
                 simultaneous solution of ordinary differential
                 equations and the associated first-order parametric
                 sensitivity equations, yielding the ODE solution vector
                 $\underline{y}(t)$ and the first-order sensitivity
                 coefficients with respect to equation parameters
                 $\underline{p}$, $\partial \underline{y}(t)/\partial
                 \underline{p}$. ODESSA is a modification of the widely
                 disseminated initial-value solver LSODE, and retains
                 many of the same operational features. Standard program
                 usage and optional capabilities, installation, and
                 verification considerations are addressed herein.",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems. {\bf G.1.7}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Error analysis. {\bf G.1.7}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Stiff equations. {\bf I.6.4}: Computing Methodologies,
                 SIMULATION AND MODELING, Model Validation and Analysis.
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Efficiency.",
}

@Article{Butcher:1988:TEI,
  author =       "J. C. Butcher",
  title =        "Towards Efficient Implementation of Singly-Implicit
                 Methods",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "68--75",
  month =        mar,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/42288.42341",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05",
  MRnumber =     "89b:65167",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p68-butcher/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  review =       "ACM CR 8812-0938",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems. {\bf G.1.7}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Single step methods. {\bf G.1.7}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations, Stiff equations. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Efficiency.",
}

@Article{Ammann:1988:RCR,
  author =       "Larry Ammann and John {Van Ness}",
  title =        "A Routine for Converting Regression Algorithms into
                 Corresponding Orthogonal Regression Algorithms",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "76--87",
  month =        mar,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/42288.42342",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65U05",
  MRnumber =     "944 765",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p76-ammann/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; reliability",
  review =       "ACM CR 8903-0155",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE. {\bf J.2}: Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING.",
}

@Article{Bratley:1988:AIS,
  author =       "Paul Bratley and Bennett L. Fox",
  title =        "{Algorithm 659}: Implementing {Sobol}'s Quasirandom
                 Sequence Generator",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "88--100",
  month =        mar,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/42288.214372",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p88-bratley/",
  abstract =     "We compare empirically accuracy and speed of
                 low-discrepancy sequence generators of Sobol' and
                 Faure. These generators are useful for multidimensional
                 integration and global optimization. We discuss our
                 implementation of the Sobol' generator.",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency.",
}

@Article{Robertazzi:1988:BOF,
  author =       "T. G. Robertazzi and S. C. Schwartz",
  title =        "Best ``Ordering'' for Floating-Point Addition",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "101--110",
  month =        mar,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/42288.42343",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G99 (65V05)",
  MRnumber =     "89b:65117",
  bibdate =      "Sat Nov 19 13:08:22 1994",
  bibsource =    "ACM Computing Archive CD-ROM database (1991);
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-1/p101-robertazzi/",
  acknowledgement = ack-nhfb,
  affiliation =  "State Univ. of New York at Stony Brook, Stony Brook;
                 Princeton Univ., Princeton, NJ",
  bibno =        "42343",
  catcode =      "G.1.0",
  content =      "This paper compares a variety of methods for
                 accumulating a floating-point sum. Wilkinson pointed
                 out that if we compute the $\sum^n_{i = 1} x_i$ in
                 strictly increasing order in magnitude of the $x_i$,
                 then we obtain a better bound on the rounding error
                 than if the sum is computed in random order
                 [1].\par

                 The authors discuss five different accumulation
                 strategies. They compare these accumulation strategies
                 for when the $x_i$ are uniformly distributed and for
                 when they are exponentially distributed. First they
                 compare a random order for summing the $x_i$, summing
                 in decreasing order of magnitude, and summing in
                 increasing order of magnitude. Not surprisingly,
                 summing in increasing order of magnitude is the best
                 and summing in decreasing order of magnitude is the
                 worst. In fact, it is not difficult to show this for
                 any class of distributions where the mean and variance
                 exist.\par

                 The interesting results in the paper concern two other
                 accumulation strategies. Both of these are shown to be
                 better than summing in increasing order of magnitude
                 for both the uniform and exponential distribution.
                 Fortunately, one of these strategies is the tree sum
                 (or fan-in sum) that is often used in parallel
                 computation. The paper calls this strategy the
                 ``adjacency'' ordering.",
  CRclass =      "G.1.0 General; G.1.0 Computer arithmetic",
  CRnumber =     "8810-0794",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  genterm =      "ALGORITHMS; PERFORMANCE",
  journal-URL =  "https://dl.acm.org/loi/toms",
  journalabbrev = "ACM Trans. Math. Softw.",
  keywords =     "accurate floating-point summation; algorithms;
                 performance",
  review =       "ACM CR 8810-0794",
  reviewer =     "Jesse L. Barlow",
  subject =      "G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS;
                 G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic",
}

@Article{Monahan:1988:CAG,
  author =       "John F. Monahan",
  title =        "Corrigendum: ``{An} Algorithm for Generating Chi
                 Random Variables''",
  journal =      j-TOMS,
  volume =       "14",
  number =       "1",
  pages =        "111--111",
  month =        mar,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/42288.356228",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "111. 65C10",
  MRnumber =     "89d:65006, 88d:65013",
  bibdate =      "Fri Mar 28 10:45:16 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Monahan:1987:AGC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Melhem:1988:MRS,
  author =       "Rami G. Melhem and K. V. S. Ramarao",
  title =        "Multicolor Reordering of Sparse Matrices Resulting
                 from Irregular Grids",
  journal =      j-TOMS,
  volume =       "14",
  number =       "2",
  pages =        "117--138",
  month =        jun,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/45054.214373",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F50 (65D30)",
  MRnumber =     "90b:65084",
  bibdate =      "Mon Dec 08 12:15:02 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-2/p117-melhem/",
  abstract =     "Many iterative algorithms for the solution of large
                 linear systems may be effectively vectorized if the
                 diagonal of the matrix is surrounded by a large band of
                 zeroes, whose width is called the zero stretch. In this
                 paper, a multicolor numbering technique is suggested
                 for maximizing the zero stretch of irregularly sparse
                 matrices. The technique, which is a generalization of a
                 known multicoloring algorithm for regularly sparse
                 matrices, executes in linear time, and produces a zero
                 stretch approximately equal to $n/2\sigma$, where
                 $2\sigma$ is the number of colors used in the
                 algorithm. For triangular meshes, it is shown that
                 $\sigma \leq 3$, and that it is possible to obtain
                 $\sigma=2$ by applying a simple backtracking scheme.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance; theory",
  reviewer =     "Stephen W. Brady",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Sparse and very
                 large systems. {\bf G.1.4}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation, Iterative methods. {\bf G.2.2}:
                 Mathematics of Computing, DISCRETE MATHEMATICS, Graph
                 Theory, Graph algorithms. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.",
}

@Article{Renka:1988:MIL,
  author =       "Robert J. Renka",
  title =        "Multivariate Interpolation of Large Sets of Scattered
                 Data",
  journal =      j-TOMS,
  volume =       "14",
  number =       "2",
  pages =        "139--148",
  month =        jun,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/45054.45055",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D05 (41A05)",
  MRnumber =     "89d:65009",
  bibdate =      "Sun Sep 04 22:00:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-2/p139-renka/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  review =       "ACM CR 8903-0148",
  subject =      "{\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Renka:1988:AQQa,
  author =       "Robert J. Renka",
  title =        "{Algorithm 660}: {QSHEP2D}: Quadratic {Shepard} Method
                 for Bivariate Interpolation of Scattered Data",
  journal =      j-TOMS,
  volume =       "14",
  number =       "2",
  pages =        "149--150",
  month =        jun,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/45054.356231",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 10:45:50 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Renka:1988:AQQb,
  author =       "Robert J. Renka",
  title =        "{Algorithm 661}: {QSHEP3D}; Quadratic {Shepard} Method
                 for Trivariate Interpolation of Scattered Data",
  journal =      j-TOMS,
  volume =       "14",
  number =       "2",
  pages =        "151--152",
  month =        jun,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/45054.214374",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-2/p151-renka/",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Wan:1988:AMD,
  author =       "S. J. Wan and S. K. M. Wong and P. Prusinkiewicz",
  title =        "An Algorithm for Multidimensional Data Clustering",
  journal =      j-TOMS,
  volume =       "14",
  number =       "2",
  pages =        "153--162",
  month =        jun,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/45054.45056",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:00:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-2/p153-wan/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  review =       "ACM CR 8912-0911",
  subject =      "{\bf I.5.3}: Computing Methodologies, PATTERN
                 RECOGNITION, Clustering, Algorithms.",
}

@Article{Garbow:1988:SIW,
  author =       "B. S. Garbow and G. Giunta and J. N. Lyness and A.
                 Murli",
  title =        "Software for an Implementation of {Weeks}' Method for
                 the Inverse {Laplace} Transform",
  journal =      j-TOMS,
  volume =       "14",
  number =       "2",
  pages =        "163--170",
  month =        jun,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/45054.45057",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65R10 (65V05)",
  MRnumber =     "89d:65107",
  bibdate =      "Sun Sep 04 22:01:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-2/p163-garbow/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  review =       "ACM CR 8903-0153",
  subject =      "{\bf G.1.9}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Integral Equations, Fredholm equations. {\bf
                 G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Nonlinear approximation. {\bf G.1.4}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Quadrature and Numerical Differentiation, Finite
                 difference methods.",
}

@Article{Garbow:1988:AFS,
  author =       "B. S. Garbow and G. Giunta and J. N. Lyness and A.
                 Murli",
  title =        "{Algorithm 662}: {A FORTRAN} Software Package for the
                 Numerical Inversion of the {Laplace} Transform Based on
                 {Weeks}' Method",
  journal =      j-TOMS,
  volume =       "14",
  number =       "2",
  pages =        "171--176",
  month =        jun,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/45054.214375",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 4 23:29:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Garbow:1990:RFS}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-2/p171-garbow/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.m}: Mathematics of Computing, MISCELLANEOUS.",
}

@Article{Louter-Nool:1988:ATA,
  author =       "Margreet Louter-Nool",
  title =        "{Algorithm 663}: Translation of {Algorithm} 539:
                 {Basic Linear Algebra Subprograms} for {FORTRAN} Usage
                 in {FORTRAN} 200 for the {Cyber} 205",
  journal =      j-TOMS,
  volume =       "14",
  number =       "2",
  pages =        "177--195",
  month =        jun,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/45054.45058",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 23:08:05 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Lawson:1979:ABL,Dodson:1982:RBL,Dodson:1983:CRB,Hanson:1987:ATA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-2/p177-louter-nool/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance",
  review =       "ACM CR 8904-0243",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency. {\bf D.3.2}: Software, PROGRAMMING
                 LANGUAGES, Language Classifications, FORTRAN.",
}

@Article{Diaz:1988:RCA,
  author =       "J. C. Diaz and G. Fairweather and P. Keast",
  title =        "Remark on ``{Algorithm} 603: {COLROW} and {ARCECO}:
                 {FORTRAN} Packages for Solving Certain Almost Block
                 Diagonal Linear Systems by Modified Alternate Row and
                 Column Elimination''",
  journal =      j-TOMS,
  volume =       "14",
  number =       "2",
  pages =        "196--196",
  month =        jun,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/45054.356237",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 21:59:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Diaz:1983:ACA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hull:1988:EHS,
  author =       "T. E. Hull and M. S. Cohen and J. T. M. Sawshuk and D.
                 B. Wortman",
  title =        "Exception Handling in Scientific Computing",
  journal =      j-TOMS,
  volume =       "14",
  number =       "3",
  pages =        "201--217",
  month =        sep,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/44128.44129",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:27:23 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-3/p201-hull/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "design; languages",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Specialized application languages.
                 {\bf D.3.3}: Software, PROGRAMMING LANGUAGES, Language
                 Constructs and Features, Control structures. {\bf
                 D.3.4}: Software, PROGRAMMING LANGUAGES, Processors,
                 Compilers. {\bf D.3.4}: Software, PROGRAMMING
                 LANGUAGES, Processors, Run-time environments. {\bf
                 G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Numerical algorithms. {\bf G.4}: Mathematics
                 of Computing, MATHEMATICAL SOFTWARE, Algorithm
                 analysis.",
}

@Article{Freeman:1988:DSM,
  author =       "Timothy S. Freeman and Gregory M. Imirzian and Erich
                 Kaltofen and Lakshman Yagati",
  title =        "{Dagwood}: a System for Manipulating Polynomials Given
                 by Straight-Line Programs",
  journal =      j-TOMS,
  volume =       "14",
  number =       "3",
  pages =        "218--240",
  month =        sep,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/44128.214376",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:27:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-3/p218-freeman/",
  abstract =     "We discuss the design, implementation, and
                 benchmarking of a system that can manipulate symbolic
                 expressions represented by their straight-line
                 computations. Our system is capable of performing
                 rational arithmetic on, evaluating, differentiating,
                 taking greatest common divisors of, and factoring
                 polynomials in straight-line format. The straight-line
                 results can also be converted to standard, sparse
                 format. We show by example that our system can handle
                 problems for which conventional methods lead to
                 excessive intermediate expression swell.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; measurement; performance",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Efficiency. {\bf I.1.1}: Computing
                 Methodologies, ALGEBRAIC MANIPULATION, Expressions and
                 Their Representation, Representations (general and
                 polynomial). {\bf I.1.3}: Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Languages and Systems,
                 Special-purpose algebraic systems.",
}

@Article{Grimes:1988:SLD,
  author =       "Roger G. Grimes and Horst D. Simon",
  title =        "Solution of Large, Dense Symmetric Generalized
                 Eigenvalue Problems Using Secondary Storage",
  journal =      j-TOMS,
  volume =       "14",
  number =       "3",
  pages =        "241--256",
  month =        sep,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/44128.44130",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65F15)",
  MRnumber =     "1 062 476",
  bibdate =      "Sun Sep 04 22:29:30 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-3/p241-grimes/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  review =       "ACM CR 8903-0149",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf
                 G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Numerical Linear Algebra, Sparse and very large
                 systems. {\bf D.4.2}: Software, OPERATING SYSTEMS,
                 Storage Management, Secondary storage.",
}

@Article{Schrauf:1988:AGA,
  author =       "G{\'e}za Schrauf",
  title =        "{Algorithm 664}: {A Gauss} Algorithm to Solve Systems
                 with Large Banded Matrices Using Random-Access Disk
                 Storage",
  journal =      j-TOMS,
  volume =       "14",
  number =       "3",
  pages =        "257--260",
  month =        sep,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/44128.214379",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-3/p257-schrauf/",
  abstract =     "A FORTRAN 77 implementation of a Gauss algorithm with
                 partial pivoting for banded matrices is described. The
                 algorithm keeps only part of the matrix that is
                 necessary for the actual computation in memory. This
                 allows large systems to be solved on machine without
                 virtual memory, or if the virtual memory is too small
                 for the problem.",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf F.2.1}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms. {\bf G.1.3}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative methods).
                 {\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Sparse and very
                 large systems.",
}

@Article{Minh:1988:GGV,
  author =       "Do Le Minh",
  title =        "Generating Gamma Variates",
  journal =      j-TOMS,
  volume =       "14",
  number =       "3",
  pages =        "261--266",
  month =        sep,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/44128.214382",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65U05)",
  MRnumber =     "1 062 477",
  bibdate =      "Sun Sep 04 22:30:10 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-3/p261-minh/",
  abstract =     "An algorithm to generate variates having a gamma
                 distribution with shape parameter greater than one is
                 presented in this paper. This algorithm is faster than
                 Schmeiser and Lal's G4PE, which is the fastest one
                 currently available, yet is equally simple and easy to
                 implement.",
  acknowledgement = ack-nhfb,
  country =      "USA",
  date =         "13/05/93",
  descriptors =  "RVG",
  enum =         "7672",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  language =     "English",
  location =     "SEL: Wi",
  references =   "0",
  revision =     "16/01/94",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS. {\bf I.6.1}: Computing Methodologies,
                 SIMULATION AND MODELING, Simulation Theory.",
}

@Article{Duff:1988:RIN,
  author =       "Iain S. Duff and Torbj{\"o}rn Wiberg",
  title =        "Remarks on Implementation of ${O}(n^{1/2}\tau)$
                 Assignment Algorithms",
  journal =      j-TOMS,
  volume =       "14",
  number =       "3",
  pages =        "267--287",
  month =        sep,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/44128.44131",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65F50)",
  MRnumber =     "1 062 478",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-3/p267-duff/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  review =       "ACM CR 8904-0244",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Sparse and very
                 large systems. {\bf G.2.2}: Mathematics of Computing,
                 DISCRETE MATHEMATICS, Graph Theory, Graph algorithms.
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Algorithm analysis.",
}

@Article{Cormack:1988:RTP,
  author =       "R. S. Cormack and I. D. Hill",
  title =        "Remark on ``{Algorithm} 346: ${F}$-Test
                 Probabilities''",
  journal =      j-TOMS,
  volume =       "14",
  number =       "3",
  pages =        "288--289",
  month =        sep,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/44128.356244",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:27:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Morris:1969:TP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Krogh:1988:AAP,
  author =       "Fred T. Krogh",
  title =        "{ACM} Algorithms Policy",
  journal =      j-TOMS,
  volume =       "14",
  number =       "3",
  pages =        "290--293",
  month =        sep,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/44128.356245",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:27:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Foley:1988:CIP,
  author =       "Thomas A. Foley",
  title =        "Corrigendum: ``{Interpolation} with Interval and Point
                 Tension Controls Using Cubic Weighted $v$-Splines''",
  journal =      j-TOMS,
  volume =       "14",
  number =       "3",
  pages =        "297--297",
  month =        sep,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/44128.356246",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:26:45 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Foley:1987:IIP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cody:1988:AMS,
  author =       "W. J. Cody",
  title =        "{Algorithm 665}: {MACHAR}: a Subroutine to Dynamically
                 Determine Machine Parameters",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "303--311",
  month =        dec,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/50063.51907",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:33:58 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p303-cody/",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Portability. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Computer
                 arithmetic.",
}

@Article{Vrahatis:1988:SSN,
  author =       "Michael N. Vrahatis",
  title =        "Solving Systems of Nonlinear Equations Using the
                 Nonzero Value of the Topological Degree",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "312--329",
  month =        dec,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/50063.214384",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65H10 90C30)",
  MRnumber =     "91g:65006",
  bibdate =      "Sun Sep 04 22:34:19 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p312-vrahatis/",
  abstract =     "Two algorithms are described here for the numerical
                 solution of a system of nonlinear equations $F(X) =
                 \Theta, Q=(0,0,\ldots,0)$ in $R$, and $F$ is a given
                 continuous mapping of a region $D$ in $R^{n}$ into
                 $R^{n}$. The first algorithm locates at least one root
                 of the sy stem within $n$-dimensional polyhedron, using
                 the nonzero value of the topological degree of $F$ at
                 [theta] relative to the polyhedron; the second
                 algorithm applies a new generalized bisection method in
                 order to compute an approximate solution to the system.
                 The size of the original $n$-dimensional polyhedron is
                 arbitrary, and the method is globally convergent in a
                 residual sense.\par

                 These algorithms, in the various function evaluations,
                 only make use of the algebraic sign of $F$ and do not
                 require computations of the topological degree.
                 Moreover, they can be applied to nondifferentiable
                 continuous functions $F$ and do not involve derivatives
                 of $F$ or approximations of such derivatives.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.5}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Systems of
                 equations. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis.",
}

@Article{Vrahatis:1988:ACM,
  author =       "Michael N. Vrahatis",
  title =        "{Algorithm 666}: {CHABIS}: a Mathematical Software
                 Package for Locating and Evaluating Roots of Systems of
                 Nonlinear Equations",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "330--336",
  month =        dec,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/50063.51906",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (90C30)",
  MRnumber =     "91g:65007",
  bibdate =      "Sat Aug 27 15:08:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p330-vrahatis/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Portability. {\bf G.1.5}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
                 Equations, Systems of equations.",
}

@Article{Garavelli:1988:AMS,
  author =       "John S. Garavelli",
  title =        "An Algorithm for the Multiplication of Symmetric
                 Polynomials",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "337--344",
  month =        dec,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/50063.214385;
                 http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p337-garavelli/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "05-04 (68Q40)",
  MRnumber =     "91f:05002",
  bibdate =      "Sun Sep 04 22:34:19 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Although the cycle index polynomial for a permutation
                 group can often be easily determined, expansion of the
                 figure counting series in a P{\'o}lya enumeration
                 presents computational difficulties for object sets
                 with higher degrees of symmetry and more than modest
                 size. An algorithm that does not require algebraic
                 symbol manipulation is derived for multiplying
                 symmetric polynomials represented by partitions.
                 Because the repetitive identification and collection of
                 common terms are eliminated and storage requirements
                 reduced, this algorithm is useful in rapidly expanding
                 the figure counting series in such P{\'o}lya
                 enumeration problems as the counting of chemical
                 isomers.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  reviewer =     "Kevin Lawrence McAvaney",
  subject =      "{\bf G.2.1}: Mathematics of Computing, DISCRETE
                 MATHEMATICS, Combinatorics, Combinatorial algorithms.
                 {\bf I.1.1}: Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Expressions and Their Representation,
                 Representations (general and polynomial). {\bf I.1.2}:
                 Computing Methodologies, ALGEBRAIC MANIPULATION,
                 Algorithms, Algebraic algorithms.",
}

@Article{Aluffi-Pentini:1988:GOA,
  author =       "Filippo Aluffi-Pentini and Valerio Parisi and
                 Francesco Zirilli",
  title =        "A Global Optimization Algorithm Using Stochastic
                 Differential Equations",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "345--365",
  month =        dec,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/50063.50064",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65K05 90C30)",
  MRnumber =     "1 062 482",
  bibdate =      "Sun Sep 04 22:36:23 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p345-aluffi-pentini/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; languages; theory; verification",
  review =       "ACM CR 8907-0480",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing.",
}

@Article{Aluffi-Pentini:1988:ASE,
  author =       "Filippo Aluffi-Pentini and Valerio Parisi and
                 Francesco Zirilli",
  title =        "{Algorithm 667}: {SIGMA}\emdash a
                 Stochastic-Integration Global Minimization Algorithm",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "366--380",
  month =        dec,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/50063.51908",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (90C30)",
  MRnumber =     "1 062 483",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p366-aluffi-pentini/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Portability. {\bf G.1.6}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization.",
}

@Article{Higham:1988:AFC,
  author =       "Nicholas J. Higham",
  title =        "{Algorithm 674}: {FORTRAN} Codes for Estimating the
                 One-Norm of a Real or Complex Matrix, with Applications
                 to Condition Estimation",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "381--396",
  month =        dec,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/50063.214386",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65F35)",
  MRnumber =     "1 062 484",
  bibdate =      "Sat Aug 27 15:05:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Higham:1989:CFC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p381-higham/",
  abstract =     "FORTRAN 77 codes SONEST and CONEST are presented for
                 estimating the 1-norm ( or the infinity-norm) of a real
                 or complex matrix, respectively. The codes are of wide
                 applicability in condition estimation since explicit
                 access to the matrix, $A$, is not required; instead,
                 matrix-vector products $Ax$ and $A^Tx$ are computed by
                 the calling program via a reverse communication
                 interface. The algorithms are based on a convex
                 optimization method for estimating the 1-norm of a real
                 matrix devised by Hager. We derive new results
                 concerning the behavior of Hager's method, extend it to
                 complex matrices, and make several algorithmic
                 modifications in order to improve the reliability and
                 efficiency.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; condition estimation; nla; software",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra.",
}

@Article{Kachitvichyanukul:1988:AHS,
  author =       "Voratas Kachitvichyanukul and Bruce W. Schmeiser",
  title =        "{Algorithm 668}: {H2PEC}: Sampling from the
                 Hypergeometric Distribution",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "397--398",
  month =        dec,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/50063.214387",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 4 22:37:31 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1988-14-4/p397-kachitvichyanukul/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Random number generation. {\bf G.m}:
                 Mathematics of Computing, MISCELLANEOUS.",
}

@Article{Dongarra:1988:CES,
  author =       "Jack J. Dongarra and Jeremy {Du Croz} and Sven
                 Hammarling and Richard J. Hanson",
  title =        "Corrigenda: ``{An} Extended Set of {FORTRAN Basic
                 Linear Algebra Subprograms}''",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "399--399",
  month =        dec,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/50063.356256",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 10:48:38 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Dongarra:1988:ESF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kearfott:1988:CTG,
  author =       "R. Baker Kearfott",
  title =        "Corrigenda: ``{Some} Tests of Generalized
                 Bisection''",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "399--399",
  month =        dec,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/50063.356257",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "399 (1989). 65H10",
  MRnumber =     "1 062 485, 88m:65081",
  bibdate =      "Sat Nov 19 13:04:08 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Kearfott:1987:STG}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Anonymous:1988:FCA,
  author =       "Anonymous",
  title =        "Five-Year Cumulative Author Index (Vol. 10--14.
                 1984--1988)",
  journal =      j-TOMS,
  volume =       "14",
  number =       "4",
  pages =        "403--411",
  month =        dec,
  year =         "1988",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/50063.356247",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "00A15",
  MRnumber =     "1 062 486",
  bibdate =      "Fri Mar 28 10:56:10 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Duff:1989:SMT,
  author =       "Iain S. Duff and Roger G. Grimes and John G. Lewis",
  title =        "Sparse Matrix Test Problems",
  journal =      j-TOMS,
  volume =       "15",
  number =       "1",
  pages =        "1--14",
  month =        mar,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/62038.62043",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:42:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-1/p1-duff/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "measurement; performance",
  review =       "ACM CR 9002-0143",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Sparse and very
                 large systems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE.",
}

@Article{Cash:1989:BRK,
  author =       "J. R. Cash",
  title =        "A Block 6(4) {Runge--Kutta} Formula for Nonstiff
                 Initial Value Problems",
  journal =      j-TOMS,
  volume =       "15",
  number =       "1",
  pages =        "15--28",
  month =        mar,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/62038.62042",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:42:48 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-1/p15-cash/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance; theory",
  review =       "ACM CR 8909-0672",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE. {\bf G.1.1}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Interpolation,
                 Interpolation formulas.",
}

@Article{Cash:1989:ABF,
  author =       "J. R. Cash",
  title =        "{Algorithm 669}: {BRKF45}: {A FORTRAN} Subroutine for
                 Solving First-Order Systems of Nonstiff Initial Value
                 Problems for Ordinary Differential Equations",
  journal =      j-TOMS,
  volume =       "15",
  number =       "1",
  pages =        "29--30",
  month =        mar,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/62038.214388",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:44:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Higham:1991:RBF}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-1/p29-cash/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Interpolation formulas. {\bf
                 G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Ordinary Differential Equations, Initial value
                 problems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE.",
}

@Article{Brankin:1989:ARK,
  author =       "R. W. Brankin and I. Gladwell and J. R. Dormand and P.
                 J. Prince and W. L. Seward",
  title =        "{Algorithm 670}: a {Runge--Kutta--Nystr{\"o}m} code",
  journal =      j-TOMS,
  volume =       "15",
  number =       "1",
  pages =        "31--40",
  month =        mar,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/62038.69650",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-1/p31-brankin/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness.",
}

@Article{Cody:1989:PEP,
  author =       "W. J. Cody and L. Stoltz",
  title =        "Performance Evaluation of Programs for Certain
                 {Bessel} Functions",
  journal =      j-TOMS,
  volume =       "15",
  number =       "1",
  pages =        "41--48",
  month =        mar,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/62038.62039",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:43:58 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-1/p41-cody/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance; reliability; verification",
  review =       "ACM CR 8911-0825",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms.",
}

@Article{Shanno:1989:NES,
  author =       "David F. Shanno and Kang Hoh Phua",
  title =        "Numerical Experience with Sequential Quadratic
                 Programming Algorithms for Equality Constrained
                 Nonlinear Programming",
  journal =      j-TOMS,
  volume =       "15",
  number =       "1",
  pages =        "49--63",
  month =        mar,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/62038.62040",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "90C30 (90B20)",
  MRnumber =     "91c:90104",
  bibdate =      "Sun Sep 04 22:44:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-1/p49-shanno/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  review =       "ACM CR 8909-0670",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Nonlinear programming. {\bf
                 G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Constrained optimization.",
}

@Article{Chang:1989:IPS,
  author =       "Michael D. Chang and Chou-Hong J. Chen and Michael
                 Engquist",
  title =        "An Improved Primal Simplex Variant for Pure Processing
                 Networks",
  journal =      j-TOMS,
  volume =       "15",
  number =       "1",
  pages =        "64--78",
  month =        mar,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/62038.62041",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-1/p64-chang/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; performance; theory",
  review =       "ACM CR 8909-0669",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Linear programming. {\bf
                 G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS,
                 Graph Theory, Network problems. {\bf G.4}: Mathematics
                 of Computing, MATHEMATICAL SOFTWARE, Efficiency.",
}

@Article{Preusser:1989:AFF,
  author =       "Albrecht Preusser",
  title =        "{Algorithm 671}: {FARB-E-2D}: Fill Area with Bicubics
                 on Rectangles\emdash a Contour Plot Program",
  journal =      j-TOMS,
  volume =       "15",
  number =       "1",
  pages =        "79--89",
  month =        mar,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/62038.69651",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:46:19 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-1/p79-preusser/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design",
  subject =      "{\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Spline and piecewise
                 polynomial interpolation. {\bf I.3.5}: Computing
                 Methodologies, COMPUTER GRAPHICS, Computational
                 Geometry and Object Modeling, Curve, surface, solid,
                 and object representations.",
}

@Article{Morgan:1989:FAI,
  author =       "Alexander P. Morgan and Andrew J. Sommese and Layne T.
                 Watson",
  title =        "Finding All Isolated Solutions to Polynomial Systems
                 Using {HOMPACK}",
  journal =      j-TOMS,
  volume =       "15",
  number =       "2",
  pages =        "93--122",
  month =        jun,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/63522.64124",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (58C30 65H10)",
  MRnumber =     "91g:65003",
  bibdate =      "Sun Sep 04 22:46:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p93-morgan/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  review =       "ACM CR 8912-0895",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, HOMPACK. {\bf G.1.5}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
                 Equations, Systems of equations. {\bf G.1.5}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations, Polynomials, methods for.",
}

@Article{Patterson:1989:AGIa,
  author =       "T. N. L. Patterson",
  title =        "An Algorithm for Generating Interpolatory Quadrature
                 Rules of the Highest Degree of Precision with
                 Preassigned Nodes for General Weight Functions",
  journal =      j-TOMS,
  volume =       "15",
  number =       "2",
  pages =        "123--136",
  month =        jun,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/63522.63523",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65D32)",
  MRnumber =     "91g:65004",
  bibdate =      "Sun Sep 04 22:46:58 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p123-patterson/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  review =       "ACM CR 9006-0500",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation,
                 Gaussian quadrature. {\bf G.1.1}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Interpolation. {\bf
                 F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on polynomials.",
}

@Article{Patterson:1989:AGIb,
  author =       "T. N. L. Patterson",
  title =        "{Algorithm 672}: Generation of Interpolatory
                 Quadrature Rules of the Highest Degree of Precision
                 with Preassigned Nodes for General Weight Functions",
  journal =      j-TOMS,
  volume =       "15",
  number =       "2",
  pages =        "137--143",
  month =        jun,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/63522.69649",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04",
  MRnumber =     "91g:65005",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p137-patterson/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; languages; performance",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.
                 {\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.",
}

@Article{Tang:1989:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Exponential
                 Function in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "15",
  number =       "2",
  pages =        "144--157",
  month =        jun,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/63522.214389",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:47:40 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p144-tang/",
  abstract =     "Algorithms and implementation details for the
                 exponential function in both single- and
                 double-precision of IEEE 754 arithmetic are presented
                 here. With a table of moderate size, the
                 implementations need only working-precision arithmetic
                 and are provably accurate to within 0.54 ulp as long as
                 the final result does not underflow. When the final
                 result suffers gradual underflow, the error is still no
                 worse than 0.77 ulp.",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@Article{Vitter:1989:ADH,
  author =       "Jeffrey Scott Vitter",
  title =        "{Algorithm 673}: Dynamic {Huffman} Coding",
  journal =      j-TOMS,
  volume =       "15",
  number =       "2",
  pages =        "158--167",
  month =        jun,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/63522.214390",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:47:58 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Novoselsky:2016:RAD}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p158-vitter/",
  abstract =     "We present a Pascal implementation of the one-pass
                 algorithm for constructing dynamic Huffman codes that
                 is described and analyzed in a companion paper. The
                 program runs in real time; that is, the processing time
                 for each letter of the message is proportional to the
                 length of its codeword. The number of bits used to
                 encode a message of $t$ letters is less than $t$ bits
                 more than that used by the well-known two-pass
                 algorithm. This is best possible for any one-pass
                 Huffman scheme. In practice, it uses fewer bits than
                 all other Huffman schemes. The algorithm has
                 applications in file compression and network
                 transmission.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; performance; theory",
  subject =      "{\bf C.2.0}: Computer Systems Organization,
                 COMPUTER-COMMUNICATION NETWORKS, General, Data
                 communications. {\bf E.1}: Data, DATA STRUCTURES,
                 Trees. {\bf E.4}: Data, CODING AND INFORMATION THEORY,
                 Data compaction and compression. {\bf E.4}: Data,
                 CODING AND INFORMATION THEORY, Nonsecret encoding
                 schemes. {\bf F.2.2}: Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems. {\bf G.2.2}: Mathematics of
                 Computing, DISCRETE MATHEMATICS, Graph Theory, Trees.
                 {\bf H.1.1}: Information Systems, MODELS AND
                 PRINCIPLES, Systems and Information Theory, Value of
                 information.",
}

@Article{Higham:1989:CFC,
  author =       "Nicholas J. Higham",
  title =        "Corrigendum: ``{Algorithm} 674: {FORTRAN} Codes for
                 Estimating the One-Norm of a Real or Complex Matrix,
                 with Applications to Condition Estimation''",
  journal =      j-TOMS,
  volume =       "15",
  number =       "2",
  pages =        "168--168",
  month =        jun,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/63522.214391",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:18:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Higham:1988:AFC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-2/p168-higham/",
  abstract =     "We omitted giving this article an ACM algorithm number
                 when it was first published in its entirety in the
                 December 1988 issue of {\em TOMS}, Vol. 14, No. 4, pp.
                 381-396. To correct this, we do so here, and reprint
                 the title as a pointer to the original article.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra.",
}

@Article{Krogh:1989:AAP,
  author =       "Fred T. Krogh",
  title =        "{ACM} Algorithms Policy",
  journal =      j-TOMS,
  volume =       "15",
  number =       "2",
  pages =        "169--172",
  month =        jun,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/63522.356273",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 10:56:42 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ribbens:1989:FAG,
  author =       "Calvin J. Ribbens",
  title =        "A Fast Adaptive Grid Scheme for Elliptic Partial
                 Differential Equations",
  journal =      j-TOMS,
  volume =       "15",
  number =       "3",
  pages =        "179--197",
  month =        sep,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/66888.66889",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:50:47 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-3/p179-ribbens/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  review =       "ACM CR 9006-0506",
  subject =      "{\bf G.1.8}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations, Elliptic
                 equations. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Parallel algorithms.",
}

@Article{Liu:1989:GPA,
  author =       "Joseph W. H. Liu",
  title =        "A Graph Partitioning Algorithm by Node Separators",
  journal =      j-TOMS,
  volume =       "15",
  number =       "3",
  pages =        "198--219",
  month =        sep,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/66888.66890",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (05-04 05C70 65F50)",
  MRnumber =     "1 062 491",
  bibdate =      "Sun Sep 04 22:51:08 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-3/p198-liu/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  review =       "ACM CR 9003-0235",
  subject =      "{\bf G.2.2}: Mathematics of Computing, DISCRETE
                 MATHEMATICS, Graph Theory, Graph algorithms. {\bf
                 G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Numerical Linear Algebra, Sparse and very large
                 systems. {\bf F.2.1}: Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices.",
}

@Article{Mahdavi-Amiri:1989:CNL,
  author =       "Nezam Mahdavi-Amiri and Richard H. Bartels",
  title =        "Constrained Nonlinear Least Squares: An Exact Penalty
                 Approach with Projected Structured Quasi-{Newton}
                 Updates",
  journal =      j-TOMS,
  volume =       "15",
  number =       "3",
  pages =        "220--242",
  month =        sep,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/66888.66891",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65K05)",
  MRnumber =     "1 062 492",
  bibdate =      "Sun Sep 04 22:51:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-3/p220-mahdavi-amiri/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  review =       "ACM CR 9004-0320",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization. {\bf G.1.5}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
                 Equations.",
}

@Article{Vanbegin:1989:AFS,
  author =       "Michel Vanbegin and Paul {Van Dooren} and Michel
                 Verhaegen",
  title =        "{Algorithm 675}: {FORTRAN} Subroutines for Computing
                 the Square Root Covariance Filter and Square Root
                 Information Filter in Dense or {Hessenberg} Forms",
  journal =      j-TOMS,
  volume =       "15",
  number =       "3",
  pages =        "243--256",
  month =        sep,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/66888.69647",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:52:41 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-3/p243-vanbegin/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Algorithm analysis. {\bf G.1.3}: Mathematics
                 of Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative methods).
                 {\bf F.2.1}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices.",
}

@Article{Dadurkevicius:1989:RA,
  author =       "Virgis Dadurkevi{\v{c}}ius",
  title =        "Remark on ``{Algorithm} 587: Two Algorithms for the
                 Linearly Constrained Least Squares Problem''",
  journal =      j-TOMS,
  volume =       "15",
  number =       "3",
  pages =        "257--261",
  month =        sep,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/66888.77344",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 20:52:30 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Hanson:1982:ATA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-3/p257-dadurkevicius/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Constrained optimization. {\bf
                 G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Least squares approximation. {\bf
                 G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Least squares methods.",
}

@Article{Buckley:1989:RA,
  author =       "A. Buckley",
  title =        "Remark on {Algorithm 630}",
  journal =      j-TOMS,
  volume =       "15",
  number =       "3",
  pages =        "262--274",
  month =        sep,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/66888.69648",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:53:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Buckley:1985:ABE}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-3/p262-buckley/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Gradient methods.",
}

@Article{Domich:1989:RHN,
  author =       "Paul D. Domich",
  title =        "Residual {Hermite} Normal Form Computations",
  journal =      j-TOMS,
  volume =       "15",
  number =       "3",
  pages =        "275--286",
  month =        sep,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/66888.66892",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "15A21 (15-04 15A36 65-04 65F05)",
  MRnumber =     "91d:15020",
  bibdate =      "Sun Sep 04 22:53:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-3/p275-domich/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  review =       "ACM CR 9007-0597",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra. {\bf F.2.1}: Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices.",
}

@Article{Corana:1989:CMF,
  author =       "A. Corana and M. Marchesi and C. Martini and S.
                 Ridella",
  title =        "Corrigenda: ``{Minimizing} Multimodal Functions of
                 Continuous Variables with the `Simulated Annealing'
                 Algorithm''",
  journal =      j-TOMS,
  volume =       "15",
  number =       "3",
  pages =        "287--287",
  month =        sep,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/66888.356281",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "287. 90C30 (65K05)",
  MRnumber =     "1 062 494, 88m:90121",
  bibdate =      "Sat Feb 24 09:58:06 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Corana:1987:MMF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Enright:1989:CFP,
  author =       "W. H. Enright and J. D. Pryce",
  title =        "Corrigenda: ``{Two FORTRAN} Packages for Assessing
                 Initial Value Methods''",
  journal =      j-TOMS,
  volume =       "15",
  number =       "3",
  pages =        "287--287",
  month =        sep,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/66888.356282",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 10:57:50 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Enright:1987:TFP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Le:1989:CED,
  author =       "D. Le",
  title =        "Corrigenda: ``{An} Efficient Derivative-Free Method
                 for Solving Nonlinear Equations''",
  journal =      j-TOMS,
  volume =       "15",
  number =       "3",
  pages =        "287--287",
  month =        sep,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/66888.356283",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "287. 65H05",
  MRnumber =     "1 062 495, 87d:65057",
  bibdate =      "Fri Mar 28 10:57:46 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Le:1985:EDF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ashcraft:1989:IRS,
  author =       "Cleve Ashcraft and Roger Grimes",
  title =        "The Influence of Relaxed Supernode Partitions on the
                 Multifrontal Method",
  journal =      j-TOMS,
  volume =       "15",
  number =       "4",
  pages =        "291--309",
  month =        dec,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/76909.76910",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:58:46 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p291-ashcraft/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; performance",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Sparse and very
                 large systems. {\bf F.2.1}: Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 matrices. {\bf G.2.2}: Mathematics of Computing,
                 DISCRETE MATHEMATICS, Graph Theory. {\bf G.1.3}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Linear systems (direct and iterative
                 methods).",
}

@Article{Liu:1989:MMP,
  author =       "Joseph W. H. Liu",
  title =        "The Multifrontal Method and Paging in Sparse
                 {Cholesky} Factorization",
  journal =      j-TOMS,
  volume =       "15",
  number =       "4",
  pages =        "310--325",
  month =        dec,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/76909.76911",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 22:59:06 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p310-liu/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; experimentation; performance",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Sparse and very
                 large systems. {\bf G.1.3}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix
                 inversion. {\bf D.4.2}: Software, OPERATING SYSTEMS,
                 Storage Management, Virtual memory. {\bf F.2.1}: Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices.",
}

@Article{Mitchell:1989:CAR,
  author =       "William F. Mitchell",
  title =        "A Comparison of Adaptive Refinement Techniques for
                 Elliptic Problems",
  journal =      j-TOMS,
  volume =       "15",
  number =       "4",
  pages =        "326--347",
  month =        dec,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/76909.76912",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65N99 (65-04)",
  MRnumber =     "1 062 496",
  bibdate =      "Sun Sep 04 22:59:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p326-mitchell/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "experimentation",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf G.1.8}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Partial
                 Differential Equations, Finite element methods. {\bf
                 G.1.8}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Partial Differential Equations, Elliptic equations.
                 {\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation.",
}

@Article{Boggs:1989:AOS,
  author =       "Paul T. Boggs and Janet R. Donaldson and Richard h.
                 Byrd and Robert B. Schnabel",
  title =        "{Algorithm 676}: {ODRPACK}: Software for Weighted
                 Orthogonal Distance Regression",
  journal =      j-TOMS,
  volume =       "15",
  number =       "4",
  pages =        "348--364",
  month =        dec,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/76909.76913",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 15:09:23 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p348-boggs/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Statistical computing. {\bf G.1.6}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Least squares methods.",
}

@Article{Montefusco:1989:ASI,
  author =       "Laura Bacchelli Montefusco and Giulio Casciola",
  title =        "{Algorithm 677}: ${C}^1$ Surface Interpolation",
  journal =      j-TOMS,
  volume =       "15",
  number =       "4",
  pages =        "365--374",
  month =        dec,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/76909.76914",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:22:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/76909.76914;
                 http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p365-montefusco/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation. {\bf G.1.6}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization.",
}

@Article{Corliss:1989:IIV,
  author =       "George Corliss and Gary Krenz",
  title =        "Indefinite Integration with Validation",
  journal =      j-TOMS,
  volume =       "15",
  number =       "4",
  pages =        "375--393",
  month =        dec,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/76909.76915",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30 (65-04)",
  MRnumber =     "1 062 497",
  bibdate =      "Sun Sep 04 23:01:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p375-corliss/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  review =       "ACM CR 9007-0598",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.
                 {\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation. {\bf G.1.2}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, Chebyshev
                 approximation and theory.",
}

@Article{Kachitvichyanukul:1989:ABS,
  author =       "Voratas Kachitvichyanukul and Bruce W. Schmeiser",
  title =        "{Algorithm 678}: {BTPEC}: Sampling from the Binomial
                 Distribution",
  journal =      j-TOMS,
  volume =       "15",
  number =       "4",
  pages =        "394--397",
  month =        dec,
  year =         "1989",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/76909.76916",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 13 17:26:53 MDT 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1989-15-4/p394-kachitvichyanukul/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Random number generation.",
}

@Article{Dongarra:1990:SLB,
  author =       "Jack J. Dongarra and Jeremy {Du Croz} and Sven
                 Hammarling and Iain Duff",
  title =        "A Set of Level 3 {Basic Linear Algebra Subprograms}",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "1--17",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.79170",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 19:10:43 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p1-dongarra/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance; reliability;
                 verification",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE. {\bf G.1.3}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra, Linear
                 systems (direct and iterative methods). {\bf F.2.1}:
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms.",
}

@Article{Dongarra:1990:ASL,
  author =       "Jack J. Dongarra and Jeremy {Du Croz} and Sven
                 Hammarling and Iain Duff",
  title =        "{Algorithm 679}: a Set of Level 3 {Basic Linear
                 Algebra Subprograms}: Model Implementation and Test
                 Programs",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "18--28",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.77627",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 27 17:29:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also
                 \cite{Higham:1990:EFM,Demmel:1992:SBA,Dayde:1994:PBI}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p18-dongarra/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance; reliability;
                 verification",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 8X. {\bf F.2.1}: Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices. {\bf G.1.3}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative methods).
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE.",
}

@Article{Cody:1990:PEP,
  author =       "W. J. Cody",
  title =        "Performance Evaluation of Programs for the Error and
                 Complementary Error Functions",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "29--37",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.77628",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65G05)",
  MRnumber =     "1 073 407",
  bibdate =      "Tue Oct 09 09:29:47 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p29-cody/;
                 http://www.acm.org/pubs/toc/Abstracts/0098-3500/77628.html",
  abstract =     "This paper presents methods for performance evaluation
                 of computer programs for the functions
                 ${\rm erf}(x)$, ${\rm erfc}(x)$, and $e^{x^2}
                 {\rm erfc}(x)$. Accuracy estimates are based on
                 comparisons using power series expansions and an
                 expansion in the repeated integrals of
                 ${\rm erfc}(x)$. Some suggestions for checking
                 robustness are also given. Details of a specific
                 implementation of a test program are included.",
  acknowledgement = ack-nhfb,
  affiliation =  "Argonne Nat. Lab., IL, USA",
  classification = "B0290B (Error analysis in numerical methods); B0290F
                 (Interpolation and function approximation); C4110
                 (Error analysis in numerical methods); C4130
                 (Interpolation and function approximation)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Complementary error functions; Computer programs;
                 FORTRAN; Power series expansions; Repeated integrals;
                 Robustness; Test program",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms.",
  thesaurus =    "Error analysis; Function approximation; Performance
                 evaluation",
}

@Article{Poppe:1990:MEC,
  author =       "G. P. M. Poppe and C. M. J. Wijers",
  title =        "More Efficient Computation of the Complex Error
                 Function",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "38--46",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.77629",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G05 (65D20)",
  MRnumber =     "91h:65068a",
  bibdate =      "Sun Sep 04 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p38-poppe/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Algorithm analysis. {\bf G.1.2}: Mathematics
                 of Computing, NUMERICAL ANALYSIS, Approximation,
                 Rational approximation.",
}

@Article{Poppe:1990:AEC,
  author =       "G. P. M. Poppe and C. M. J. Wijers",
  title =        "{Algorithm 680}: Evaluation of the Complex Error
                 Function",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "47--47",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.77630",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "47. 65G05 (65-04)",
  MRnumber =     "91h:65068b",
  bibdate =      "Sun Sep 04 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Zaghloul:2019:RO}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p47-poppe/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Rational approximation.",
}

@Article{Arney:1990:AMM,
  author =       "David C. Arney and Joseph E. Flaherty",
  title =        "An Adaptive Mesh-Moving and Local Refinement Method
                 for Time-Dependent Partial Differential Equations",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "48--71",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.77631",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65M50",
  MRnumber =     "91f:65154",
  bibdate =      "Sun Sep 04 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p48-arney/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; performance",
  subject =      "{\bf G.1.8}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations, Finite
                 element methods. {\bf G.1.8}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Partial Differential Equations,
                 Difference methods. {\bf G.1.7}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations, Boundary value problems. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency.",
}

@Article{Schryer:1990:DSO,
  author =       "N. L. Schryer",
  title =        "Designing Software for One-Dimensional Partial
                 Differential Equations",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "72--85",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.77632",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65P05)",
  MRnumber =     "1 073 411",
  bibdate =      "Sun Sep 04 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p72-schryer/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE. {\bf G.1.8}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Partial Differential Equations.
                 {\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Boundary
                 value problems.",
}

@Article{Hansen:1990:PES,
  author =       "Eldon R. Hansen and Merrell L. Patrick and Richard L.
                 C. Wang",
  title =        "Polynomial Evaluation with Scaling",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "86--93",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.77633",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65Y10",
  MRnumber =     "1 073 412",
  bibdate =      "Fri Aug 26 23:38:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p86-hansen/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Computer arithmetic. {\bf F.2.1}: Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on polynomials.",
  xxnote =       "Original article has incorrect ``Merell'' instead of
                 ``Merrell''.",
}

@Article{Snow:1990:WGO,
  author =       "Dennis M. Snow",
  title =        "{Weyl} Group Orbits",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "94--108",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.77634",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "20G99 (22E15)",
  MRnumber =     "91j:20115",
  bibdate =      "Sun Sep 04 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-1/p94-snow/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance; theory",
  reviewer =     "V. L. Popov",
  subject =      "{\bf F.2.2}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Computations on discrete
                 structures. {\bf I.1.2}: Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency.",
}

@Article{Sewell:1990:RSP,
  author =       "Granville Sewell",
  title =        "Remark on ``{Algorithm 657}: Software for Plotting
                 Contour Surfaces of a Function of Three Variables''",
  journal =      j-TOMS,
  volume =       "16",
  number =       "1",
  pages =        "109--109",
  month =        mar,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/77626.356300",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:03:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Sewell:1988:ASP}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Zenios:1990:INO,
  author =       "Stavros A. Zenios",
  title =        "Integrating Network Optimization Capabilities into a
                 High-Level Modeling Language",
  journal =      j-TOMS,
  volume =       "16",
  number =       "2",
  pages =        "113--142",
  month =        jun,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/78928.78929",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:09:48 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-2/p113-zenios/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; experimentation; languages;
                 performance; theory",
  subject =      "{\bf G.2.2}: Mathematics of Computing, DISCRETE
                 MATHEMATICS, Graph Theory, Network problems. {\bf
                 G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Constrained optimization. {\bf G.1.6}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Nonlinear programming. {\bf G.1.6}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming. {\bf C.2.1}: Computer
                 Systems Organization, COMPUTER-COMMUNICATION NETWORKS,
                 Network Architecture and Design. {\bf C.4}: Computer
                 Systems Organization, PERFORMANCE OF SYSTEMS, Modeling
                 techniques.",
}

@Article{Meintjes:1990:CES,
  author =       "Keith Meintjes and Alexander P. Morgan",
  title =        "Chemical Equilibrium Systems as Numerical Test
                 Problems",
  journal =      j-TOMS,
  volume =       "16",
  number =       "2",
  pages =        "143--151",
  month =        jun,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/78928.78930",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:09:48 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-2/p143-meintjes/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.5}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Systems of
                 equations. {\bf G.1.5}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Roots of Nonlinear Equations,
                 Polynomials, methods for. {\bf J.2}: Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Chemistry.",
}

@Article{Kearfott:1990:AIP,
  author =       "R. Baker Kearfott and Manuel {Novoa III}",
  title =        "{Algorithm 681}: {INTBIS}, a Portable Interval
                 {Newton}\slash Bisection Package",
  journal =      j-TOMS,
  volume =       "16",
  number =       "2",
  pages =        "152--157",
  month =        jun,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/78928.78931",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:09:48 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-2/p152-kearfott/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.5}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Systems of
                 equations. {\bf G.1.2}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation.",
}

@Article{Murli:1990:ATM,
  author =       "A. Murli and M. Rizzardi",
  title =        "{Algorithm 682}: {Talbot}'s Method for the {Laplace}
                 Inversion Problem",
  journal =      j-TOMS,
  volume =       "16",
  number =       "2",
  pages =        "158--168",
  month =        jun,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/78928.78932",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:09:48 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-2/p158-murli/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation. {\bf G.1.0}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Numerical
                 algorithms. {\bf F.2.1}: Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computation of
                 transforms. {\bf G.1.4}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation, Equal interval integration. {\bf
                 G.1.9}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Integral Equations, Fredholm equations.",
}

@Article{Amos:1990:CEI,
  author =       "Donald E. Amos",
  title =        "Computation of Exponential Integrals of a Complex
                 Argument",
  journal =      j-TOMS,
  volume =       "16",
  number =       "2",
  pages =        "169--177",
  month =        jun,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/78928.78933",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "92k:65025",
  bibdate =      "Sun Sep 04 23:09:48 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-2/p169-amos/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.9}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Integral Equations. {\bf G.1.m}: Mathematics
                 of Computing, NUMERICAL ANALYSIS, Miscellaneous.",
}

@Article{Amos:1990:APF,
  author =       "Donald E. Amos",
  title =        "{Algorithm 683}: a Portable {FORTRAN} Subroutine for
                 Exponential Integrals of a Complex Argument",
  journal =      j-TOMS,
  volume =       "16",
  number =       "2",
  pages =        "178--182",
  month =        jun,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/78928.78934",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65Y10)",
  MRnumber =     "92k:65026",
  bibdate =      "Sun Sep 04 23:09:48 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-2/p178-amos/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf D.3.2}:
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN.",
}

@Article{Tang:1990:AET,
  author =       "Ping Tak Peter Tang",
  title =        "Accurate and Efficient Testing of the Exponential and
                 Logarithm Functions",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "185--200",
  month =        sep,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/79505.79506",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65G99)",
  MRnumber =     "1 070 797",
  bibdate =      "Sun Sep 04 23:14:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p185-tang/",
  abstract =     "Table-driven techniques can be used to test highly
                 accurate implementation of EXP LOG. The largest error
                 observed in EXP and LOG accurately to within 1/500 unit
                 in the last place are reported in our tests. Methods to
                 verify the tests' reliability are discussed. Results of
                 applying the tests to our own as well as to a number of
                 other implementations of EXP and LOG are presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; languages; verification",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Portability.",
}

@Article{Cash:1990:VOR,
  author =       "J. R. Cash and Alan H. Karp",
  title =        "A Variable Order {Runge--Kutta} Method for Initial
                 Value Problems with Rapidly Varying Right-Hand Sides",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "201--222",
  month =        sep,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/79505.79507",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05 (65-04)",
  MRnumber =     "1 070 798",
  bibdate =      "Sun Sep 04 23:14:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p201-cash/",
  abstract =     "Explicit Runge--Kutta methods (RKMs) are among the
                 most popular classes of formulas for the approximate
                 numerical integration of nonstiff, initial value
                 problems. However, high-order Runge--Kutta methods
                 require more function evaluations per integration step
                 than, for example, Adams methods used in PECE mode, and
                 so, with RKMs, it is especially important to avoid
                 rejected steps. Steps are often rejected when certain
                 derivatives of the solutions are very large for part of
                 the region of integration. This corresponds, for
                 example, to regions where the solution has a sharp
                 front or, in the limit, some derivative of the solution
                 is discontinuous. In these circumstances the assumption
                 that the local truncation error is changing slowly is
                 invalid, and so any step-choosing algorithm is likely
                 to produce an unacceptable step. In this paper we
                 derive a family of explicit Runge--Kutta formulas. Each
                 formula is very efficient for problems with smooth
                 solution as well as problems having rapidly varying
                 solutions. Each member of this family consists of a
                 fifty-order formula that contains imbedded formulas of
                 all orders 1 through 4. By computing solutions at
                 several different orders, it is possible to detect
                 sharp fronts or discontinuities before all the function
                 evaluations defining the full Runge--Kutta step have
                 been computed. We can then either accept a lower order
                 solution or abort the step, depending on which course
                 of action seems appropriate. The efficiency of the new
                 algorithm is demonstrated on the DETEST test set as
                 well as on some difficult test problems with sharp
                 fronts or discontinuities.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems. {\bf G.1.2}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation.",
}

@Article{Weiss:1990:SSC,
  author =       "Shlomo Weiss and James E. Smith",
  title =        "A Study of Scalar Compilation Techniques for Pipelined
                 Supercomputers",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "223--245",
  month =        sep,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/79505.79508",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:14:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p223-weiss/",
  abstract =     "This paper studies two compilation techniques for
                 enhancing scalar performance in high-speed scientific
                 processors: software pipelining and loop unrolling. We
                 study the impact of the architecture (size of the
                 register file) and of the hardware (size of instruction
                 buffer) on the efficiency of loop unrolling. We also
                 develop a methodology for classifying software
                 pipelining techniques. For loop unrolling, a
                 straightforward scheduling algorithm is shown to
                 produce near-optimal results when not inhibited by
                 recurrences or memory hazards. Our study indicates that
                 the performance produced with a modified CRAY-1S scalar
                 architecture and a code scheduler utilizing loop
                 unrolling is comparable to the performance achieved by
                 the CRAY-1S with a vector unit and the CFT vectorizing
                 compiler.\par

                 Finally, we show that the combination of loop unrolling
                 and dynamic software pipelining, as implemented by a
                 decoupled computer, substantially outperforms the
                 vector CRAY-1S.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "design; experimentation; performance",
  subject =      "{\bf C.1.1}: Computer Systems Organization, PROCESSOR
                 ARCHITECTURES, Single Data Stream Architectures,
                 Pipeline processors. {\bf C.4}: Computer Systems
                 Organization, PERFORMANCE OF SYSTEMS, Performance
                 attributes. {\bf D.3.4}: Software, PROGRAMMING
                 LANGUAGES, Processors, Compilers. {\bf C.5.1}: Computer
                 Systems Organization, COMPUTER SYSTEM IMPLEMENTATION,
                 Large and Medium (``Mainframe'') Computers.",
}

@Article{Preusser:1990:EFB,
  author =       "Albrecht Preusser",
  title =        "Efficient Formulation of a Bivariate Nonic
                 ${C}^2$-{Hermite} Polynomial on Triangles",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "246--252",
  month =        sep,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/79505.79509",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D05 (65-04)",
  MRnumber =     "1 070 799",
  bibdate =      "Sun Sep 04 23:14:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p246-preusser/",
  abstract =     "Bivariate polynomials over triangular domains are
                 widely in use for the definition of surfaces that are
                 continuously differentiable across a set of triangles.
                 A description is given of how explicit formulas for the
                 coefficients of bivariate nonic polynomials can be
                 found with the help of a computer algebra system. A
                 linear system with 55 equations and 45 nonzero right
                 hand sides must be solved algebraically. The
                 interpolant is twice differentiable across triangle
                 sides and based on function values and partial
                 derivatives up to fourth order at the nodes. Horner's
                 scheme for evaluating polynomials can be applied
                 directly, leading to optimal efficiency during the
                 evaluation phase (54 additions and multiplications for
                 one point). Starting with transformed nodal data, the
                 calculation of one set of coefficients takes about 350
                 additions, the same number of multiplications, and 30
                 divisions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Spline and piecewise
                 polynomial interpolation. {\bf I.3.5}: Computing
                 Methodologies, COMPUTER GRAPHICS, Computational
                 Geometry and Object Modeling, Curve, surface, solid,
                 and object representations. {\bf G.1.3}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative
                 methods).",
}

@Article{Preusser:1990:AIT,
  author =       "Albrecht Preusser",
  title =        "{Algorithm 684}: ${C}^1$- and ${C}^2$-Interpolation on
                 Triangles with Quintic and Nonic Bivariate
                 Polynomials",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "253--257",
  month =        sep,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/79505.79510",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65D05)",
  MRnumber =     "1 070 800",
  bibdate =      "Sun Sep 04 23:14:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p253-preusser/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Spline and piecewise
                 polynomial interpolation. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Shacham:1990:FBD,
  author =       "Orit Shacham and Mordechai Shacham",
  title =        "Finding Boundaries of the Domain of Definition for
                 Functions Along a One-Dimensional Ray",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "258--268",
  month =        sep,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/79505.79511",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65D99)",
  MRnumber =     "1 070 801",
  bibdate =      "Sun Sep 04 23:14:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p258-shacham/",
  abstract =     "A program for finding boundaries of function domains
                 along a one-dimensional ray has been developed. The
                 program decomposes the function into subexpressions
                 which are recursively tested for intervals where they
                 are undefined, negative, or fractional, or points where
                 they equal zero. The intervals in which the
                 subexpressions are undefined are then united to create
                 the boundaries of the domain of definition of the whole
                 function. The advantages of the use of such a program
                 in solution of systems of nonlinear algebraic equations
                 and nonlinear optimization are demonstrated.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.5}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations. {\bf G.1.6}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization.",
}

@Article{Nair:1990:IAO,
  author =       "K. Aiyappan Nair",
  title =        "An Improved Algorithm for Ordered Sequential Random
                 Sampling",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "269--274",
  month =        sep,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/79505.356313",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65C10",
  MRnumber =     "1 070 802",
  bibdate =      "Sat Aug 27 15:57:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Palacios-Velez:1990:DHS,
  author =       "Oscar Palacios-V{\'e}lez and Baltazar Cuevas Renaud",
  title =        "A Dynamic Hierarchical Subdivision Algorithm for
                 Computing {Delaunay} Triangulations and Other
                 Closest-Point Problems",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "275--292",
  month =        sep,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/79505.79512",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04",
  MRnumber =     "1 070 803",
  bibdate =      "Sat Aug 27 15:57:45 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-3/p275-palacios-velez/",
  abstract =     "A new, dynamic, hierarchical subdivision and recursive
                 algorithm for computing Delaunay triangulations is
                 presented. The algorithm has four main steps: (1)
                 location of the already formed triangle that contains
                 the point (2) identification of other adjoining
                 triangles whose circumcircle contains the point (3)
                 formation of the new triangles, and (4) database
                 update. Different search procedures are analyzed. It is
                 shown that the ``oriented walk'' search, when the total
                 number of points is less than 417 or when the points
                 are presorted by distance or coordinates. The algorithm
                 has point-deletion capabilities which are discussed in
                 detail.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design",
  subject =      "{\bf F.2.2}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf I.3.5}:
                 Computing Methodologies, COMPUTER GRAPHICS,
                 Computational Geometry and Object Modeling, Geometric
                 algorithms, languages, and systems. {\bf I.3.5}:
                 Computing Methodologies, COMPUTER GRAPHICS,
                 Computational Geometry and Object Modeling, Hierarchy
                 and geometric transformations. {\bf F.2.2}: Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Sorting and searching.",
}

@Article{Krogh:1990:AAP,
  author =       "Fred T. Krogh",
  title =        "{ACM} Algorithms Policy",
  journal =      j-TOMS,
  volume =       "16",
  number =       "3",
  pages =        "293--296",
  month =        sep,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/79505.356315",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:14:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pothen:1990:CBT,
  author =       "Alex Pothen and Chin-Ju Fan",
  title =        "Computing the Block Triangular Form of a Sparse
                 Matrix",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "303--324",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/98267.98287",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F50",
  MRnumber =     "91k:65075",
  bibdate =      "Sat Aug 27 15:58:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p303-pothen/",
  abstract =     "We consider the problem of permuting the rows and
                 columns of a rectangular or square, unsymmetric sparse
                 matrix to compute its block triangular form. This block
                 triangular form is based on a canonical decomposition
                 of bipartite graphs induced by a maximum matching and
                 was discovered by Dulmage and Mendelsohn. We describe
                 implementations of algorithms to compute the block
                 triangular form and provide computational results on
                 sparse matrices from test collections. Several
                 applications of the block triangular form are also
                 included.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; perm; sparse",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Sparse and very
                 large systems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf G.2.1}:
                 Mathematics of Computing, DISCRETE MATHEMATICS,
                 Combinatorics, Permutations and combinations. {\bf
                 G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS,
                 Graph Theory.",
}

@Article{Kaufman:1990:APS,
  author =       "Linda Kaufman and Daniel D. Warner",
  title =        "{Algorithm 685}: a Program for Solving Separable
                 Elliptic Equations",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "325--351",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/98267.98289",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:21:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p325-kaufman/",
  abstract =     "This paper presents a program SERRG2 that solves
                 separable elliptic equations on a rectangle. The
                 program uses a matrix decomposition technique to
                 directly solve the linear system arising from a
                 Rayleigh--Ritz--Galerkin approach with tensor product
                 B-splines to solve the separable partial differential
                 equation. This approach permits high-order
                 discretizations, variable meshes, and multiple knots.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.8}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Higham:1990:EFM,
  author =       "Nicholas J. Higham",
  title =        "Exploiting Fast Matrix Multiplication Within the Level
                 3 {BLAS}",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "352--368",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/98267.98290",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65F99)",
  MRnumber =     "1 095 133",
  bibdate =      "Sun Sep 04 23:21:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "Describes algorithms based on Strassen's method which
                 are asymptotically faster than the standard ${N}^3$
                 algorithm, and in practice, faster for ${N}\approx100$,
                 and examines their numerical stability. See
                 \cite{Dongarra:1990:ASL,Demmel:1992:SBA,Dayde:1994:PBI}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p352-higham/",
  abstract =     "The Level 3 BLAS (BLAS3) are a set of specifications
                 of FORTRAN 77 subprograms for carrying out matrix
                 multiplications and the solution of triangular systems
                 with multiple right-hand sides. They are intended to
                 provide efficient and portable building blocks for
                 linear algebra algorithms on high-performance
                 computers. We describe algorithms for the BLAS3
                 operations that are asymptotically faster than the
                 conventional ones. These algorithms are based on
                 Strassen's method for fast matrix multiplication, which
                 is now recognized to be a practically useful technique
                 once matrix dimensions exceed about 100. We pay
                 particular attention to the numerical stability of
                 these ``fast BLAS3.'' Error bounds are given and their
                 significance is explained and illustrated with the aid
                 of numerical experiments. Our conclusion is that the
                 fast BLAS3, although not as strongly stable as
                 conventional implementations, are stable enough to
                 merit careful consideration in many applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra. {\bf D.3.2}:
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77.",
}

@Article{Reichel:1990:AFS,
  author =       "L. Reichel and W. B. Gragg",
  title =        "{Algorithm 686}: {FORTRAN} Subroutines for Updating
                 the {QR} Decomposition",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "369--377",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/98267.98291",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:25:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p369-reighel/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; Gram--Schmidt algorithm; nla; qrd;
                 software; updating",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@Article{Tang:1990:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the Logarithm Function
                 in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "378--400",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/98267.98294",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:26:09 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p378-tang/",
  abstract =     "Algorithms and implementation details for the
                 logarithm functions in both single and double precision
                 of IEEE 754 arithmetic are presented here. With a table
                 of moderate size, the implementation need only working-
                 precision arithmetic and are provably accurate to
                 within 0.57 ulp.",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; performance; reliability;
                 standardization; theory; verification",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@Article{Hopkins:1990:RRK,
  author =       "Tim Hopkins and David Morse",
  title =        "Remark on ``{Algorithm 620}: References and Keywords
                 for {\em {Collected Algorithms} of the {ACM}}''",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "401--403",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/98267.98297",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Feb 24 09:58:26 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Rice:1984:ARK,Hamilton:1985:RRK}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p401-hopkins/",
  abstract =     "The authors report on an enhanced version of the
                 database originally reported in `Algorithm 620:
                 references and keywords for collected algorithms from
                 ACM', J. R. Rice and R. J. Hanson, ACM Trans Math.
                 Soft. vol. 10, no. 4, p. 359-360 (1984). In this new
                 version they have included all the information
                 necessary to generate full bibliographic references.
                 Extra information includes the author's name (including
                 any accents), the page range of the original reference
                 (rather than just the starting page), the month and
                 year of publication and an abbreviated journal name.
                 The programming language used to code the algorithm is
                 also given. Any mathematical notation used within the
                 algorithm title and accents in the author's name have
                 been defined using {\TeX}. Following the practice used
                 with Bib{\TeX}, all letters within the title that need
                 to remain capitalized in a printed version of the
                 reference (e.g. Fortran, Bessel) are enclosed in
                 braces. (3 Refs.)",
  acknowledgement = ack-nhfb,
  affiliation =  "Kent Univ., UK",
  classification = "C4100 (Numerical analysis); C7250C (Bibliographic
                 systems); C7310 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Abbreviated journal name; Algorithm title; algorithms;
                 Bibliographic references; BibTeX; Mathematical
                 notation; TeX",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis.",
  thesaurus =    "Bibliographic systems; Mathematics computing;
                 Numerical methods",
}

@Article{Amos:1990:RPP,
  author =       "D. E. Amos",
  title =        "Remark on ``{Algorithm 644}: a Portable Package for
                 {Bessel} Functions of a Complex Argument and
                 Nonnegative Order''",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "404--404",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/98267.98299",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:26:24 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Amos:1986:APP,Amos:1995:RAP,Kodama:2007:RA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p404-amos/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf F.2.2}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems.",
}

@Article{Garbow:1990:RFS,
  author =       "B. S. Garbow and J. N. Lyness",
  title =        "Remark on ``{Algorithm 662}: {A FORTRAN} Software
                 Package for the Numerical Inversion of the {Laplace}
                 Transform Based on {Weeks}' Method''",
  journal =      j-TOMS,
  volume =       "16",
  number =       "4",
  pages =        "405--406",
  month =        dec,
  year =         "1990",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/98267.98302",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:21:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Garbow:1988:AFS}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1990-16-4/p405-garbow/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE. {\bf F.2.2}: Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems.",
}

@Article{Addison:1991:ADT,
  author =       "C. A. Addison and W. H. Enright and P. W. Gaffney and
                 I. Gladwell and P. M. Hanson",
  title =        "{Algorithm 687}: a Decision Tree for the Numerical
                 Solution of Initial Value Ordinary Differential
                 Equations",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "1--10",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/103147.103148",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p1-addison/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems.",
}

@Article{Shampine:1991:RSS,
  author =       "L. F. Shampine and I. Gladwell and R. W. Brankin",
  title =        "Reliable Solutions of Special Event Location Problems
                 for {ODEs}",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "11--25",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/103147.103149",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L05",
  MRnumber =     "92e:65093",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p11-shampine/",
  abstract =     "Computing the solution of the initial value problem in
                 ordinary differential equations (ODEs) may be only part
                 of a larger task. One such task is finding where an
                 algebraic function of the solution (an event function)
                 has a root (an event occurs). This is a task which is
                 difficult both in theory and in software practice. For
                 certain useful kinds of event functions, it is possible
                 to avoid two fundamental difficulties. It is described
                 how to achieve the reliable solutions of such problems
                 in a way that allows the capability to be grafted onto
                 popular codes for the initial value problem.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; theory",
  reviewer =     "H. Shintani",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems.",
}

@Article{Gal:1991:AEM,
  author =       "Shmuel Gal and Boris Bachelis",
  title =        "An Accurate Elementary Mathematical Library for the
                 {IEEE} Floating Point Standard",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "26--45",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/103147.103151",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65-04 65D15)",
  MRnumber =     "92a:65069",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p26-gal/",
  abstract =     "The algorithms used by the IBM Israel Scientific
                 Center for the elementary mathematical library using
                 the IEEE standard for binary floating point arithmetic
                 are described. The algorithms are based on the
                 ``accurate tables method.'' This methodology achieves
                 high performance and produces very accurate results. It
                 overcomes one of the main problems encountered in
                 elementary mathematical functions computations:
                 achieving last bit accuracy. The results obtained are
                 correctly rounded for almost all argument
                 values.\par

                 Our main idea in the accurate tables method is to use
                 ``nonstandard tables,'' which are different from the
                 natural tables of equally spaced points in which the
                 rounding error prevents obtaining last bit accuracy. In
                 order to achieve a small error we use the following
                 idea: Perturb the original, equally spaced, points in
                 such a way that the table value (or tables values in
                 case we need several tables) will be very close to
                 numbers which can be exactly represented by the
                 computer (much closer than the usual double precision
                 representation). Thus we were able to control the error
                 introduced by the computer representation of real
                 numbers and extended the accuracy without actually
                 using extended precision arithmetic.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation.",
}

@Article{Cody:1991:PEP,
  author =       "W. J. Cody",
  title =        "Performance Evaluation of Programs Related to the Real
                 Gamma Function",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "46--54",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/103147.103153",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65Y20)",
  MRnumber =     "91m:65052",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p46-cody/",
  abstract =     "Methods are presented for evaluating the performance
                 of programs for the functions $\Gamma(x)$, $\ln
                 \Gamma(x)$, and $\psi(x)$. Accuracy estimates are based
                 on comparisons using the manipulation theorem. Ideas
                 for checking robustness are also given, and details on
                 specific implementations of test programs are
                 included.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "measurement; performance; reliability",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing.",
}

@Article{Cody:1991:UTS,
  author =       "W. J. Cody and L. Stoltz",
  title =        "The Use of {Taylor} Series to Test Accuracy of
                 Function Programs",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "55--63",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/103147.103154",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20 (65Y20)",
  MRnumber =     "91m:65053",
  bibdate =      "Sun Sep 04 23:36:36 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p55-cody/",
  abstract =     "This paper discusses the use of local Taylor series
                 expansions for determining the accuracy of computer
                 programs for special functions. The main example is
                 testing of programs for exponential integrals.
                 Additional applications include testing of programs for
                 certain Bessel functions, Dawson's integral, and error
                 functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance; verification",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
}

@Article{Dax:1991:CAB,
  author =       "Achiya Dax",
  title =        "On Computational Aspects of Bounded Linear Least
                 Squares Problems",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "64--73",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/103147.103155",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65K10",
  MRnumber =     "91m:65179",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p64-dax/",
  abstract =     "The paper describes numerical experiments with active
                 set methods for solving bounded linear least squares
                 problems. It concentrates on two problems that arise in
                 the implementation of the active set method. One
                 problem is the choice of a good starting point. The
                 second problem is how to move out of a ``{\em dead
                 point}.'' The paper investigates the use of simple
                 iterative methods to solve these problems. The results
                 of our experiments indicate that the use of
                 Gauss--Seidel iterations to obtain a starting point is
                 likely to provide large gains in efficiency. Another
                 interesting conclusion is that dropping one constraint
                 at a time is advantageous to dropping several
                 constraints at a time.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; experimentation; performance; theory",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Least squares methods.",
}

@Article{Pardalos:1991:CTP,
  author =       "Panos M. Pardalos",
  title =        "Construction of Test Problems in Quadratic Bivalent
                 Programming",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "74--87",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/103147.103156",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65K05",
  MRnumber =     "92c:65075",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p74-pardalos/",
  abstract =     "A method of constructing test problems for constrained
                 bivalent quadratic programming is presented. For any
                 feasible integer point for a given domain, the method
                 generates quadratic functions whose minimum over the
                 given domain occurs at the selected point.\par

                 Certain properties of unconstrained quadratic zero-one
                 programs that determine the difficulty of the test
                 problems are also discussed. In addition, a
                 standardized random test problem generator for
                 unconstrained quadratic zero-one programming is
                 given.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; experimentation; performance",
  reviewer =     "P. K. Subramanian",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Integer programming. {\bf
                 G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Nonlinear programming. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Klier:1991:FCB,
  author =       "Peter Klier and Richard J. Fateman",
  title =        "On Finding the Closest Bitwise Matches in a Fixed
                 Set",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "88--97",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/103147.103157",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68Q20",
  MRnumber =     "1 103 630",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p88-klier/",
  abstract =     "In a given large fixed table of bit-vectors, we would
                 like to find, as rapidly as possible, those bit-vectors
                 which have the least Hamming distances from a
                 newly-presented arbitrary bit-vector.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf F.2.2}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Pattern matching. {\bf E.2}:
                 Data, DATA STORAGE REPRESENTATIONS. {\bf F.2.2}: Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Nonnumerical Algorithms and Problems,
                 Sorting and searching. {\bf H.3.3}: Information
                 Systems, INFORMATION STORAGE AND RETRIEVAL, Information
                 Search and Retrieval, Search process.",
}

@Article{LEcuyer:1991:IRN,
  author =       "Pierre L'Ecuyer and Serge C{\^o}t{\'e}",
  title =        "Implementing a Random Number Package with Splitting
                 Facilities",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "98--111",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/103147.103158",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65C10",
  MRnumber =     "91m:65016",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p98-lecuyer/",
  abstract =     "A portable set of software tools is described for
                 uniform random variates generation. It provides for
                 multiple generators running simultaneously, and each
                 generator has its sequence of numbers partitioned into
                 many long (disjoint) substreams. Simple procedure calls
                 allow the user to make any generator ``jump'' ahead to
                 the beginning of its next substream, back to the
                 beginning of its current substream, or back to the
                 beginning of its first substream\ldots. Implementation
                 issues are discussed\ldots. A Pascal implementation for
                 32-bit computers is described.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Random number generation. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Liu:1991:GEM,
  author =       "Joseph W. H. Liu",
  title =        "A Generalized Envelope Method for Sparse Factorization
                 by Rows",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "112--129",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/103147.103159",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F50",
  MRnumber =     "92b:65037",
  bibdate =      "Sun Sep 04 23:43:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p112-liu/",
  abstract =     "A generalized form of the envelope method is proposed
                 for the solution of large sparse symmetric and positive
                 definite matrices by rows. The method is demonstrated
                 to have practical advantages over the conventional
                 column-oriented factorization using compressed column
                 storage or the multifrontal method using full frontal
                 submatrices.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; functional algorithm",
  reviewer =     "R. P. Tewarson",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Sparse and very
                 large systems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis.",
}

@Article{Mohideen:1991:RCG,
  author =       "Saleem Mohideen and Vladimir Cherkassky",
  title =        "On Recursive Calculation of the Generalized Inverse of
                 a Matrix",
  journal =      j-TOMS,
  volume =       "17",
  number =       "1",
  pages =        "130--147",
  month =        mar,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/103147.103160",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F10 (65F20)",
  MRnumber =     "92c:65042",
  bibdate =      "Sun Sep 04 23:33:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-1/p130-mohideen/",
  abstract =     "The generalized inverse of a matrix is an extension of
                 the ordinary square matrix inverse which applies to any
                 matrix (e.g., singular, rectangular). The generalized
                 inverse has numerous important applications such as
                 regression analysis, filtering, optimization and, more
                 recently, linear associative memories. In this latter
                 application known as Distributed Associative Memory,
                 stimulus vectors are associated with response vectors
                 and the result of many associations is spread over the
                 entire memory matrix, which is calculated as the
                 generalized inverse. Addition/deletion of new
                 associations requires recalculation of the generalized
                 inverse, which becomes computationally costly for large
                 systems. A better solution is to calculate the
                 generalized inverse recursively. The proposed algorithm
                 is a modification of the well known algorithm due to
                 Rust et al. [2], originally introduced for nonrecursive
                 computation. We compare our algorithm with Greville's
                 recursive algorithm and conclude that our algorithm
                 provides better numerical stability at the expense of
                 little extra computation time and additional storage.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance; theory",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Matrix inversion.
                 {\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Pseudoinverses.
                 {\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf G.4}: Mathematics
                 of Computing, MATHEMATICAL SOFTWARE, Algorithm
                 analysis.",
}

@Article{Keast:1991:AEM,
  author =       "P. Keast and P. H. Muir",
  title =        "{Algorithm 688}: {EPDCOL}: a More Efficient {PDECOL}
                 Code",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "153--166",
  month =        jun,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/108556.108558",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:44:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p153-keast/",
  abstract =     "The software package PDECOL [7] is a popular code
                 among scientists wishing to solve systems of nonlinear
                 partial differential equations. The code is based on a
                 method-of-lines approach, with collocation in the space
                 variable to reduce the problem to a system of ordinary
                 differential equations. There are three principal
                 components: the basis functions employed in the
                 collocation; the method used to solve the system of
                 ordinary differential equations; and the linear
                 equation solver which handles the linear algebra. This
                 paper will concentrate on the third component, and will
                 report on the improvement in the performance of PDECOL
                 resulting from replacing the current linear algebra
                 modules of the code by modules which take full
                 advantage of the special structure of the equations
                 which arise. Savings of over 50 percent in total
                 execution time can be realized.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.8}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations. {\bf G.1.5}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations. {\bf G.1.7}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE.",
}

@Article{Blom:1991:ADC,
  author =       "J. G. Blom and H. Brunner",
  title =        "{Algorithm 689}: Discretized Collocation and Iterated
                 Collocation for Nonlinear {Volterra} Integral Equations
                 of the Second Kind",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "167--177",
  month =        jun,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/108556.108562",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:44:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p167-blom/",
  abstract =     "This paper describes a FORTRAN code for calculating
                 approximate solutions to systems of nonlinear Volterra
                 integral equations of the second kind. The algorithm is
                 based on polynomial spline collocation, with the
                 possibility of combination with the corresponding
                 iterated collocation. It exploits certain local
                 superconvergence properties for the error estimation
                 and the stepsize strategy.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance; reliability",
  subject =      "{\bf G.1.9}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Integral Equations, Volterra equations. {\bf
                 G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Numerical algorithms. {\bf G.1.2}: Mathematics
                 of Computing, NUMERICAL ANALYSIS, Approximation, Spline
                 and piecewise polynomial approximation. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Berzins:1991:ACP,
  author =       "M. Berzins and P. M. Dew",
  title =        "{Algorithm 690}: {Chebyshev} Polynomial Software for
                 Elliptic-Parabolic Systems of {PDEs}",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "178--206",
  month =        jun,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/108556.108566",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:44:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p178-berzins/",
  abstract =     "PDECHEB is a FORTRAN 77 software package that
                 semidiscretizes a wide range of time-dependent partial
                 differential equations in one space variable. The
                 software implements a family of spacial discretization
                 formulas, based on piecewise Chebyshev polynomial
                 expansions with $C^{0}$ continuity. The package has
                 been designed to be used in conjunction with a general
                 integrator for initial value problems to provide a
                 powerful software tool for the solution of
                 parabolic-elliptic PDEs with coupled differential
                 algebraic equations. Examples are provided to
                 illustrate the use of the package with the DASSL d.a.e
                 integrator of Petzold [18].",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.8}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations, Elliptic
                 equations. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE. {\bf G.1.8}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Partial Differential
                 Equations, Parabolic equations.",
}

@Article{Favati:1991:IIF,
  author =       "Paola Favati and Grazia Lotti and Francesco Romani",
  title =        "Interpolatory Integration Formulas for Optimal
                 Composition",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "207--217",
  month =        jun,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/108556.108571",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30",
  MRnumber =     "92k:65035",
  bibdate =      "Sun Sep 04 23:44:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p207-favati/",
  abstract =     "A set of symmetric, closed, interpolatory integration
                 formulas on the interval [-1, 1] with positive weights
                 and increasing degree of precision is introduced. These
                 formulas, called recursive monotone stable (RMS)
                 formulas, allow applying higher order or compound rules
                 without wasting previously computed functional values.
                 An exhaustive search shows the existence of 27 families
                 of RMS formulas, stemming from the simple trapezoidal
                 rule.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation,
                 Adaptive quadrature. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE. {\bf G.1.1}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation, Interpolation formulas.",
}

@Article{Favati:1991:AIQ,
  author =       "Paola Favati and Grazia Lotti and Francesco Romani",
  title =        "{Algorithm 691}: Improving {QUADPACK} Automatic
                 Integration Routines",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "218--232",
  month =        jun,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/108556.108580",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30 (65Y10)",
  MRnumber =     "92k:65036",
  bibdate =      "Sun Sep 04 23:44:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p218-favati/",
  abstract =     "Two automatic adaptive integrators from QUADPACK
                 (namely, QAG, and QAGS) are modified by substituting
                 the Gauss--Kronrod rules used for local quadrature with
                 recursive monotone stable (RMS) formulas. Extensive
                 numerical tests, both for one-dimensional and
                 two-dimensional integrals, show that the resulting
                 programs are faster, perform less functional
                 evaluations, and are more suitable",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation,
                 Adaptive quadrature. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Berntsen:1991:EEA,
  author =       "Jarle Berntsen and Terje O. Espelid",
  title =        "Error Estimation in Automatic Quadrature Routines",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "233--252",
  month =        jun,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/108556.108575",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G99 (65D20 65Y10)",
  MRnumber =     "92m:65067",
  bibdate =      "Sun Sep 04 23:44:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p233-berntsen/",
  abstract =     "A new algorithm for estimating the error in quadrature
                 approximations is presented. Based on the same
                 integrand evaluations that we need for approximating
                 the integral, one may, for many quadrature rules,
                 compute a sequence of null rule approximations. These
                 null rule approximations are then used to produce an
                 estimate of the local error. The algorithm allows us to
                 take advantage of the degree of precision of the basic
                 quadrature rule. In the experiments we show that the
                 algorithm works satisfactorily for a selection of
                 different quadrature rules on all test families of
                 integrals.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; experimentation",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation,
                 Adaptive quadrature. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation.",
}

@Article{Dodson:1991:SEF,
  author =       "David S. Dodson and Roger G. Grimes and John G.
                 Lewis",
  title =        "Sparse Extensions to the {FORTRAN Basic Linear Algebra
                 Subroutines}",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "253--263",
  month =        jun,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/108556.108577",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:44:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p253-dodson/",
  abstract =     "This paper describes an extension to the set of Basic
                 Linear Algebra Subprograms. The extension is targeted
                 at sparse vector operations, with the goal of providing
                 efficient, but portable, implementations of algorithms
                 for high-performance computers.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; standardization",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Sparse and very
                 large systems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Portability. {\bf D.3.2}:
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf D.2.2}: Software,
                 SOFTWARE ENGINEERING, Tools and Techniques, Software
                 libraries. {\bf F.2.1}: Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices.",
}

@Article{Dodson:1991:AMI,
  author =       "David S. Dodson and Roger G. Grimes and John G.
                 Lewis",
  title =        "{Algorithm 692}: Model Implementation and Test Package
                 for the Sparse {Basic Linear Algebra Subroutines}",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "264--272",
  month =        jun,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/108556.108582",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:44:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p264-dodson/",
  abstract =     "This paper describes a model implementation and test
                 software for the Sparse Basic Linear Algebra
                 Subprograms (Sparse BLAS). The Sparse BLAS perform
                 vector operations common in sparse linear algebra, with
                 the goal of providing efficient, but portable,
                 implementations of algorithms for high performance
                 computers. The model implementation provides a portable
                 set of FORTRAN 77 Sparse BLAS for the use on machines
                 where specially tuned implementations do not exist or
                 are not required. The test software is designed to
                 verify that tuned implementations meet the
                 specifications of the Sparse BLAS and that
                 implementations are correctly installed.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Sparse and very
                 large systems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE. {\bf D.3.2}: Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 FORTRAN 77.",
}

@Article{Smith:1991:AFP,
  author =       "David M. Smith",
  title =        "{Algorithm 693}: {A FORTRAN} Package for
                 Floating-Point Multiple-Precision Arithmetic",
  journal =      j-TOMS,
  volume =       "17",
  number =       "2",
  pages =        "273--283",
  month =        jun,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/108556.108585",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Dec 13 18:36:25 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-2/p273-smith/",
  abstract =     "FM is a collection of FORTRAN-77 routines which
                 performs floating-point multiple-precision arithmetic
                 and elementary functions. Results are almost always
                 correctly rounded, and due to improved algorithms used
                 for elementary functions, reasonable efficiency is
                 obtained.",
  acknowledgement = ack-nhfb,
  affiliation =  "Loyola Marymount Univ., Los Angeles, CA, USA",
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods); C7310
                 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Accuracy; Elementary functions; Floating-point
                 multiple-precision arithmetic; FM; FORTRAN-77 routines;
                 Mathematical library; Portable software; Rounding off",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf D.3.2}:
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77.",
  thesaurus =    "Digital arithmetic; Function approximation;
                 Mathematics computing; Software packages; Subroutines",
}

@Article{Higham:1991:ACT,
  author =       "Nicholas J. Higham",
  title =        "{Algorithm 694}: a Collection of Test Matrices in
                 {MATLAB}",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "289--305",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/114697.116805",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:52:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p289-higham/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; experimentation; performance; theory",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra.",
}

@Article{Eskow:1991:ASN,
  author =       "Elizabeth Eskow and Robert B. Schnabel",
  title =        "{Algorithm 695}: Software for a New Modified
                 {Cholesky} Factorization",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "306--312",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/114697.116806",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:52:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p306-eskow/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE. {\bf G.1.3}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra.",
}

@Article{Rothberg:1991:ESM,
  author =       "Edward Rothberg and Anoop Gupta",
  title =        "Efficient Sparse Matrix Factorization on
                 High-Performance Workstations\emdash Exploiting the
                 Memory Hierarchy",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "313--334",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/114697.116809",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:52:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p313-rothberg/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; experimentation; performance",
  subject =      "{\bf B.3.2}: Hardware, MEMORY STRUCTURES, Design
                 Styles, Cache memories. {\bf C.5.3}: Computer Systems
                 Organization, COMPUTER SYSTEM IMPLEMENTATION,
                 Microcomputers, Workstations. {\bf G.1.3}: Mathematics
                 of Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Sparse and very large systems. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Schrauf:1991:AIR,
  author =       "G{\'e}za Schrauf",
  title =        "{Algorithm 696}: An Inverse {Rayleigh} Iteration for
                 Complex Band Matrices",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "335--340",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/114697.116807",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:52:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p335-schrauf/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf
                 F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on matrices. {\bf D.3.2}:
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77.",
}

@Article{Akima:1991:MUI,
  author =       "Hiroshi Akima",
  title =        "A Method for Univariate Interpolation that Has the
                 Accuracy of a Third-Degree Polynomial",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "341--366",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/114697.116810",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:52:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p341-akima/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Spline and piecewise
                 polynomial interpolation.",
}

@Article{Akima:1991:AUI,
  author =       "Hiroshi Akima",
  title =        "{Algorithm 697}: Univariate Interpolation that Has the
                 Accuracy of a Third-Degree Polynomial",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "367--367",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/114697.116808",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:52:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p367-akima/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Spline and piecewise
                 polynomial interpolation.",
}

@Article{Higham:1991:HCR,
  author =       "D. J. Higham",
  title =        "Highly Continuous {Runge--Kutta} Interpolants",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "368--386",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/114697.103150",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L06",
  MRnumber =     "92m:65092",
  bibdate =      "Sun Sep 04 23:52:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p368-higham/",
  abstract =     "To augment the discrete Runge--Kutta solution to the
                 minimal value problem, piecewise Hermite interpolants
                 have been used to provide a continuous approximation
                 with a continuous first derivative. We show that it is
                 possible to construct interpolants with arbitrarily
                 many continuous derivatives which have the same
                 asymptotic accuracy and basic cost as the Hermite
                 interpolants. We also show that the usual truncation
                 coefficient analysis can be applied to these new
                 interpolants, allowing their accuracy to be examined in
                 more detail. As an illustration, we present some
                 globally $C^2$ interpolants for use with a popular 4th
                 and 5th order Runge--Kutta pair of Dormand and Prince,
                 and we compare them theoretically and numerically with
                 existing interpolants.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Single step
                 methods. {\bf G.1.7}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Initial value problems. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation. {\bf
                 G.1.1}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation.",
}

@Article{Sharp:1991:NCS,
  author =       "P. W. Sharp",
  title =        "Numerical Comparisons of Some Explicit {Runge--Kutta}
                 Pair of Orders 3 Through 8",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "387--409",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/114697.116811",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:52:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p387-sharp/",
  abstract =     "We performed numerical testing of six explicit
                 Runge--Kutta pairs ranging in order from a (3,4) pair
                 to a (7,8) pair. All the test problems had smooth
                 solutions and we assumed dense output was not required.
                 The pairs were implemented in a uniform way. In
                 particular, the stepsize selection for all pairs was
                 based on the locally optimal formula. We tested the
                 efficiency of the pairs, to what extent tolerance
                 proportionality held, the accuracy of the local error
                 estimate and stepsize prediction, and the performance
                 on mildly stiff problems. We also showed, for these
                 pairs, how the performance could be altered noticeably
                 by making simple changes to the stepsize selection
                 strategy. As part of the work, we demonstrated new ways
                 of presenting numerical comparisons.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance; reliability",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing.",
}

@Article{Ziv:1991:FEE,
  author =       "Abraham Ziv",
  title =        "Fast Evaluation of Elementary Mathematical Functions
                 with Correctly Rounded Last Bit",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "410--423",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/114697.116813",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Sep 1 10:15:31 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p410-ziv/",
  acknowledgement = ack-nj,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; standardization; theory",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency.",
}

@Article{Higham:1991:RBF,
  author =       "Desmond J. Higham",
  title =        "Remark on ``{Algorithm 669}: {BRKF45}: {A FORTRAN}
                 Subroutine for Solving First-Order Systems of Nonstiff
                 Initial Value Problems for Ordinary Differential
                 Equations''",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "424--426",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/114697.116814",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:52:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Cash:1989:ABF}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-3/p424-higham/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation.",
}

@Article{Krogh:1991:AAP,
  author =       "Fred T. Krogh",
  title =        "{ACM} Algorithms Policy",
  journal =      j-TOMS,
  volume =       "17",
  number =       "3",
  pages =        "427--430",
  month =        sep,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/114697.356357",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:52:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Berntsen:1991:AAA,
  author =       "Jarle Berntsen and Terje O. Espelid and Alan Genz",
  title =        "An Adaptive Algorithm for the Approximate Calculation
                 of Multiple Integrals",
  journal =      j-TOMS,
  volume =       "17",
  number =       "4",
  pages =        "437--451",
  month =        dec,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210232.210233",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65D30)",
  MRnumber =     "1 140 034",
  bibdate =      "Sun Sep 04 23:59:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p437-berntsen/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE.",
}

@Article{Berntsen:1991:ADA,
  author =       "Jarle Berntsen and Terje O. Espelid and Alan Genz",
  title =        "{Algorithm 698}: {DCUHRE}: An Adaptive
                 Multidimensional Integration Routine for a Vector of
                 Integrals",
  journal =      j-TOMS,
  volume =       "17",
  number =       "4",
  pages =        "452--456",
  month =        dec,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210232.210234",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65D30)",
  MRnumber =     "1 140 035",
  bibdate =      "Sun Sep 04 23:59:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p452-berntsen/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE.",
}

@Article{Krogh:1991:ANR,
  author =       "Fred T. Krogh and W. Van Snyder",
  title =        "{Algorithm 699}: a New Representation of {Patterson}'s
                 Quadrature Formulae",
  journal =      j-TOMS,
  volume =       "17",
  number =       "4",
  pages =        "457--461",
  month =        dec,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210232.210235",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 09:54:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p457-krogh/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE.",
}

@Article{Broughan:1991:SHL,
  author =       "Kevin A. Broughan",
  title =        "{SENAC}: a High-Level Interface for the {NAG}
                 Library",
  journal =      j-TOMS,
  volume =       "17",
  number =       "4",
  pages =        "462--480",
  month =        dec,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210232.210236",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:59:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p462-broughan/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "design; languages; performance; theory",
  subject =      "{\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and
                 Techniques. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE. {\bf I.1.3}: Computing
                 Methodologies, ALGEBRAIC MANIPULATION, Languages and
                 Systems. {\bf I.2.2}: Computing Methodologies,
                 ARTIFICIAL INTELLIGENCE, Automatic Programming.",
}

@Article{Marletta:1991:CAN,
  author =       "Marco Marletta",
  title =        "Certification of {Algorithm 700}: Numerical Tests of
                 the {SLEIGN} Software for {Sturm--Liouville} Problems",
  journal =      j-TOMS,
  volume =       "17",
  number =       "4",
  pages =        "481--490",
  month =        dec,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210232.210237",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Sep 04 23:59:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p481-marletta/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance; reliability",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE. {\bf G.1}: Mathematics of Computing,
                 NUMERICAL ANALYSIS.",
}

@Article{Bailey:1991:EEC,
  author =       "Paul B. Bailey and Burton S. Garbow and Hans G. Kaper
                 and Anton Zettl",
  title =        "Eigenvalue and Eigenfunction Computations for
                 {Sturm--Liouville} Problems",
  journal =      j-TOMS,
  volume =       "17",
  number =       "4",
  pages =        "491--499",
  month =        dec,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210232.210238",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L15",
  MRnumber =     "1 140 036",
  bibdate =      "Sun Sep 04 23:59:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p491-bailey/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations.",
}

@Article{Bailey:1991:AFS,
  author =       "Paul B. Bailey and Burton S. Garbow and Hans G. Kaper
                 and Anton Zettl",
  title =        "{Algorithm 700}: {A FORTRAN} Software Package for
                 {Sturm--Liouville} Problems",
  journal =      j-TOMS,
  volume =       "17",
  number =       "4",
  pages =        "500--501",
  month =        dec,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210232.210239",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L15",
  MRnumber =     "1 140 037",
  bibdate =      "Sun Sep 04 23:59:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p500-bailey/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.m}: Mathematics of Computing, MISCELLANEOUS.",
}

@Article{Alfeld:1991:EAS,
  author =       "Peter Alfeld and David J. Eyre",
  title =        "The Exact Analysis of Sparse Rectangular Linear
                 Systems",
  journal =      j-TOMS,
  volume =       "17",
  number =       "4",
  pages =        "502--518",
  month =        dec,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210232.210240",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65F50)",
  MRnumber =     "1 140 038",
  bibdate =      "Sun Sep 04 23:59:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p502-alfeld/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "measurement; performance; theory",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra.",
}

@Article{Alfeld:1991:AGE,
  author =       "Peter Alfeld and David J. Eyre",
  title =        "{Algorithm 701}: {Goliath}\emdash a Software System
                 for the Exact Analysis of Rank-Deficient Sparse
                 Rational Linear Systems",
  journal =      j-TOMS,
  volume =       "17",
  number =       "4",
  pages =        "519--532",
  month =        dec,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210232.210241",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65F50)",
  MRnumber =     "1 140 039",
  bibdate =      "Sun Sep 04 23:59:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p519-alfeld/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra.",
}

@Article{Gustafsson:1991:CTT,
  author =       "Kjell Gustafsson",
  title =        "Control Theoretic Techniques for Stepsize Selection in
                 Explicit {Runge--Kutta} Methods",
  journal =      j-TOMS,
  volume =       "17",
  number =       "4",
  pages =        "533--554",
  month =        dec,
  year =         "1991",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210232.210242",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65L06)",
  MRnumber =     "1 140 040",
  bibdate =      "Sun Sep 04 23:59:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1991-17-4/p533-gustafsson/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Reliability and robustness.",
}

@Article{Boubez:1992:PED,
  author =       "Toufic I. Boubez and Andy M. Froncioni and Richard L.
                 Peskin",
  title =        "A Prototyping Envelope for Differential Equations",
  journal =      j-TOMS,
  volume =       "18",
  number =       "1",
  pages =        "1--10",
  month =        mar,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/128745.128746",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 08:43:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-1/p1-boubez/",
  abstract =     "A system is presented to allow end users to solve
                 nonlinear differential equations without need to write
                 computer programs. The system treats $n$th order space
                 (one dimensional), first order time systems with
                 initial and/or two point boundary value specification.
                 Users of the system need only enter the problem in
                 direct mathematical notation, and output is
                 automatically presented as a solution graph. The system
                 allows the user to alter this equations, in-situ, that
                 is to computationally steer his model. Thus the system
                 is suited for model prototyping. Implementation is
                 based on an object-oriented paradigm, well established
                 and robust numerical procedures, and distributed
                 computing to supported needed resources for numerically
                 intensive tasks.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "design; experimentation; languages",
  subject =      "{\bf D.2.6}: Software, SOFTWARE ENGINEERING,
                 Programming Environments. {\bf D.2.m}: Software,
                 SOFTWARE ENGINEERING, Miscellaneous. {\bf G.1.5}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of
                 Nonlinear Equations. {\bf D.3.2}: Software, PROGRAMMING
                 LANGUAGES, Language Classifications, Smalltalk.",
}

@Article{Lucks:1992:ASM,
  author =       "Michael Lucks and Ian Gladwell",
  title =        "Automated Selection of Mathematical Software",
  journal =      j-TOMS,
  volume =       "18",
  number =       "1",
  pages =        "11--34",
  month =        mar,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/128745.128747",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 08:43:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-1/p11-lucks/",
  abstract =     "Current approaches to recommending mathematical
                 software are qualitative and categorical. These
                 approaches are unsatisfactory when the problem to be
                 solved has features that can ``trade-off'' in the
                 recommendation process. A quantitative system is
                 proposed that permits tradeoffs and can be built and
                 modified incrementally. This quantitative approach
                 extends other knowledge-engineering techniques in its
                 knowledge representation and aggregation facilities.
                 The system is demonstrated on the domain of ordinary
                 differential equation initial value problems. The
                 results are significantly superior to an existing
                 qualitative (decision tree) system.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE. {\bf G.1.7}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 Initial value problems. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE. {\bf I.2.4}:
                 Computing Methodologies, ARTIFICIAL INTELLIGENCE,
                 Knowledge Representation Formalisms and Methods,
                 Representation languages.",
}

@Article{Olszewski:1992:FTA,
  author =       "Jan Olszewski",
  title =        "A Flexible Thinning Algorithm Allowing Parallel,
                 Sequential, and Distributed Application",
  journal =      j-TOMS,
  volume =       "18",
  number =       "1",
  pages =        "35--45",
  month =        mar,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/128745.128748",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 09:54:33 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-1/p35-olszewski/",
  abstract =     "A parallel thinning algorithm for digital patterns is
                 presented. This algorithm can also be used for
                 sequential thinning without the simulation of parallel
                 computation. The mathematical background of the
                 algorithm bases on the notion of the Euler
                 characteristic. The proposed algorithm is simple and
                 particularly faster than other parallel algorithms.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; theory",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Parallel algorithms. {\bf I.5.2}:
                 Computing Methodologies, PATTERN RECOGNITION, Design
                 Methodology. {\bf I.4.1}: Computing Methodologies,
                 IMAGE PROCESSING, Digitization. {\bf D.1.3}: Software,
                 PROGRAMMING TECHNIQUES, Concurrent Programming.",
}

@Article{Schlick:1992:TETa,
  author =       "Tamar Schlick and Aaron Fogelson",
  title =        "{TNPACK}\emdash a Truncated {Newton} Minimization
                 Package for Large-Scale Problems: {I}. Algorithm and
                 Usage",
  journal =      j-TOMS,
  volume =       "18",
  number =       "1",
  pages =        "46--70",
  month =        mar,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/128745.150973",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Feb 10 08:50:20 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-1/p46-schlick/",
  abstract =     "We present a FORTRAN package of subprograms for
                 minimizing multivariate functions without constraints
                 by a truncated Newton algorithm. The algorithm is
                 especially suited for problems involving a large number
                 of variables. Truncated Newton methods allow
                 approximate, rather than exact, solutions to the Newton
                 equations. Truncation is accomplished in the present
                 version by using the preconditioned Conjugate Gradient
                 algorithm (PCG) to solve approximately the Newton
                 equations. The preconditioner $M$ is factored in PCG
                 using a sparse modified Cholesky factorization based on
                 the Yale Sparse Matrix Package. In this paper we
                 briefly describe the method and provide details for
                 program usage.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE. {\bf G.1.3}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse
                 and very large systems. {\bf G.1.6}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear
                 programming.",
}

@Article{Schlick:1992:TETb,
  author =       "Tamar Schlick and Aaron Fogelson",
  title =        "{TNPACK}\emdash a Truncated {Newton} Minimization
                 Package for Large-Scale Problems: {II}. Implementation
                 Examples",
  journal =      j-TOMS,
  volume =       "18",
  number =       "1",
  pages =        "71--111",
  month =        mar,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/128745.150975",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Feb 10 08:50:15 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-1/p71-schlick/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE. {\bf G.1.3}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse
                 and very large systems. {\bf G.1.6}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear
                 programming. {\bf I.6.3}: Computing Methodologies,
                 SIMULATION AND MODELING, Applications. {\bf J.2}:
                 Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING. {\bf J.3}: Computer Applications, LIFE AND
                 MEDICAL SCIENCES.",
}

@Article{Hanson:1992:QTM,
  author =       "R. J. Hanson and Fred T. Krogh",
  title =        "A Quadratic-Tensor Model Algorithm for Nonlinear
                 Least-Squares Problems with Linear Constraints",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "115--133",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146857",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65Y10 (49M30)",
  MRnumber =     "1 167 883",
  bibdate =      "Mon Sep 05 08:48:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p115-hanson/",
  abstract =     "A new algorithm is presented for solving nonlinear
                 least-squares and nonlinear equation problems. The
                 algorithm is based on approximating the nonlinear
                 functions using the quadratic-tensor model proposed by
                 Schnabel and Frank. The problem statement may include
                 simple bounds or more general linear constraints on the
                 unknowns. The algorithm uses a trust-region defined by
                 a box containing the current values of the unknowns.
                 The objective function (Euclidean length of the
                 functions) is allowed to increase at intermediate
                 steps. These increases are allowed as long as our
                 predictor indicates that a new set of best values
                 exists in the trust-region. There is logic provided to
                 retreat to the current best values, should that be
                 required. The computations for the model-problem
                 require a constrained nonlinear least-squares solver.
                 This is done using a simpler version of the algorithm.
                 In its present form the algorithm is effective for
                 problems with linear constraints and dense Jacobian
                 matrices. Results on standard test problems are
                 presented in the Appendix. The new algorithm appears to
                 be efficient in terms of function and Jacobian
                 evaluations.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Nonlinear programming.",
}

@Article{Gurwitz:1992:TCE,
  author =       "Chaya Gurwitz",
  title =        "A Test for Cancellation Errors In Quasi-{Newton}
                 Methods",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "134--140",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146876",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65K10 (90C30)",
  MRnumber =     "1 167 884",
  bibdate =      "Mon Sep 05 08:48:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p134-gurwitz/",
  abstract =     "It has recently been shown that cancellation errors in
                 a quasi-Newton method can increase without bound as the
                 method converges. A simple test is presented to
                 determine when cancellation errors could lead to
                 significant contamination of the approximating
                 matrix.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Reliability and
                 robustness.",
}

@Article{Schlick:1992:ATE,
  author =       "Tamar Schlick and Aaron Fogelson",
  title =        "{Algorithm 702}: {TNPACK}\emdash a Truncated
                 {Newton} Minimization Package for Large-Scale Problems:
                 {I}. Algorithm and Usage",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "141--141",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146921;
                 http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p141-schlick/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Feb 10 08:50:33 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Xie:1999:RAU}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE. {\bf G.1.3}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra, Sparse
                 and very large systems. {\bf G.1.6}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization, Nonlinear
                 programming.",
}

@Article{Cash:1992:MCS,
  author =       "J. R. Cash and S. Considine",
  title =        "An {MEBDF} Code for Stiff Initial Value Problems",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "142--155",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146922",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D05 (65L06)",
  MRnumber =     "1 167 885",
  bibdate =      "Mon Sep 05 08:48:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p142-cash/",
  abstract =     "In two recent papers one of the present authors has
                 proposed a class of modified extended backward
                 differentiation formulae for the numerical integration
                 of stiff initial value problems. In this paper we
                 describe a code based on this class of formulae and
                 discuss its performance on a large set of stiff test
                 problems.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems. {\bf G.1.1}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Interpolation. {\bf G.1.7}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Multistep methods. {\bf G.1.7}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Stiff equations. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Cash:1992:AMF,
  author =       "J. R. Cash and S. Considine",
  title =        "{Algorithm 703}: {MEBDF}: {A FORTRAN} Subroutine for
                 Solving First-Order Systems of Stiff Initial Value
                 Problems for Ordinary Differential Equations",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "156--158",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146923",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D05 (65L06)",
  MRnumber =     "1 167 886",
  bibdate =      "Sat Jan 27 07:37:25 MST 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p156-cash/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems. {\bf G.1.1}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Interpolation. {\bf G.1.7}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Multistep methods. {\bf G.1.7}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Stiff equations. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Neidinger:1992:EMN,
  author =       "Richard D. Neidinger",
  title =        "An Efficient Method for the Numerical Evaluation of
                 Partial Derivatives of Arbitrary Order",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "159--173",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146924",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D25 (65Y10)",
  MRnumber =     "93b:65040",
  bibdate =      "Mon Sep 05 08:48:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p159-neidinger/",
  abstract =     "For any typical multivariable expression $f$, point
                 $a$ in the domain of $f$, and positive integer
                 maxorder, this method produces the numerical values of
                 all partial derivatives at $a$ up through order
                 maxorder. By the technique known as automatic
                 differentiation, theoretically exact results are
                 obtained using numerical (as opposed to symbolic)
                 manipulation. The key ideas are a hyperpyramid data
                 structure and a generalized Leibniz's rule. Any
                 expression in $n$ variables corresponds to a
                 hyperpyramid array, in $n$-dimensional space,
                 containing the numerical values of all unique partial
                 derivatives (not wasting space on different
                 permutations of derivatives). The arrays for simple
                 expressions are combined by hyperpyramid operators to
                 form the arrays for more complicated expressions. These
                 operators are facilitated by a generalized Leibniz's
                 rule which, given a product of multivariable functions,
                 produces any partial derivative by forming the minimum
                 number of products (between two lower partials)
                 together with a product of binomial coefficients. The
                 algorithms are described in abstract pseudo-code. A
                 section on implementation shows how these ideas can be
                 converted into practical and efficient programs in a
                 typical computing environment. For any specific
                 problem, only the expression itself would require
                 recoding.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.
                 {\bf I.1.2}: Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms, Nonalgebraic algorithms. {\bf
                 G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Numerical algorithms. {\bf G.4}: Mathematics
                 of Computing, MATHEMATICAL SOFTWARE, Algorithm
                 analysis. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Efficiency.",
}

@Article{Edwards:1992:EEN,
  author =       "John A. Edwards",
  title =        "Exact Equations of the Nonlinear Spline",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "174--192",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146925",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "41A15 (65D05 65D07 65K10 65Y25)",
  MRnumber =     "93c:41018",
  bibdate =      "Mon Sep 05 08:48:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p174-edwards/",
  abstract =     "We define the spline interpolating function, and
                 obtain in directly computable form the elementary set
                 of nonlinear equations describing nonlinear spline
                 curves. Using Newton's and Newton-like methods, we
                 solve typical spline configurations, and hence infer
                 that the procedure will reliably yield precise
                 extremum-energy solutions to nonlinear splines of
                 arbitrary (but presumably reasonable) size and
                 complexity.\par

                 In order to distinguish between stable and unstable
                 states of spline equilibria, we evaluate the energy
                 change resulting from a perturbation, and we briefly
                 discuss aspects of spline existence and uniqueness in
                 relation to the solved examples. We demonstrate the
                 abrupt transition which occurs at the threshold between
                 spline existence and nonexistence, and conclude that
                 proof of a spline's existence is implicit in the
                 solution set of constants yielded by the
                 method.\par

                 The procedure may be regarded on the one hand as a
                 precise and efficient research instrument for
                 investigating the properties of true splines and
                 elastica, and on the other as an everyday method for
                 obtaining ``the smoothest interpolating curve of
                 all''.\par

                 Contact is always maintained with the physical analogue
                 to the curve, the thin uniform elastic beam, since the
                 four assignable parameters used in each spline interval
                 comprise the necessary and sufficient three angles and
                 one length dimension of the actual physical
                 spline.\par

                 On an historical note, the method may be seen to offer
                 progress in the search, begun in the late 17th century,
                 for a definitive solution to the elastica problem.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation, Spline and piecewise
                 polynomial interpolation. {\bf G.1.6}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization,
                 Constrained optimization. {\bf G.1.7}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations, Boundary value problems. {\bf I.3.5}:
                 Computing Methodologies, COMPUTER GRAPHICS,
                 Computational Geometry and Object Modeling, Splines.
                 {\bf J.2}: Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Engineering. {\bf J.2}: Computer
                 Applications, PHYSICAL SCIENCES AND ENGINEERING,
                 Physics.",
}

@Article{Majaess:1992:SAB,
  author =       "Fouad Majaess and Patrick Keast and Graeme Fairweather
                 and Karin R. Bennett",
  title =        "The Solution of Almost Block Diagonal Linear Systems
                 Arising in Spline Collocation at {Gaussian} Points with
                 Monomial Basis Functions",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "193--204",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146926",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65D15 65F05)",
  MRnumber =     "93a:65002",
  bibdate =      "Mon Sep 05 08:48:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p193-majaess/",
  abstract =     "Numerical techniques based on piecewise polynomial
                 (that is, spline) collation at Gaussian points are
                 exceedingly effective for the approximate solution of
                 boundary value problems, both for ordinary differential
                 equations and for time dependent partial differential
                 equations. There are several widely available computer
                 codes based on this approach, all of which have at
                 their core a particular choice of basis representation
                 for the piecewise polynomials used to approximate the
                 solutions. Until recently, the most popular approach
                 was to use a B-spline representation, but it has been
                 shown that the B-spline basis is inferior, both in
                 operation counts and conditioning, to a certain
                 monomial basis, and the latter has come more into
                 favor. In this paper, we describe a linear algebraic
                 equations which arise in spline collocation at Gaussian
                 points with such a monomial basis. It is shown that the
                 new package, which implements an alternate column and
                 row pivoting algorithm, is a distinct improvement over
                 existing packages from the points of view of speed and
                 storage requirements. In addition, we describe a second
                 package, an important special case of the first, for
                 solving the almost block diagonal systems which arise
                 when condensation is applied to the systems arising in
                 spline collocation at Gaussian points, and also in
                 other methods for solving two-point boundary value
                 problems, such as implicit Runge--Kutta methods and
                 multiple shooting.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Algorithm analysis. {\bf G.1.3}: Mathematics
                 of Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative
                 methods).",
}

@Article{Majaess:1992:AAA,
  author =       "Fouad Majaess and Patrick Keast and Graeme Fairweather
                 and Karin R. Bennett",
  title =        "{Algorithm 704}: {ABDPACK} and {ABBPACK}\emdash
                 {FORTRAN} Programs for the Solution of Almost Block
                 Diagonal Linear Systems Arising in Spline Collocation
                 at {Gaussian} Points with Monomial Basis Functions",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "205--210",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146927",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65F05)",
  MRnumber =     "93a:65003",
  bibdate =      "Mon Sep 05 08:48:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p205-majaess/",
  abstract =     "ABDPACK is a package of FORTRAN programs for the
                 solution of systems of linear equations with the almost
                 block diagonal structure arising in spline collocation
                 at Gaussian points with monomial spline basis
                 functions, when applied to two-point boundary value
                 problems with separated boundary conditions. The
                 package ABBPACK is designed to handle a subclass of
                 such linear systems which have what may be called an
                 almost block bidiagonal structure. Such systems result,
                 for example, when condensation is applied to the full
                 spline collocation linear system. This package may also
                 be used to solve the almost block bidiagonal systems
                 arising in multiple shooting techniques and implicit
                 Runge--Kutta methods for solving two-point boundary
                 value problems. The algorithms implemented in the
                 package are based on an alternate column and row
                 pivoting scheme which avoids most of the fill-in
                 introduced by more commonly used techniques.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; standardization",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf G.1.2}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Spline and piecewise polynomial
                 approximation. {\bf I.1.2}: Computing Methodologies,
                 ALGEBRAIC MANIPULATION, Algorithms. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@Article{Tang:1992:TDI,
  author =       "Ping Tak Peter Tang",
  title =        "Table-Driven Implementation of the {{\tt Expm1}}
                 Function in {IEEE} Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "211--222",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146928",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D15",
  MRnumber =     "1 167 891",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See independent analysis and accuracy confirmation of
                 this algorithm in \cite{Kramer:1998:PWC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p211-tang/",
  abstract =     "Algorithms and implementation details for the function
                 $e^x - 1$ in both single and double precision of IEEE
                 754 arithmetic are presented here. With a table of
                 moderate size, the implementations need only
                 working-precision arithmetic and are provably accurate
                 to within 0.58 ulp.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Error analysis. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@Article{Gardiner:1992:SSM,
  author =       "Judith D. Gardiner and Alan J. Laub and James J. Amato
                 and Cleve B. Moler",
  title =        "Solution of the {Sylvester} Matrix Equation
                 {$AXB^{\sc{T}}+CXD^{\sc{T}}=E$}",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "223--231",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146929",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05 (65-04 65F10 65F35)",
  MRnumber =     "1 167 892",
  bibdate =      "Mon Sep 05 08:48:51 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p223-gardiner/",
  abstract =     "A software package has been developed to solve
                 efficiently the Sylvester-type matrix equation $AXB^{T}
                 + CXD^{T} = E$. A transformation method is used which
                 employs the QZ algorithm to structure the equation in
                 such a way that it can be solved columnwise by a back
                 substitution technique. The algorithm is an extension
                 of the Bartels--Stewart method and the
                 Hessenberg--Schur method. The numerical performance of
                 the algorithms and software is demonstrated by
                 application to near-singular systems.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf G.1.3}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Conditioning. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Efficiency. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Reliability and
                 robustness. {\bf F.2.1}: Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Numerical Algorithms and Problems, Computations on
                 matrices.",
}

@Article{Gardiner:1992:AFS,
  author =       "Judith D. Gardiner and Matthew R. Wette and Alan J.
                 Laub and James J. Amato and Cleve B. Moler",
  title =        "{Algorithm 705}: {A FORTRAN-77} Software Package for
                 Solving the {Sylvester} Matrix Equation
                 {$AXB^{\sc{T}}+CXD^{\sc{T}}=E$}",
  journal =      j-TOMS,
  volume =       "18",
  number =       "2",
  pages =        "232--238",
  month =        jun,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/146847.146930",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05 (65-04 65F10 65F35)",
  MRnumber =     "1 167 893",
  bibdate =      "Tue Mar 14 17:31:30 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See corrections \cite{Hopkins:2002:RAF}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-2/p232-gardiner/",
  abstract =     "This paper documents a software package for solving
                 the Sylvester matrix equation (1) $AXB^{T} + CXD^{T} =
                 E$.\par

                 All quantities are real matrices; $A$ and $C$ are $m
                 \times n$; $B$ and $D$ are $m \times n$; and $X$ and
                 $E$ are $m \times n$. The unknown is $X$. Two symmetric
                 forms of Eq. (1) are treated separately for efficiency.
                 They are the continuous-time symmetric Sylvester
                 equation (2) $AXE^{T} + EXA^{T} + C = 0$ and the
                 discrete time equation (3) $AXA^{T} + C = 0$, for which
                 $A$, $E$, and $C$ is symmetric. The software also
                 provides a means for estimating the condition number of
                 these three equations. The algorithms employed are more
                 fully described in an accompanying paper [3].",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf G.1.3}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Conditioning. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Efficiency. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Reliability and
                 robustness.",
}

@Article{Weerawarana:1992:PCG,
  author =       "Sanjiva Weerawarana and Paul S. Wang",
  title =        "A Portable Code Generator for {CRAY FORTRAN}",
  journal =      j-TOMS,
  volume =       "18",
  number =       "3",
  pages =        "241--255",
  month =        sep,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/131766.131767",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 09:15:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p241-weerawarana/",
  abstract =     "One way to combine the powers of symbolic computing
                 with numeric computing is to automatically derive and
                 produce numeric code. This approach has important
                 applications in science and engineering. Once the
                 desired formulas and procedures are derived in a
                 symbolic manipulation system, they can be translated
                 into a target numeric language by a {\em code
                 generator}. GENCRAY is a code generator written in the
                 C language for portability. GENCRAY defines a
                 LISP-style input language that is translated into
                 either FORTRAN 77 or CRAY FORTRAN. By defining its own
                 input syntax, GENCRAY becomes a free-standing code
                 translator that can be made to work with any symbolic
                 manipulation system. GENCRAY is portable to any
                 computer system with a standard C compiler. Input to
                 GENCRAY can come from a file or directly from a
                 symbolic system through a pipe. On UNIX systems with
                 Berkeley networking, GENCRAY also runs as a network
                 server. The input syntax is customizable to allow both
                 Common and Franz LISP input styles. In addition to
                 generating easily vectorizable CRAY FORTRAN code,
                 GENCRAY also provides high-level, easy-to-use parallel
                 programming macros to produce parallel code for the
                 multiprocessor CRAY systems. The features,
                 applications, usage, and implementation of GENCRAY are
                 described. Techniques for producing parallel codes are
                 discussed and illustrated by a substantial example
                 contained in the Appendix.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; theory",
  subject =      "{\bf D.3.4}: Software, PROGRAMMING LANGUAGES,
                 Processors, Code generation. {\bf D.1.2}: Software,
                 PROGRAMMING TECHNIQUES, Automatic Programming. {\bf
                 D.1.3}: Software, PROGRAMMING TECHNIQUES, Concurrent
                 Programming. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General. {\bf I.1.4}: Computing
                 Methodologies, ALGEBRAIC MANIPULATION, Applications.
                 {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf C.1.2}: Computer Systems
                 Organization, PROCESSOR ARCHITECTURES, Multiple Data
                 Stream Architectures (Multiprocessors), Array and
                 vector processors. {\bf D.3.2}: Software, PROGRAMMING
                 LANGUAGES, Language Classifications, C.",
}

@Article{Hansen:1992:FSG,
  author =       "Per Christian Hansen and Tony F. Chan",
  title =        "{FORTRAN} Subroutines for General {Toeplitz} Systems",
  journal =      j-TOMS,
  volume =       "18",
  number =       "3",
  pages =        "256--273",
  month =        sep,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/131766.131768",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:08:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Hansen:1994:CAF}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p256-hansen/",
  abstract =     "This paper presents FORTRAN 77 implementations of the
                 lookahead Levinson algorithm of Chan and Hansen [7, 8]
                 for solving symmetric indefinite and general Toeplitz
                 systems. The algorithms are numerically stable for all
                 Toeplitz matrices that do not have many {\em
                 consecutive} ill-conditioned leading principal
                 submatrices, and also produce estimates of the
                 algorithm and matrix condition numbers. In contrast,
                 the classical Levinson algorithm is only guaranteed to
                 be numerically stable for symmetric positive definite
                 Toeplitz matrices, and no condition estimate is
                 produced.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Algorithm analysis. {\bf G.1.3}: Mathematics
                 of Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative methods).
                 {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77.",
}

@Article{Demmel:1992:SBA,
  author =       "James W. Demmel and Nicholas J. Higham",
  title =        "Stability of Block Algorithms with Fast Level-3
                 {BLAS}",
  journal =      j-TOMS,
  volume =       "18",
  number =       "3",
  pages =        "274--291",
  month =        sep,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/131766.131769",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:27:16 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Dongarra:1990:ASL,Higham:1990:EFM,Dayde:1994:PBI}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p274-demmel/",
  abstract =     "Block algorithms are becoming increasingly popular in
                 matrix computations. Since their basic unit of data is
                 a submatrix rather than a scalar, they have a higher
                 level of granularity than point algorithms, and this
                 makes them well suited to high-performance computers.
                 The numerical stability of the block algorithms in the
                 new linear algebra program library LAPACK is
                 investigated here. It is shown that these algorithms
                 have backward error analyses in which the backward
                 error bounds are commensurate with the error bounds for
                 the underlying level-3 BLAS (BLAS3). One implication is
                 that the block algorithms are as stable as the
                 corresponding point algorithms when conventional BLAS3
                 are used. A second implication is that the use of BLAS3
                 based on fast matrix multiplication techniques affects
                 the stability only insofar as it increases the constant
                 terms in the normwise backward error bounds. For linear
                 equation solvers employing {\em LU} factorization, it
                 is shown that fixed precision iterative refinement
                 helps to mitigate the effect of the larger error
                 constants. Despite the positive results presented here,
                 not all plausible block algorithms are stable; we
                 illustrate this with the example of {\em LU}
                 factorization with block triangular factors and
                 describe how to check a block algorithm for stability
                 without doing a full error analysis.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra. {\bf F.2.1}: Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices.",
}

@Article{Ammar:1992:IDC,
  author =       "G. S. Ammar and L. Reichel and D. C. Sorensen",
  title =        "An Implementation of a Divide and Conquer Algorithm
                 for the Unitary Eigenproblem",
  journal =      j-TOMS,
  volume =       "18",
  number =       "3",
  pages =        "292--307",
  month =        sep,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/131766.131770",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:08:42 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Ammar:1994:CAI}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p292-ammar/",
  abstract =     "We present a FORTRAN implementation of a
                 divide-and-conquer method for computing the spectral
                 resolution of a unitary upper Hessenberg matrix $H$.
                 Any such matrix $H$ of order $n$, normalized so that
                 its subdiagonal elements are nonnegative, can be
                 written as a product of $n-1$ Givens matrices and a
                 diagonal matrix. This representation, which we refer to
                 as the Schur parametric form of $H$, arises naturally
                 in applications such as in signal processing and in the
                 computation of Gauss--Szeg{\H{o}} quadrature rules. Our
                 programs utilize the Schur parametrization to compute
                 the spectral decomposition of $H$ without explicitly
                 forming the elements of $H$. If only the eigenvalues
                 and first components of the eigenvectors are desired,
                 as in the applications mentioned above, the algorithm
                 requires only $O(n^{2})$ arithmetic operations.
                 Experimental results presented indicate that the
                 algorithm is reliable and competitive with the general
                 QR algorithm applied to this problem. Moreover, the
                 algorithm can be easily adapted for parallel
                 implementation.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance; reliability",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.
                 {\bf F.2.1}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices.",
}

@Article{Toint:1992:LFS,
  author =       "Ph. L. Toint and D. Tuyttens",
  title =        "{LSNNO}, {A FORTRAN} Subroutine for Solving
                 Large-Scale Nonlinear Network Optimization Problems",
  journal =      j-TOMS,
  volume =       "18",
  number =       "3",
  pages =        "308--328",
  month =        sep,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/131766.131771",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:27:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p308-toint/",
  abstract =     "The implementation and testing of LSNNO, a new FORTRAN
                 subroutine for solving large-scale nonlinear network
                 optimization problems is described. The implemented
                 algorithm applies the concepts of partial separability
                 and partitioned quasi-Newton updating to
                 high-dimensional nonlinear network optimization
                 problems. Some numerical results on both academic and
                 practical problems are reported.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Nonlinear programming. {\bf
                 G.1.6}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Constrained optimization. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf
                 G.2.2}: Mathematics of Computing, DISCRETE MATHEMATICS,
                 Graph Theory, Network problems. {\bf D.3.2}: Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 FORTRAN.",
}

@Article{Berntsen:1992:ADA,
  author =       "Jarle Berntsen and Terje O. Espelid",
  title =        "{Algorithm 706}: {DCUTRI}: An Algorithm for Adaptive
                 Cubature Over a Collection of Triangles",
  journal =      j-TOMS,
  volume =       "18",
  number =       "3",
  pages =        "329--342",
  month =        sep,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/131766.131772",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:18:59 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Espelid:1998:RAD}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p329-berntsen/",
  abstract =     "An adaptive algorithm for computing an approximation
                 to the integral of each element in a vector function
                 $f(x,y)$ over a two-dimensional region made up of
                 triangles is presented. A FORTRAN implementation of the
                 algorithm is included. The basic cubature rule used
                 over each triangle is a 37-point symmetric rule of
                 degree 13. Based on the same evaluation points the
                 local error for each element in the approximation
                 vector and for each triangle is computed using a
                 sequence of null rule evaluations. A sophisticated
                 error-estimation procedure tries, in a cautious manner,
                 to decide whether we have asymptotic behavior locally
                 for each function. Different actions are taken
                 depending on that decision, and the procedure takes
                 advantage of the basic rule's polynomial degree when
                 computing the error estimate in the asymptotic case.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; reliability",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation,
                 Adaptive quadrature. {\bf G.1.4}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation, Multiple quadrature. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Reliability and robustness.",
}

@Article{Hopkins:1992:RPG,
  author =       "Tim Hopkins",
  title =        "Remark on ``{Algorithm 540}: {PDECOL}, General
                 Collocation Software for Partial Differential Equations
                 [{D3}]''",
  journal =      j-TOMS,
  volume =       "18",
  number =       "3",
  pages =        "343--344",
  month =        sep,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/131766.131773",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:27:53 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Madsen:1979:APG}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p343-hopkins/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Algorithm analysis. {\bf D.3.2}: Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 FORTRAN.",
}

@Article{Nardin:1992:ACN,
  author =       "Mark Nardin and W. F. Perger and Atul Bhalla",
  title =        "{Algorithm 707}: {CONHYP}: a Numerical Evaluator of
                 the Confluent Hypergeometric Function for Complex
                 Arguments of Large Magnitudes",
  journal =      j-TOMS,
  volume =       "18",
  number =       "3",
  pages =        "345--349",
  month =        sep,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/131766.131774",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 01:28:04 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p345-nardin/",
  abstract =     "A numerical evaluator for the confluent hypergeometric
                 function for complex arguments with large magnitudes
                 using a direct summation of Kummer's series is
                 presented. Extended precision subroutines using large
                 arrays to accumulate a single numerator and denominator
                 are ultimately used in a single division to arrive at
                 the final result. The accuracy has been verified
                 through a variety of tests and they show the evaluator
                 to be consistently accurate to 13 significant figures,
                 and on rare occasion accurate to only 9 for magnitudes
                 of the arguments ranging into the thousands in any
                 quadrant in the complex plane. Because the evaluator
                 automatically determines the number of significant
                 figures of machine precision, and because it is written
                 in FORTRAN 77, tests on various computers have shown
                 the evaluator to provide consistently accurate results,
                 making the evaluator very portable. The principal
                 drawback is that, for certain arguments, the evaluator
                 is slow; however, the evaluator remains valuable as a
                 benchmark even in such cases.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf J.2}: Computer Applications, PHYSICAL SCIENCES
                 AND ENGINEERING. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis. {\bf D.3.2}:
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77.",
}

@Article{Schweikard:1992:RZI,
  author =       "Achim Schweikard",
  title =        "Real Zero Isolation for Trigonometric Polynomials",
  journal =      j-TOMS,
  volume =       "18",
  number =       "3",
  pages =        "350--359",
  month =        sep,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/131766.131775",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65H05 (65D15)",
  MRnumber =     "93g:65066",
  bibdate =      "Fri Sep 30 01:28:05 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p350-schweikard/",
  abstract =     "An exact and practical method for determining the
                 number, location, and multiplicity of all real zeros of
                 the trigonometric polynomials is described. All
                 computations can be performed without loss of accuracy.
                 The method is based on zero isolation techniques for
                 algebraic polynomials. An efficient method for the
                 calculation of the coefficients of a corresponding
                 algebraic polynomial is stated. The complexity of
                 trigonometric zero isolation depending on the degree
                 and the coefficient size of the given trigonometric
                 polynomial is analyzed. In an experimental evaluation,
                 the performance of the method is compared to the
                 performance of recently developed numeric techniques
                 for the approximate determination of all roots of
                 trigonometric polynomials. The case of exponential or
                 hyperbolic polynomials is treated in an appendix.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf F.2.1}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on polynomials. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@Article{DiDonato:1992:ASD,
  author =       "Armido R. DiDonato and Alfred H. {Morris, Jr.}",
  title =        "{Algorithm 708}: Significant Digit Computation of the
                 Incomplete Beta Function Ratios",
  journal =      j-TOMS,
  volume =       "18",
  number =       "3",
  pages =        "360--373",
  month =        sep,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/131766.131776",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:14:47 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Brown:1994:CAS}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-3/p360-didonato/",
  abstract =     "An algorithm is given for evaluating the incomplete
                 beta function ratio $I_{x}(a,b)$ and its complement $1
                 - I^{x}(a,b)$. A new continued fraction and a new
                 asymptotic series are used with classical results. A
                 transportable Fortran subroutine based on this
                 algorithm is currently in use. It is accurate to 14
                 significant digits when precision is not restricted by
                 inherent error.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation.",
}

@Article{Buckley:1992:ATA,
  author =       "A. G. Buckley",
  title =        "{Algorithm 709}: Testing Algorithm Implementations",
  journal =      j-TOMS,
  volume =       "18",
  number =       "4",
  pages =        "375--391",
  month =        dec,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/138351.138378",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 00:52:09 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p375-buckley/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; experimentation",
  subject =      "{\bf D.2.5}: Software, SOFTWARE ENGINEERING, Testing
                 and Debugging, Monitors. {\bf G.1.6}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization, Gradient
                 methods. {\bf G.1.6}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Optimization, Nonlinear
                 programming. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing.",
}

@Article{Dongarra:1992:AFS,
  author =       "J. J. Dongarra and G. A. Geist and C. H. Romine",
  title =        "{Algorithm 710}: {FORTRAN} Subroutines for Computing
                 the Eigenvalues and Eigenvectors of a General Matrix by
                 Reduction to General Tridiagonal Form",
  journal =      j-TOMS,
  volume =       "18",
  number =       "4",
  pages =        "392--400",
  month =        dec,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/138351.138352",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 00:52:57 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p392-dongarra/",
  abstract =     "This paper describes programs to reduce a nonsymmetric
                 matrix to tridiagonal form, to compute the eigenvalues
                 of the tridiagonal matrix, to improve the accuracy of
                 an eigenvalue, and to compute the corresponding
                 eigenvector. The intended purpose of the software is to
                 find a few eigenpairs of a dense nonsymmetric matrix
                 faster and more accurately than previous methods. The
                 performance and accuracy of the new routines are
                 compared to two EISPACK paths: RG and HQR-INVIT. The
                 results show that the new routines are more accurate
                 and also faster if less than 20 percent of the
                 eigenpairs are needed.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf F.2.1}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices. {\bf G.1.3}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Eigenvalues. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.",
}

@Article{Fisher:1992:DTO,
  author =       "M. E. Fisher and L. S. Jennings",
  title =        "Discrete-Time Optimal Control Problems with General
                 Constraints",
  journal =      j-TOMS,
  volume =       "18",
  number =       "4",
  pages =        "401--413",
  month =        dec,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/138351.138356",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "49M05 (65K99)",
  MRnumber =     "1 199 848",
  bibdate =      "Fri Sep 30 00:52:58 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p401-fisher/",
  abstract =     "This paper presents a computational procedure for
                 solving combined discrete-time optimal control and
                 optimal parameter selection problems subject to general
                 constraints. The approach adopted is to convert the
                 problem into a nonlinear programming problem which can
                 be solved using standard optimization software. The
                 main features of the procedure are the way the controls
                 are parametrized and the conversion of all constraints
                 into a standard form suitable for computation. The
                 software is available commercially as a FORTRAN program
                 DMISER3 together with a companion program MISER3 for
                 solving continuous-time problems.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance; theory",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Constrained optimization. {\bf
                 G.1.0}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Numerical algorithms. {\bf G.1.6}: Mathematics
                 of Computing, NUMERICAL ANALYSIS, Optimization,
                 Nonlinear programming. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Efficiency.",
}

@Article{Nash:1992:ABS,
  author =       "Stephen G. Nash and Ariela Sofer",
  title =        "{Algorithm 711}: {BTN}: Software for Parallel
                 Unconstrained Optimization",
  journal =      j-TOMS,
  volume =       "18",
  number =       "4",
  pages =        "414--448",
  month =        dec,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/138351.138359",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 00:53:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p414-nash/",
  abstract =     "BTN is a collection of FORTRAN subroutines for solving
                 unconstrained nonlinear optimization problems. It
                 currently runs on both Intel hypercube computers
                 (distributed memory) and Sequent computers (shared
                 memory), and can take advantage of vector processors if
                 they are available. The software can also be run on
                 traditional computers to simulate the performance of a
                 parallel computer. BTN is a general-purpose algorithm,
                 capable of solving problems with a large numbers of
                 variables and suitable for users inexperienced with
                 parallel computing. It is designed to be as easy to use
                 as traditional algorithms for this problem, requiring
                 only that a (scalar) subroutine be provided to evaluate
                 the objective function and its gradient vector of first
                 derivatives. The algorithm is based on a block
                 truncated-Newton method. Truncated-Newton methods
                 obtain the search direction by approximately solving
                 the Newton equations via some iterative method. The
                 particular method used in BTN is a block version of the
                 Lanczos method, which is numerically stable for
                 nonconvex problems. In addition to the optimization
                 software, a parallel derivative checker is also
                 provided.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; documentation",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Parallel algorithms. {\bf G.1.6}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Gradient methods. {\bf G.1.6}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Nonlinear programming.",
}

@Article{Leva:1992:FNR,
  author =       "Joseph L. Leva",
  title =        "A Fast Normal Random Number Generator",
  journal =      j-TOMS,
  volume =       "18",
  number =       "4",
  pages =        "449--453",
  month =        dec,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/138351.138364",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 00:53:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p449-leva/",
  abstract =     "A method is presented for generating pseudorandom
                 numbers with a normal distribution. The technique uses
                 the ratio of uniform deviates method discovered by
                 Kinderman and Monahan with an improved set of bounding
                 curves. An optimized quadratic fit reduces the expected
                 number of logarithm evaluations to 0.012 per normal
                 deviate. The method gives a theoretically correct
                 distribution and can be implemented in 15 lines of
                 FORTRAN. Timing and source size comparisons are made
                 with other methods for generating normal deviates. The
                 proposed algorithm compares favorably with some of the
                 better algorithms.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance; theory",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Random number generation. {\bf G.3}:
                 Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing.",
}

@Article{Leva:1992:ANR,
  author =       "Joseph L. Leva",
  title =        "{Algorithm 712}: a Normal Random Number Generator",
  journal =      j-TOMS,
  volume =       "18",
  number =       "4",
  pages =        "454--455",
  month =        dec,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/138351.138367",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 00:53:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p454-leva/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Random number generation. {\bf G.3}:
                 Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical software.",
}

@Article{Boisvert:1992:PVS,
  author =       "Ronald F. Boisvert and Bonita V. Saunders",
  title =        "Portable Vectorized Software for {Bessel} Function
                 Evaluation",
  journal =      j-TOMS,
  volume =       "18",
  number =       "4",
  pages =        "456--469",
  month =        dec,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/138351.138370",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 00:53:41 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Boisvert:1993:CPV}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p456-boisvert/",
  abstract =     "A suite of computer programs for the evaluation of
                 Bessel functions and modified Bessel functions of
                 orders zero and one for a vector of real arguments is
                 described. Distinguishing characteristics of these
                 programs are that (a) they are portable across a wide
                 range of machines, and (b) they are vectorized in the
                 case when multiple function evaluations are to be
                 performed. The performance of the new programs are
                 compared with software from the FNLIB collection of
                 Fullerton on which the new software is based.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Chebyshev approximation and
                 theory. {\bf G.1.0}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Parallel algorithms. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Portability.",
}

@Article{Drezner:1992:CMN,
  author =       "Zvi Drezner",
  title =        "Computation of the Multivariate Normal Integral",
  journal =      j-TOMS,
  volume =       "18",
  number =       "4",
  pages =        "470--480",
  month =        dec,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/138351.138375",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:08:39 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Drezner:1993:CAC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p470-drezner/",
  abstract =     "This paper presents a direct computation of the
                 multivariate normal integral by the Gauss Quadrature
                 method. An error control method is given. Results are
                 presented for multivariate integrals consisting of up
                 to twelve normal distributions. A computer program in
                 FORTRAN is given.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Statistical software. {\bf G.1.4}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Quadrature and Numerical Differentiation, Multiple
                 quadrature.",
}

@Article{Aberth:1992:PCU,
  author =       "Oliver Aberth and Mark J. Schaefer",
  title =        "Precise Computation Using Range Arithmetic, via
                 {C++}",
  journal =      j-TOMS,
  volume =       "18",
  number =       "4",
  pages =        "481--491",
  month =        dec,
  year =         "1992",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/138351.138377",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 00:53:58 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1992-18-4/p481-aberth/",
  abstract =     "An arithmetic is described that can replace
                 floating-point arithmetic for programming tasks
                 requiring assured accuracy. A general explanation is
                 given of how the arithmetic is constructed with C++,
                 and a programming example in this language is supplied.
                 Times for solving representative problems are
                 presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; languages",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf D.3.2}:
                 Software, PROGRAMMING LANGUAGES, Language
                 Classifications, C++.",
}

@Article{Cody:1993:ACP,
  author =       "W. J. Cody",
  title =        "{Algorithm 714}: {CELEFUNT}: a Portable Test Package
                 for Complex Elementary Functions",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "1--21",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151272",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 20 18:24:35 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p1-cody/;
                 http://www.acm.org/pubs/toc/Abstracts/toms/151272.html",
  abstract =     "This paper discusses CELEFUNT, a package of Fortran
                 programs for testing complex elementary functions.",
  abstract-2 =   "The author discusses CELEFUNT, a package of Fortran
                 programs for testing complex elementary functions.
                 CELEFUNT is a collection of test programs for the
                 complex floating-point elementary functions required by
                 the 1978 ANSI Fortran Standard (CABS), CSQRT, CLOG,
                 CEXP, CSIN/CCOS, and the complex power function.",
  acknowledgement = ack-nhfb,
  affiliation =  "Div. of Math. and Comput. Sci., Argonne Nat. Lab., IL,
                 USA",
  classification = "C4100 (Numerical analysis); C5230 (Digital
                 arithmetic methods); C7310 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; CABS; CELEFUNT; CEXP; CLOG; Complex
                 elementary functions; Complex power function;
                 CSIN/CCOS; CSQRT; Floating-point elementary functions;
                 Fortran programs; measurement; performance; Portable
                 test package",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
  thesaurus =    "Conformance testing; Digital arithmetic; FORTRAN;
                 Mathematics computing; Numerical analysis; Program
                 testing; Software packages",
}

@Article{Cody:1993:ASE,
  author =       "W. J. Cody",
  title =        "{Algorithm 715}: {SPECFUN}\emdash a Portable
                 {FORTRAN} Package of Special Function Routines and Test
                 Drivers",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "22--32",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151273",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:23:18 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Price:1996:RA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p22-cody/",
  abstract =     "SPECFUN is a package containing transportable FORTRAN
                 special function programs for real arguments and
                 accompanying test drivers. Components include Bessel
                 functions, exponential integrals, error functions and
                 related functions, and gamma functions and related
                 functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
}

@Article{Wu:1993:ACH,
  author =       "Trong Wu",
  title =        "An Accurate Computation of the Hypergeometric
                 Distribution Function",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "33--43",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151274",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 09:15:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p33-wu/",
  abstract =     "The computation of the cumulative hypergeometric
                 distribution function is of interest to many
                 researchers who are working in the computational
                 sciences and related areas. Presented here is a new
                 method for computing this function that applies prime
                 number factorization to the factorials. We also apply
                 cancellation to the numerator and denominator to reduce
                 the computational complexity of the initial, the tail
                 end, or weighted probabilities to achieve maximum
                 accuracy. The new method includes two algorithms, one
                 using recursion and the other using iteration. These
                 two algorithms are machine independent; precision is
                 arbitrary, subject to storage limitation. The
                 development of the algorithms is discussed, and some
                 test results and the comparison of these two algorithms
                 are given. To implement both algorithms, we use the Ada
                 programming language that is an American National
                 Standard Institute standardized language. The language
                 has special features such as {\em exception handling}
                 and {\em tasks}. {\em Exception handling} is used to
                 make programming easier and to prevent overflow or
                 underflow conditions during the execution of the
                 program. {\em Tasks} are used to compute the numerator
                 and denominator concurrently, and to maximize the
                 possible number of integer multiplications in the
                 numerator and denominator. All of the computations can
                 be done on currently available machines, and the time
                 consumed by these computations remains reasonably
                 small.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; languages",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Numerical algorithms. {\bf G.3}:
                 Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.
                 {\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Ada. {\bf D.3.3}: Software,
                 PROGRAMMING LANGUAGES, Language Constructs and
                 Features, Control structures.",
}

@Article{Kamel:1993:OES,
  author =       "M. S. Kamel and K. S. Ma and W. H. Enright",
  title =        "{ODEXPERT}: An Expert System to Select Numerical
                 Solvers for Initial Value {ODE} Systems",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "44--62",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151275",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 09:15:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p44-kamel/",
  abstract =     "ODEXPERT is a prototype knowledge-based system which
                 selects the appropriate numerical solvers for initial
                 value ordinary differential equations. It is capable of
                 deriving some knowledge about the input problem by
                 performing automated tests to detect properties and
                 structures in the problem which guide the selection
                 process.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design",
  subject =      "{\bf I.2.1}: Computing Methodologies, ARTIFICIAL
                 INTELLIGENCE, Applications and Expert Systems. {\bf
                 G.1.7}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Ordinary Differential Equations, Initial value
                 problems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE.",
}

@Article{Cash:1993:MAM,
  author =       "J. R. Cash and S. Semnani",
  title =        "A Modified {Adams} Method for {NonStiff} and Mildly
                 Stiff Initial Value Problems",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "63--80",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151276",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 09:15:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p63-cash/",
  abstract =     "Adams predictor-corrector methods, and explicit
                 Runge--Kutta formulas, have been widely used for the
                 numerical solution of nonstiff initial value problems.
                 Both of these classes of methods have certain
                 drawbacks, however, and it has long been the aim of
                 numerical analysts to derive a class of formulas that
                 has the advantages of both Adams and Runge--Kutta
                 methods and the disadvantages of neither! In this paper
                 we derive a class of modified Adams formulas that
                 attempts to achieve this aim. When used in a certain
                 precisely defined predictor-corrector mode, these new
                 formulas require three function evaluations per step,
                 but have much better stability than Adams formulas.
                 This improved stability makes the modified Adams
                 formulas particularly effective for mildly stiff
                 problems, and some numerical evidence of this is given.
                 We also consider the performance of the new class of
                 methods on the well-known DETEST test set to show their
                 potential on general nonstiff initial value problems.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; performance",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.1.7}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Initial value problems.",
}

@Article{Renka:1993:ATT,
  author =       "R. J. Renka",
  title =        "{Algorithm 716}: {TSPACK}: Tension Spline
                 Curve-Fitting Package",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "81--94",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151277;
                 http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p81-renka/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 15 18:57:35 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Testa:1999:RA}.",
  abstract =     "The primary purpose of TSPACK is to construct a smooth
                 function which interpolates a discrete set of data
                 points. The function may be required to have either one
                 or two continuous derivatives. If the accuracy of the
                 data does not warrant interpolation, a smoothing
                 function (which does not pass through the data points)
                 may be constructed instead. The fitting method is
                 designed to avoid extraneous inflection points
                 (associated with rapidly varying data values) and
                 preserve local shape properties of the data
                 (monotonicity and convexity), or to satisfy the more
                 general constraints of bounds on function values or
                 first derivatives. The package also provides a
                 parametric representation for construction general
                 planar curves and space curves.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE. {\bf G.1.2}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation. {\bf G.1.1}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Interpolation.",
}

@Article{Snow:1993:CTP,
  author =       "Dennis M. Snow",
  title =        "Computing Tensor Product Decompositions",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "95--108",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151278",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "22-04 (17B10 22E47)",
  MRnumber =     "94e:22001",
  bibdate =      "Mon Sep 05 09:15:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p95-snow/",
  abstract =     "An algorithm is presented for computing the
                 decomposition of a tensor product of two irreducible
                 representations of a semisimple complex Lie group into
                 its irreducible components. The algorithm uses a known
                 formula which expresses the multiplicities of the
                 highest weight vectors in the decomposition as an
                 alternating sum indexed by the Weyl group. This sum is
                 accomplished with minimal memory requirements using
                 techniques developed previously by the author for
                 efficiently computing Weyl group orbits. Examples are
                 given for each of the exceptional Lie groups.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; experimentation; measurement; performance;
                 theory",
  reviewer =     "Jeffrey Adams",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Algorithm analysis. {\bf F.2.1}: Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems.",
}

@Article{Bunch:1993:ASM,
  author =       "David S. Bunch and David M. Gay and Roy E. Welsch",
  title =        "{Algorithm 717}: Subroutines for Maximum Likelihood
                 and Quasi-Likelihood Estimation of Parameters in
                 Nonlinear Regression Models",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "109--130",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/151271.151279",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 09:15:25 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-1/p109-bunch/",
  abstract =     "We present FORTRAN 77 subroutines that solve
                 statistical parameter estimation problems for general
                 nonlinear models, e.g., nonlinear least-squares,
                 maximum likelihood, maximum quasi-likelihood,
                 generalized nonlinear least-squares, and some robust
                 fitting problems. The accompanying test examples
                 include members of the generalized linear model family,
                 extensions using nonlinear predictors (``nonlinear
                 GLIM''), and probabilistic choice models, such as
                 linear-in-parameter multinomial probit models. The
                 basic method, a generalization of the NL2SOL algorithm
                 for nonlinear least-squares, employs a
                 model/trust-region scheme for computing trial steps,
                 exploits special structure by maintaining a secant
                 approximation to the second-order part of the Hessian,
                 and adaptively switches between a Gauss--Newton and an
                 augmented Hessian approximation. Gauss--Newton steps
                 are computed using a corrected seminormal equations
                 approach. The subroutines include variants that handle
                 simple bounds on the parameters, and that compute
                 approximate regression diagnostics.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Statistical computing. {\bf G.3}:
                 Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical software. {\bf G.1.6}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Boisvert:1993:CPV,
  author =       "Ronald F. Boisvert and Bonita V. Saunders",
  title =        "Corrigendum: ``{Algorithm 713}: Portable Vectorized
                 Software for {Bessel} Function Evaluation''",
  journal =      j-TOMS,
  volume =       "19",
  number =       "1",
  pages =        "131--131",
  month =        mar,
  year =         "1993",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 09:33:37 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Boisvert:1992:PVS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  xxURL =        "Missing from ACM Digital Library",
}

@Article{Boisvert:1993:E,
  author =       "Ronald F. Boisvert",
  title =        "Editorial",
  journal =      j-TOMS,
  volume =       "19",
  number =       "2",
  pages =        "135--135",
  month =        jun,
  year =         "1993",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 09:34:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  xxURL =        "Missing from ACM Digital Library",
}

@Article{Duff:1993:CSE,
  author =       "I. S. Duff and J. A. Scott",
  title =        "Computing Selected Eigenvalues of Sparse Unsymmetric
                 Matrices Using Subspace Iteration",
  journal =      j-TOMS,
  volume =       "19",
  number =       "2",
  pages =        "137--159",
  month =        jun,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/152613.152614",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F50 (65F15)",
  MRnumber =     "96c:65078",
  bibdate =      "Tue Nov 14 09:56:28 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Duff:1995:CCS}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-2/p137-duff/",
  abstract =     "This paper discusses the design and development of a
                 code to calculate the eigenvalues of a large sparse
                 real unsymmetric matrix that are the rightmost,
                 leftmost, or are of the largest modulus. A subspace
                 iteration algorithm is used to compute a sequence of
                 sets of vectors that converge to an orthonormal basis
                 for the invariant subspace corresponding to the
                 required eigenvalues. This algorithm is combined with
                 Chebychev acceleration if the rightmost or leftmost
                 eigenvalues are sought, or if the eigenvalues of
                 largest modulus are known to be the rightmost or
                 leftmost eigenvalues. An option exists for computing
                 the corresponding eigenvectors. The code does not need
                 the matrix explicitly since it only requires the user
                 to multiply sets of vectors by the matrix.
                 Sophisticated and novel iteration controls, stopping
                 criteria, and restart facilities are provided. The code
                 is shown to be efficient and competitive on a range of
                 test problems.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@Article{Demmel:1993:GSDa,
  author =       "James Demmel and Bo K{\aa}gstr{\"o}m",
  title =        "The Generalized {Schur} Decomposition of an Arbitrary
                 Pencil {$A-\lambda{B}$}: Robust Software with Error
                 Bounds and Applications. {Part I}: {Theory} and
                 Algorithms",
  journal =      j-TOMS,
  volume =       "19",
  number =       "2",
  pages =        "160--174",
  month =        jun,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/152613.152615",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F15 (65-04)",
  MRnumber =     "96d:65060a",
  bibdate =      "Fri Aug 26 23:38:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-2/p160-demmel/",
  abstract =     "Robust software with error bounds for computing the
                 generalized Schur decomposition of an arbitrary matrix
                 pencil $A - \lambda B$ (regular or singular) is
                 presented. The decomposition is a generalization of the
                 Schur canonical form of $A - \lambda I$ to matrix
                 pencils and reveals the Kronecker structure of a
                 singular pencil. Since computing the Kronecker
                 structure of a singular pencil is a potentially
                 ill-posed problem, it is important to be able to
                 compute rigorous and reliable error bounds for the
                 computed features. The error bounds rely on
                 perturbation theory for reducing subspaces and
                 generalized eigenvalues of singular matrix pencils. The
                 first part of this two-part paper presents the theory
                 and algorithms for the decomposition and its error
                 bounds, while the second part describes the computed
                 generalized Schur decomposition and the software, and
                 presents applications and an example of its use.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; geig; generalized Schur decomposition;
                 matrix pencil; nla; reliability; theory",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf
                 G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Numerical Linear Algebra, Conditioning. {\bf F.4.1}:
                 Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
                 LANGUAGES, Mathematical Logic. {\bf G.4}: Mathematics
                 of Computing, MATHEMATICAL SOFTWARE, Algorithm
                 analysis.",
}

@Article{Demmel:1993:GSDb,
  author =       "James Demmel and Bo K{\aa}gstr{\"o}m",
  title =        "The Generalized {Schur} Decomposition of an Arbitrary
                 Pencil {$A-\lambda B$}: {Robust} Software with Error
                 Bounds and Applications. {Part II}: {Software} and
                 Applications",
  journal =      j-TOMS,
  volume =       "19",
  number =       "2",
  pages =        "175--201",
  month =        jun,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/152613.152616",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F15 (65-04)",
  MRnumber =     "96d:65060b",
  bibdate =      "Mon Sep 05 09:34:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-2/p175-demmel/",
  abstract =     "Robust software with error bounds for computing the
                 generalized Schur decomposition of an arbitrary matrix
                 pencil $A - \lambda B$ (regular or singular) is
                 presented. The decomposition is a generalization of the
                 Schur canonical form of $A - \lambda I$ to matrix
                 pencils and reveals the Kronecker structure of a
                 singular pencil. The second part of this two-part paper
                 describes the computed generalized Schur decomposition
                 in more detail and the software, and presents
                 applications and an example of its use. Background
                 theory and algorithms for the decomposition and its
                 error bounds are presented in Part I of this paper.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; geig; generalized Schur decomposition;
                 matrix pencil; nla; reliability; theory",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf
                 G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Numerical Linear Algebra, Conditioning. {\bf F.4.1}:
                 Theory of Computation, MATHEMATICAL LOGIC AND FORMAL
                 LANGUAGES, Mathematical Logic. {\bf G.4}: Mathematics
                 of Computing, MATHEMATICAL SOFTWARE, Algorithm
                 analysis.",
}

@Article{Bai:1993:CCN,
  author =       "Z. Bai and J. Demmel and A. McKenney",
  title =        "On Computing Condition Numbers for the Nonsymmetric
                 Eigenproblem",
  journal =      j-TOMS,
  volume =       "19",
  number =       "2",
  pages =        "202--223",
  month =        jun,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/152613.152617",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F35 (65-04 65F15)",
  MRnumber =     "96c:65074",
  bibdate =      "Mon Sep 05 09:34:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-2/p202-bai/",
  abstract =     "We review the theory of condition numbers for the
                 nonsymmetric eigenproblem and give a tabular summary of
                 bounds for eigenvalues, means of clusters of
                 eigenvalues, eigenvectors, invariant subspaces, and
                 related quantities. We describe the design of new
                 algorithms for estimating these condition numbers.
                 Fortran subroutines implementing these algorithms are
                 in the LAPACK library [1].",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; reliability",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf
                 F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on matrices. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness.",
}

@Article{Miminis:1993:AFS,
  author =       "George Miminis and Michael Reid",
  title =        "{Algorithm 718}: {A FORTRAN} Subroutine to Solve the
                 Eigenvalues Allocation Problem for Single-Input
                 Systems",
  journal =      j-TOMS,
  volume =       "19",
  number =       "2",
  pages =        "224--232",
  month =        jun,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/152613.152618",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 09:34:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-2/p224-miminis/",
  abstract =     "An efficient implementation of an algorithm for the
                 eigenvalue allocation (pole placement) problem of
                 single-input linear systems using state feedback is
                 given in this paper. The implementation uses the BLAS
                 level-1 [2] subroutines when possible for better
                 performance. A brief description of the algorithm along
                 with some computational details is also given.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Eigenvalues. {\bf
                 F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on matrices. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms.",
}

@Article{Greenberg:1993:EAC,
  author =       "Harvey J. Greenberg",
  title =        "Enhancements of {ANALYZE}: a Computer-Assisted
                 Analysis System for Linear Programming",
  journal =      j-TOMS,
  volume =       "19",
  number =       "2",
  pages =        "233--256",
  month =        jun,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/152613.152619",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 05 09:34:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-2/p233-greenberg/",
  abstract =     "This describes enhancements to provide more advanced
                 computer-assisted analysis of instances of linear
                 programming models. Three categories of enhancements
                 are described: views, engines for obtaining
                 information, and rule-based advising. Examples of their
                 uses include redundancy and infeasibility diagnoses.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "design; experimentation; languages; performance",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, ANALYZE. {\bf G.1.6}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming. {\bf I.6.2}:
                 Computing Methodologies, SIMULATION AND MODELING,
                 Simulation Languages. {\bf I.6.4}: Computing
                 Methodologies, SIMULATION AND MODELING, Model
                 Validation and Analysis.",
}

@Article{Fishman:1993:GSC,
  author =       "George S. Fishman and L. Stephen Yarberry",
  title =        "Generating a Sample from a $k$-Cell Table with
                 Changing Probabilities in {$O(\log_2k)$} Time",
  journal =      j-TOMS,
  volume =       "19",
  number =       "2",
  pages =        "257--261",
  month =        jun,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/152613.152621",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 30 00:48:36 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-2/p257-fishman/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS.",
}

@Article{Bentley:1993:TDI,
  author =       "Jon L. Bentley and Mary F. Fernandez and Brian W.
                 Kernighan and Norman L. Schryer",
  title =        "Template-Driven Interfaces for Numerical Subroutines",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "265--287",
  month =        sep,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/155743.155757",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 16 19:17:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p265-bentley/",
  abstract =     "This paper describes a set of interfaces for numerical
                 subroutines. Typing a short (often one-line)
                 description allows one to solve problems in application
                 domains including least-squares data fitting,
                 differential equations, minimization, root finding, and
                 integration. Our approach of ``template-driven
                 programming'' makes it easy to build such an interface:
                 a simple one takes a few hours to construct, while a
                 few days suffice to build the most complex program we
                 describe.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "awk; design; experimentation; Fortran; languages;
                 Maple; UNIX shell",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE. {\bf D.2.2}: Software, SOFTWARE ENGINEERING,
                 Tools and Techniques, User interfaces. {\bf D.2.2}:
                 Software, SOFTWARE ENGINEERING, Tools and Techniques,
                 Software libraries. {\bf D.3.4}: Software, PROGRAMMING
                 LANGUAGES, Processors, Preprocessors. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms. {\bf D.2.m}: Software, SOFTWARE
                 ENGINEERING, Miscellaneous, Reusable software.",
}

@Article{Bailey:1993:AMT,
  author =       "David H. Bailey",
  title =        "{Algorithm 719}: Multiprecision Translation and
                 Execution of {FORTRAN} Programs",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "288--319",
  month =        sep,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/155743.155767",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Dec 13 18:37:31 1995",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p288-bailey/",
  abstract =     "This paper describes two Fortran utilities for
                 multiprecision computation. The first is a package of
                 Fortran subroutines that perform a variety of
                 arithmetic operations and transcendental functions on
                 floating point numbers of arbitrarily high precision.
                 This package is in some cases over 200 times faster
                 than that of certain other packages that have been
                 developed for this purpose.\par

                 The second utility is a translator program, which
                 facilitates the conversion of ordinary Fortran programs
                 to use this package. By means of source directives
                 (special comments) in the original Fortran program, the
                 user declares the precision level and specifies which
                 variables in each subprogram are to be treated as
                 multiprecision. The translator program reads this
                 source program and outputs a program with the
                 appropriate multiprecision subroutine calls.\par

                 This translator supports multiprecision integer, real,
                 and complex datatypes. The required array space for
                 multiprecision data types is automatically allocated.
                 In the evaluation of computational expressions, all of
                 the usual conventions for operator precedence and mixed
                 mode operations are upheld. Furthermore, most of the
                 Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP
                 are supported and produce true multiprecision values.",
  abstract-2 =   "The author describes two Fortran utilities for
                 multiprecision computation. The first is a package of
                 Fortran subroutines that perform a variety of
                 arithmetic operations and transcendental functions on
                 floating point numbers of arbitrarily high precision.
                 This package is in some cases over 200 times faster
                 than that of certain other packages that have been
                 developed for this purpose. The second utility is a
                 translator program, which facilitates the conversion of
                 ordinary Fortran programs to use this package. By means
                 of source directives (special comments) in the original
                 Fortran program, the user declares the precision level
                 and specifies which variables in each subprogram are to
                 be treated as multiprecision. The translator program
                 reads this source program and outputs a program with
                 the appropriate multiprecision subroutine calls. This
                 translator supports multiprecision integer, real, and
                 complex datatypes. The required array space for
                 multiprecision data types is automatically allocated.
                 In the evaluation of computational expressions, all of
                 the usual conventions for operator precedence and mixed
                 mode operations are upheld. Furthermore, most of the
                 Fortran-77 intrinsics, such as ABS, MOD, NINT, COS, EXP
                 are supported and produce true multiprecision values.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "NASA Ames Res. Center, Moffett Field, CA, USA",
  classification = "C5230 (Digital arithmetic methods); C6120 (File
                 organisation); C6140D (High level languages); C6150C
                 (Compilers, interpreters and other processors); C7310
                 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithm 719; Arithmetic operations; Array space;
                 Complex data types; Computational expressions; Floating
                 point numbers; Fortran programs; Fortran subroutines;
                 Fortran utilities; Fortran-77 intrinsics; Mixed mode
                 operations; Multiprecision computation; Multiprecision
                 data types; Multiprecision subroutine calls;
                 Multiprecision translation; Operator precedence; Source
                 directives; Transcendental functions; Translator
                 program",
  subject =      "F.2.1 [Analysis of Algorithms and Problem Complexity]:
                 Numerical Algorithms and Problems; G.1.0 [Numerical
                 Analysis]: General; G.1.2 [Numerical Analysis];
                 Approximation",
  thesaurus =    "Data structures; Digital arithmetic; FORTRAN;
                 Mathematics computing; Program interpreters;
                 Subroutines",
}

@Article{Berntsen:1993:AAA,
  author =       "Jarle Berntsen and Ronald Cools and Terje O. Espelid",
  title =        "{Algorithm 720}: An Algorithm for Adaptive Cubature
                 Over a Collection of $3$-Dimensional Simplices",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "320--332",
  month =        sep,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/155743.155785;
                 http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p320-berntsen/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 16 19:17:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "An adaptive algorithm for computing an approximation
                 to the integral of each element in a vector of
                 functions over a 3-dimensional region covered by
                 simplices is presented. The algorithm is encoded in
                 FORTRAN 77.\par

                 Locally, a cubature formula of degree 8 with 43 points
                 is used to approximate an integral. The local error
                 estimate is based on the same evaluation points. The
                 error estimation procedure tries to decide whether the
                 approximation for each function has asymptotic
                 behavior, and different actions are taken depending on
                 that decision.\par

                 The simplex with the largest error is subdivided into 8
                 simplices. The local procedure is then applied to each
                 new region. This procedure is repeated until
                 convergence.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; automatic integration; cubature; cubature
                 rules; error estimation; null rules; reliability;
                 symmetry; tetrahedrons",
  subject =      "G.1.4 [Numerical Analysis]: Quadrature and Numerical
                 Differentiation -- adaptive quadrature; multiple
                 quadrature; G.4 [Mathematics of Computing]:
                 Mathematical Software -- efficiency; reliability and
                 robustness",
}

@Article{Duffy:1993:NIL,
  author =       "Dean G. Duffy",
  title =        "On the Numerical Inversion of {Laplace} Transforms:
                 Comparison of Three New Methods on Characteristic
                 Problems from Applications",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "333--359",
  month =        sep,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/155743.155788",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 16 19:17:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p333-duffy/",
  abstract =     "Three frequently used methods for numerically
                 inverting Laplace transforms are tested on complicated
                 transforms taken from the literature. The first method
                 is a straightforward application of the trapezoidal
                 rule to Bromwich's integral. The second method,
                 developed by Weeks [22], integrates Bromwich's integral
                 by using Laguerre polynomials. The third method,
                 devised by Talbot [18], deforms Bromwich's contour so
                 that the integrand of Bromwich's integral is small at
                 the beginning and end of the contour. These methods are
                 also applied to joint Laplace-Fourier transform
                 problems. All three methods give satisfactory results;
                 Talbot's, however, has an accurate method for choosing
                 required parameters.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; theory",
  subject =      "F.2.1 [Analysis of Algorithms and Problem Complexity]:
                 Numerical Algorithms and Problems",
}

@Article{Pruess:1993:MSS,
  author =       "Steven Pruess and Charles T. Fulton",
  title =        "Mathematical Software for {Sturm--Liouville}
                 Problems",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "360--376",
  month =        sep,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/155743.155791",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 16 19:17:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p360-pruess/",
  abstract =     "Software is described for the Sturm--Liouville
                 eigenproblem. Eigenvalues, eigenfunctions, and spectral
                 density functions can be estimated with global error
                 control. The method of approximating the coefficients
                 forms the mathematical basis. The underlying algorithms
                 are briefly described, and several examples are
                 presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; approximating the coefficients;
                 eigenfunctions; performance; shooting methods; spectral
                 classification; spectral density functions;
                 Sturm--Liouville eigenvalues",
  subject =      "G.1.7 [Numerical Analysis]: Ordinary Differential
                 Equations -- boundary value problems; G.4 [Mathematics
                 of Computing]: Mathematical Software -- algorithm
                 analysis",
}

@Article{Shirts:1993:CES,
  author =       "Randall B. Shirts",
  title =        "The Computation of Eigenvalues and Solutions of
                 {Mathieu}'s Differential Equation for Noninteger
                 Order",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "377--390",
  month =        sep,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/155743.155796",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 16 19:17:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p377-shirts/",
  abstract =     "Two algorithms for calculating the eigenvalues and
                 solutions of Mathieu's differential equation for
                 noninteger order are described. In the first algorithm,
                 Leeb's method is generalized, expanding the Mathieu
                 equation in Fourier series and diagonalizing the
                 symmetric tridiagonal matrix that results. Numerical
                 testing was used to parameterize the minimum matrix
                 dimension that must be used to achieve accuracy in the
                 eigenvalue of one part in $10^{12}$. This method
                 returns a set of eigenvalues below a given order and
                 their associated solutions simultaneously. A second
                 algorithm is presented which uses approximations to the
                 eigenvalues (Taylor series and asymptotic expansions)
                 and then iteratively corrects the approximations using
                 Newton's method until the corrections are less than a
                 given tolerance. A backward recursion of the continued
                 fraction expansion is used. The second algorithm is
                 faster and is optimized to obtain accuracy of one part
                 in $10^{14}$, but has only been implemented for orders
                 less than 10.5.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; eigenvalues; Floquet solutions; Mathieu
                 equation; noninteger order; numerical software;
                 ordinary differential equations; performance",
  subject =      "G.1.0 [Numerical Analysis]: General -- numerical
                 algorithms",
}

@Article{Shirts:1993:AMM,
  author =       "Randall B. Shirts",
  title =        "{Algorithm 721}: {MTIEU1} and {MTIEU2}: Two
                 Subroutines to Compute Eigenvalues and Solutions to
                 {Mathieu}'s Differential Equation for Noninteger and
                 Integer Order",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "391--406",
  month =        sep,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/155743.155847",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 16 19:17:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p391-shirts/",
  abstract =     "Two FORTRAN routines are described which calculate
                 eigenvalues and eigenfunctions of Mathieu's
                 differential equation for noninteger as well as integer
                 order, MTIEU1 uses standard matrix techniques with
                 dimension parameterized to give accuracy in the
                 eigenvalue of one part in $10^{12}$. MTIEU2 used
                 continued fraction techniques and is optimized to give
                 accuracy in the eigenvalue of one part in $10^{14}$.
                 The limitations of the algorithms are also discussed
                 and illustrated.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; eigenvalues; Floquet solutions; FORTRAN;
                 Mathieu equation; noninteger order; numerical software;
                 ordinary differential equations; performance",
  subject =      "G.1.0 [General Numerical Analysis]",
}

@Article{Haag:1993:QLA,
  author =       "J. B. Haag and D. S. Watkins",
  title =        "{QR}-Like Algorithms for the Nonsymmetric Eigenvalue
                 Problem",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "407--418",
  month =        sep,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/155743.155849",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 16 19:17:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p407-haag/",
  abstract =     "Hybrid codes that combine elements of the QR and LR
                 algorithms are described. The codes can calculate the
                 eigenvalues and, optionally, eigenvectors of real,
                 nonsymmetric matrices. Extensive tests are presented as
                 evidence that, for certain choices of parameters, the
                 hybrid codes possess the same high reliability as the
                 QR algorithm and are significantly faster. The greatest
                 success has been achieved with the codes that calculate
                 eigenvalues only. These can do the task in 15\% to 50\%
                 less time than the QR algorithm.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; chasing the bulge; eigenvalue;
                 eigenvector; experimentation; GR algorithm; LR
                 algorithm; measurement; performance; QR algorithm;
                 verification",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Efficiency. {\bf G.1.3}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Eigenvalues. {\bf F.2.1}: Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems.",
}

@Article{Chang:1993:ICR,
  author =       "S. Frank Chang and S. Thomas McCormick",
  title =        "Implementation and Computational Results for the
                 Hierarchical Algorithm for Making Sparse Matrices
                 Sparser",
  journal =      j-TOMS,
  volume =       "19",
  number =       "3",
  pages =        "419--441",
  month =        sep,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/155743.152620",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 16 19:17:34 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-3/p419-chang/",
  abstract =     "If A is the (sparse) coefficient matrix of
                 linear-equality constraints, for what nonsingular $T$
                 is A = TA as sparse as possible, and how can it be
                 efficiently computed? An efficient algorithm for this
                 {\em Sparsity Problem} (SP) would be a valuable
                 preprocessor for linearly constrained optimization
                 problems. In a companion paper we developed a two-pass
                 approach to solve SP called the {\em Hierarchical
                 Algorithm}. In this paper we report on how we
                 implemented the Hierarchical Algorithm into a code
                 called HASP, and our computational experience in
                 testing HASP on the NETLIB linear-programming problems.
                 We found that HASP substantially outperformed a
                 previous code for SP and that it produced a net savings
                 in optimization time on the NETLIB problems. The
                 results allow us to give guidelines for its use in
                 practice.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance; verification",
  subject =      "F.2.1 [Analysis of Algorithms and Problem Complexity]:
                 Numerical Algorithms and Problems -- computations on
                 matrices; G.1.6 [Numerical Analysis]: Optimization --
                 linear programming; G.4 [Mathematics of Computing]:
                 Mathematical Software -- algorithms analysis;
                 efficiency",
}

@Article{Cody:1993:AFS,
  author =       "W. J. Cody and Jerome T. Coonen",
  title =        "{Algorithm 722}: Functions to Support the {IEEE}
                 Standard for Binary Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "443--451",
  month =        dec,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/168173.168185",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Feb 24 15:01:45 MST 1996",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p443-cody/",
  abstract =     "This paper describes C programs for the support
                 functions {\em copysign(x,y), logb(x), scalb(x,n),
                 nextafter(x,y), finite(x)}, and {\em isnan(x)}
                 recommended in the Appendix to the {\em IEEE Standard
                 for Binary Floating-Point Arithmetic.} In the case of
                 {\em logb}, the modified definition given in the later
                 {\em IEEE Standard for Radix-Independent Floating-Point
                 Arithmetic} is followed. These programs should run
                 without modification on most systems conforming to the
                 binary standard.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  affiliation =  "Argonne Nat. Lab., IL, USA",
  classification = "C5230 (Digital arithmetic methods); C6130 (Data
                 handling techniques); C7310 (Mathematics)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "C programs; Copysign(x,y); Finite(x); IEEE Standard
                 for Binary Floating-point arithmetic; Isnan(x);
                 Logb(x); Nextafter(x,y); Numerical software;
                 Scalb(x,n)",
  subject =      "G.1.0 [Numerical Analysis]: General -- numerical
                 algorithms; G.4 [Numerical Analysis]: Mathematical
                 Software -- certification and testing",
  thesaurus =    "Data handling; Digital arithmetic; Mathematics
                 computing; Standards",
}

@Article{Snyder:1993:AFI,
  author =       "W. Van Snyder",
  title =        "{Algorithm 723}: {Fresnel} Integrals",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "452--456",
  month =        dec,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/168173.168193",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 29 15:24:56 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remarks \cite{Snyder:1996:RAF,Snyder:2021:CRA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p452-van_snyder/",
  abstract =     "An implementation of approximations for Fresnel
                 integrals and associated functions is described. The
                 approximations were originally developed by W. J. Cody,
                 but a Fortran implementation using them has not
                 previously been published.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; special functions",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Rational approximation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing.",
}

@Article{Ribbens:1993:TPM,
  author =       "Calvin J. Ribbens and Layne T. Watson and Colin Desa",
  title =        "Toward Parallel Mathematical Software for Elliptic
                 Partial Differential Equations",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "457--473",
  month =        dec,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/168173.168383",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 16 19:47:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p457-ribbens/",
  abstract =     "Three approaches to parallelizing important components
                 of the mathematical software package ELLPACK are
                 considered: an explicit approach using compiler
                 directives available only on the target machine, an
                 automatic approach using an optimizing and
                 parallelizing precompiler, and a two-level approach
                 based on extensive use of a set of low level
                 computational kernels. The focus is on shared memory
                 architectures. Each approach to parallelization is
                 described in detail, along with a discussion of the
                 effort involved. Performance on a test problem, using
                 up to sixteen processors of a Sequent Symmetry S81, is
                 reported and discussed. Implications for the
                 parallelization of a broad class of mathematical
                 software are drawn.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "G.1.0 [Numerical Analysis]: General -- parallel
                 algorithms; G.1.8 [Numerical Analysis]: Partial
                 Differential Equations -- elliptic equations; G.4
                 [Mathematics of Computing]: Mathematical Software --
                 efficiency; portability",
}

@Article{Abernathy:1993:ASE,
  author =       "Roger W. Abernathy and Robert P. Smith",
  title =        "Applying Series Expansion to the Inverse Beta
                 Distribution to Find Percentiles of the
                 ${F}$-Distribution",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "474--480",
  month =        dec,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/168173.168387",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 16 19:47:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p474-abernathy/",
  abstract =     "Let $0 <= 1$ and $F$ be the cumulative distribution
                 function (cdf) of the $F$-Distribution. We wish to find
                 $x_{p}$ such that $F(x_{p}|n_{1}, n_{2}) = p$, where
                 $n_{1}$ and $n_{2}$ are the degrees of freedom.
                 Traditionally, $x_{p}$ is found using a numerical
                 root-finding method, such as Newton's method. In this
                 paper, a procedure based on a series expansion for
                 finding $x_{p}$is given. The series expansion method
                 has been applied to the normal, chi-square, and $t$
                 distributions, but because of computational
                 difficulties, it has not been applied to the
                 $F$-Distribution. These problems have been overcome by
                 making the standard transformation to the beta
                 distribution.\par

                 The procedure is explained in Sections 3 and 4.
                 Empirical results of a comparison of CPU times are
                 given in Section 5. The series expansion is compared to
                 some of the standard root-finding methods. A table is
                 given for $p = 0.90$.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; cumulative distribution function;
                 cumulative distribution function (cdf); distribution
                 function; F-distribution; Newton's method; performance;
                 root-finding methods; Taylor series",
  subject =      "G.1.5 [Numerical Analysis]: Roots of Nonlinear
                 Equations; G.3 [Probability and Statistics]",
}

@Article{Abernathy:1993:APC,
  author =       "Roger W. Abernathy and Robert P. Smith",
  title =        "{Algorithm 724}: Program to Calculate $ {F}
                 $-Percentiles",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "481--483",
  month =        dec,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/168173.168405",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 16 19:47:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/sgml.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p481-abernathy/",
  abstract =     "Let $ 0 < p < 1 $ be given and let $F$ be the
                 cumulative distribution function of the
                 $F$-Distribution with $ (M, N) $, degrees of freedom.
                 This FORTRAN 77 routine is a complement to [1] where a
                 method was presented to find the inverse of the
                 $F$-Distribution function, FINV($ M, N, P $ ), using a
                 series expansion technique to find the inverse for the
                 Beta Distribution function.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; cumulative distribution function (cdf);
                 distribution function; experimentation; F-distribution;
                 Newton's method; root-finding methods; Taylor series;
                 theory",
  subject =      "G.1.5 [Numerical Analysis]: Roots of Nonlinear
                 Equations",
}

@Article{Clarkson:1993:RAF,
  author =       "Douglas B. Clarkson and Yuan-an Fan and Harry Joe",
  title =        "A Remark on {Algorithm 643}: {FEXACT}: An Algorithm
                 for Performing {Fisher}'s Exact Test in $r\times{c}$
                 Contingency Tables",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "484--488",
  month =        dec,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/168173.168412",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 16 19:47:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Mehta:1986:AFF}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p484-clarkson/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; experimentation; measurement; performance;
                 theory",
  subject =      "{\bf G.1.2}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation.",
}

@Article{Hormann:1993:PRN,
  author =       "Wolfgang H{\"o}rmann and G. Deflinger",
  title =        "A Portable Random Number Generator Well Suited for the
                 Rejection Method",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "489--495",
  month =        dec,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/168173.168414",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 16 19:47:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p489-hormann/",
  abstract =     "Up to now, all known efficient portable
                 implementations of linear congruential random number
                 generators with modulus $ 2^{31} - 1 $ have worked only
                 with multipliers that are small compared with the
                 modulus. We show that for nonuniform distributions, the
                 rejection method may generate random numbers of bad
                 qualify if combined with a linear congruential
                 generator with small multiplier. A method is described
                 that works for any multiplier smaller than $ 2^{30} $.
                 It uses the decomposition of multiplier and seed in
                 high-order and low-order bits to compute the upper and
                 lower half of the product. The sum of the two halves
                 gives the product of multiplier and seed modulo $
                 2^{21} - 1 $. Coded in ANSI-C and FORTRAN77 the method
                 results in a portable implementation of the linear
                 congruential generator that is as fast or faster than
                 other portable methods.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; linear congruential generator;
                 portability; quality of nonuniform random numbers;
                 rejection method; uniform random number generator",
  subject =      "G.3 [Mathematics of Computation]: Probability and
                 Statistics -- random number generation",
}

@Article{Grassmann:1993:REC,
  author =       "Winifred K. Grassmann",
  title =        "Rounding Errors in Certain Algorithms Involving
                 {Markov} Chains",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "496--508",
  month =        dec,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/168173.168416",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Feb 07 16:38:26 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p496-grassmann/",
  abstract =     "A number of algorithms involving Markov chains contain
                 no subtractions. This property makes the analysis of
                 rounding errors particularly simple. To show this, some
                 principles for analyzing the propagation and generation
                 of rounding errors in algorithms containing no
                 subtraction are discussed first. These principles are
                 then applied in the context of a simple recursive
                 algorithm involving the transient solution of
                 discrete-time Markov chains, Jensen's algorithm, and
                 state reduction. Jensen's algorithm, also known as
                 randomization or uniformization, is an algorithm for
                 finding transient solutions of continuous-time Markov
                 chains. State reduction is a method for finding
                 equilibrium probabilities for discrete-time or
                 continuous-time Markov chains.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS. {\bf F.2.2}: Theory of Computation,
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY,
                 Nonnumerical Algorithms and Problems.",
}

@Article{Khoury:1993:TPG,
  author =       "B. N. Khoury and P. M. Pardalos and D.-Z. Du",
  title =        "A Test Problem Generator for the {Steiner} Problem in
                 Graphs",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "509--522",
  month =        dec,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/168173.168420",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Nov 06 07:19:45 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p509-khoury/",
  abstract =     "In this paper we present a new binary-programming
                 formulation for the Steiner problem in graphs (SPG),
                 which is well known to be NP-hard. We use this
                 formulation to generate test problems with known
                 optimal solutions. The technique uses the KKT
                 optimality conditions on the corresponding
                 quadratically constrained optimization problem.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; experimentation; integer programming;
                 performance; Steiner problem in graphs; test problems",
  subject =      "G.1.6 [Numerical Analysis]: Optimization -- integer
                 programming; G.4 [Mathematics of Computing]:
                 Mathematical Software -- certification and testing;
                 efficiency",
}

@Article{Joe:1993:ILM,
  author =       "Stephen Joe and Ian H. Sloan",
  title =        "Implementation of a Lattice Method for Numerical
                 Multiple Integration",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "523--545",
  month =        dec,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/168173.168425",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:08:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also \cite{Joe:1994:CIL}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p523-joe/",
  abstract =     "An implementation of a method for numerical multiple
                 integration based on a sequence of imbedded lattice
                 rules is given. Besides yielding an approximation to
                 the integral, this implementation also provides an
                 error estimate which does not require much extra
                 computation. The results of some numerical experiments
                 conclude the paper.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; lattice rules; performance",
  subject =      "G.1.4 [Numerical Analysis]: Quadrature and Numerical
                 Differentiation -- multiple quadrature",
}

@Article{Drezner:1993:CAC,
  author =       "Zvi Drezner",
  title =        "Corrigendum: ``{Algorithm 725}. Computation of the
                 Multivariate Normal Integral''",
  journal =      j-TOMS,
  volume =       "19",
  number =       "4",
  pages =        "546--546",
  month =        dec,
  year =         "1993",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/168173.168428",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:05:07 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Drezner:1992:CMN}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1993-19-4/p546-drezner/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; multivariate normal probability",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Statistical software. {\bf G.1.4}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Quadrature and Numerical Differentiation, Multiple
                 quadrature.",
}

@Article{Boisvert:1994:CST,
  author =       "Ronald F. Boisvert",
  title =        "Charter and Scope: Transactions on Mathematical
                 Software ({TOMS})",
  journal =      j-TOMS,
  volume =       "20",
  number =       "1",
  pages =        "1--2",
  month =        mar,
  year =         "1994",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 06 19:02:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  xxURL =        "Missing from ACM Digital Library",
}

@Article{Renka:1994:CSC,
  author =       "Robert J. Renka",
  title =        "Charter and Scope: Collected Algorithms ({CALGO})",
  journal =      j-TOMS,
  volume =       "20",
  number =       "1",
  pages =        "3--3",
  month =        mar,
  year =         "1994",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 06 19:02:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  xxURL =        "Missing from ACM Digital Library",
}

@Article{Neusius:1994:NTA,
  author =       "Christian Neusius and Jan Olszewski",
  title =        "A Noniterative Thinning Algorithm",
  journal =      j-TOMS,
  volume =       "20",
  number =       "1",
  pages =        "5--20",
  month =        mar,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/174603.174604",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68U10",
  MRnumber =     "96h:68221",
  bibdate =      "Tue Sep 06 19:02:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p5-neusius/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gautschi:1994:ACP,
  author =       "Walter Gautschi",
  title =        "{Algorithm 726}: {ORTHPOL}\emdash a Package of
                 Routines for Generating Orthogonal Polynomials and
                 {Gauss}-Type Quadrature Rules",
  journal =      j-TOMS,
  volume =       "20",
  number =       "1",
  pages =        "21--62",
  month =        mar,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/174603.174605",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:16:24 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Gautschi:1998:RAO}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p21-gautschi/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pennington:1994:NNL,
  author =       "S. V. Pennington and M. Berzins",
  title =        "New {NAG} Library Software for First-Order Partial
                 Differential Equations",
  journal =      j-TOMS,
  volume =       "20",
  number =       "1",
  pages =        "63--99",
  month =        mar,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/174603.155272",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 06 19:02:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p63-pennington/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hashem:1994:AQE,
  author =       "Sherif Hashem and Bruce Schmeiser",
  title =        "{Algorithm 727}: Quantile Estimation Using Overlapping
                 Batch Statistics",
  journal =      j-TOMS,
  volume =       "20",
  number =       "1",
  pages =        "100--102",
  month =        mar,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/174603.174412",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 06 19:02:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p100-hashem/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Calamai:1994:GQB,
  author =       "Paul H. Calamai and Luis N. Vicente",
  title =        "Generating Quadratic Bilevel Programming Test
                 Problems",
  journal =      j-TOMS,
  volume =       "20",
  number =       "1",
  pages =        "103--119",
  month =        mar,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/174603.174411",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65K05)",
  MRnumber =     "1 368 021",
  bibdate =      "Tue Sep 06 19:02:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p103-calamai/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Calamai:1994:AFS,
  author =       "Paul H. Calamai and Luis N. Vicente",
  title =        "{Algorithm 728}: {FORTRAN} Subroutines for Generating
                 Quadratic Bilevel Programming Test Problems",
  journal =      j-TOMS,
  volume =       "20",
  number =       "1",
  pages =        "120--123",
  month =        mar,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/174603.174410",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65K05)",
  MRnumber =     "1 368 022",
  bibdate =      "Tue Sep 06 19:02:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p120-calamai/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Jeffrey:1994:ETI,
  author =       "D. J. Jeffrey and A. D. Rich",
  title =        "The Evaluation of Trigonometric Integrals Avoiding
                 Spurious Discontinuities",
  journal =      j-TOMS,
  volume =       "20",
  number =       "1",
  pages =        "124--135",
  month =        mar,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/174603.174409",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30 (65-04)",
  MRnumber =     "96h:65034",
  bibdate =      "Tue Sep 06 19:02:59 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p124-jeffrey/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Matstoms:1994:SQF,
  author =       "Pontus Matstoms",
  title =        "Sparse {QR} Factorization in {MATLAB}",
  journal =      j-TOMS,
  volume =       "20",
  number =       "1",
  pages =        "136--159",
  month =        mar,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/174603.174408",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Aug 26 23:38:18 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p136-matstoms/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "multfr; qrd; sparse",
}

@Article{Hansen:1994:CAF,
  author =       "Per Christian Hansen and Tony F. Chan",
  title =        "Corrigendum: ``{Algorithm 729}: {FORTRAN} Subroutines
                 for General {Toeplitz} Systems''",
  journal =      j-TOMS,
  volume =       "20",
  number =       "1",
  pages =        "160--160",
  month =        mar,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/174603.174407",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:10:19 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Hansen:1992:FSG}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p160-hansen/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ammar:1994:CAI,
  author =       "G. S. Ammar and L. Reichel and D. C. Sorensen",
  title =        "Corrigendum: ``{Algorithm 730}: An Implementation of a
                 Divide and Conquer Algorithm for the Unitary
                 Eigenproblem''",
  journal =      j-TOMS,
  volume =       "20",
  number =       "1",
  pages =        "161--161",
  month =        mar,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/174603.174406",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:05:32 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Ammar:1992:IDC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-1/p161-ammar/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Salvy:1994:GMP,
  author =       "Bruno Salvy and Paul Zimmerman",
  title =        "{GFUN}: a {Maple} Package for the Manipulation of
                 Generating and Holonomic Functions in One Variable",
  journal =      j-TOMS,
  volume =       "20",
  number =       "2",
  pages =        "163--177",
  month =        jun,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/178365.178368",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:27:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-2/p163-salvy/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; computer algebra; generating functions;
                 linear differential equations; linear recurrences",
  subject =      "G.2.1 [Discrete Mathematics]:
                 Combinatorics--generating functions; recurrences and
                 difference equations; I.1.2 [Algebraic Manipulation]:
                 Algorithms",
}

@Article{Dayde:1994:PBI,
  author =       "Michael J. Dayd{\'e} and Iain S. Duff and Antoine
                 Petitet",
  title =        "A Parallel Block Implementation of Level-3 {BLAS} for
                 {MIMD} Vector Processors",
  journal =      j-TOMS,
  volume =       "20",
  number =       "2",
  pages =        "178--193",
  month =        jun,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/178365.174413",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 09 13:52:29 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Dongarra:1990:ASL,Higham:1990:EFM,Demmel:1992:SBA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-2/p178-dayde/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; Level-3 BLAS; matrix-matrix kernels;
                 measurement; parallelization; performance;
                 vectorization",
  subject =      "F.2.1 [Analysis of Algorithms and Problem Complexity]:
                 Numerical Algorithms and Problems--computations on
                 matrices; G.1.0 [Numerical Analysis]:
                 General--numerical algorithms; G.1.3 [Numerical
                 Analysis]: Numerical Linear Algebra--linear systems
                 (direct and iterative methods); G.4 [Mathematics of
                 Computing]: Mathematical Software--certification and
                 testing; efficiency; portability; reliability and
                 robustness; verification",
}

@Article{Blom:1994:AMG,
  author =       "J. G. Blom and P. A. Zegeling",
  title =        "{Algorithm 731}: a Moving-Grid Interface for Systems
                 of One-Dimensional Time-Dependent Partial Differential
                 Equations",
  journal =      j-TOMS,
  volume =       "20",
  number =       "2",
  pages =        "194--214",
  month =        jun,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/178365.178391",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:27:31 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-2/p194-blom/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; Lagrangian methods; mathematical software;
                 method of lines; moving grids; partial differential
                 equations; performance; reliability; time-dependent
                 problems",
  subject =      "G.1.0 [Numerical Analysis]: General; G.1.8 [Numerical
                 Analysis]: Partial Differential Equations; G.4
                 [Mathematics of Computing]: Mathematical Software",
}

@Article{Hull:1994:ICE,
  author =       "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter
                 Tang",
  title =        "Implementing Complex Elementary Functions Using
                 Exception Handling",
  journal =      j-TOMS,
  volume =       "20",
  number =       "2",
  pages =        "215--244",
  month =        jun,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/178365.178404",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 21 15:10:29 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See correction \cite{Anonymous:1994:C}, and improved
                 analysis, tightened bounds, and exhibition of worst
                 cases for complex square roots
                 \cite{Jeannerod:2017:REC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-2/p215-hull/",
  abstract =     "Algorithms are developed for reliable and accurate
                 evaluations of the complex elementary functions
                 required in Fortran 77 and Fortran 90, namely cabs,
                 csqrt, cexp, clog, csin, and ccos. The algorithms are
                 presented in a pseudocode that has a convenient
                 exception-handling facility. A tight error bound is
                 derived for each algorithm. Corresponding Fortran
                 programs for an IEEE environment have also been
                 developed to illustrate the practicality of the
                 algorithms, and these programs have been tested very
                 carefully to help confirm the correctness of the
                 algorithms and their error bounds. The results are of
                 these tests are included in the paper, but the Fortran
                 programs are not; the programs are available from
                 Fairgrieve, (tff@cs.toronto.edu).",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; complex elementary functions; design;
                 implementation",
  subject =      "G.1.0 [Numerical Analysis]: General--error analysis;
                 numerical algorithms; G.1.2 [Numerical Analysis]:
                 Approximation--elementary function approximation; G.4
                 [Mathematics of Computing]: Mathematical
                 Software--algorithm analysis; reliability and
                 robustness; verification",
}

@Article{Joe:1994:CIL,
  author =       "Stephen Joe and Ian H. Sloan",
  title =        "Corrigendum: ``{Implementation} of a Lattice Method
                 for Numerical Multiple Integration''",
  journal =      j-TOMS,
  volume =       "20",
  number =       "2",
  pages =        "245--245",
  month =        jun,
  year =         "1994",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 13:05:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Joe:1993:ILM}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  xxURL =        "Missing from ACM Digital Library",
}

@Article{Cummins:1994:ASS,
  author =       "Patrick F. Cummins and Geoffrey K. Vallis",
  title =        "{Algorithm 732}: Solvers for Self-Adjoint Elliptic
                 Problems in Irregular Two-Dimensional Domains",
  journal =      j-TOMS,
  volume =       "20",
  number =       "3",
  pages =        "247--261",
  month =        sep,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/192115.192118",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 12:53:13 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p247-cummins/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; capacitance iteration; capacitance matrix;
                 elliptic equations; fast Poisson solvers; Green's
                 function",
  subject =      "G.1.0 [Numerical Analysis]: General -- numerical
                 algorithms; G.1.8 [Numerical Analysis]: Partial
                 Differential Equations -- elliptic equations",
}

@Article{Kraft:1994:ATF,
  author =       "Dieter Kraft",
  title =        "{Algorithm 733}: {TOMP}---{Fortran} Modules for
                 Optimal Control Calculations",
  journal =      j-TOMS,
  volume =       "20",
  number =       "3",
  pages =        "262--281",
  month =        sep,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/192115.192124",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 09:25:54 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p262-kraft/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; boundary value problems; manipulators;
                 optimal control; robotics; shooting method",
  subject =      "G.1.6 [Numerical Analysis]: Optimization; G.1.7
                 [Numerical Analysis]: Ordinary Differential Equations;
                 G.4 [Mathematics of Computing]: Mathematical Software;
                 I.2.9 [Artificial Intelligence]: Robotics",
}

@Article{Averbukh:1994:RA,
  author =       "Victoria Z. Averbukh and Samuel Figueroa and Tamar
                 Schlick",
  title =        "Remark on {Algorithm 566}",
  journal =      j-TOMS,
  volume =       "20",
  number =       "3",
  pages =        "282--285",
  month =        sep,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/192115.192128",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 12:53:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{More:1981:AFS}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p282-averbukh/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Hessian subroutines; performance",
  subject =      "D.2.7 [Software Engineering]: Distribution and
                 Maintenance -- documentation; enhancement; G.1.6
                 [Numerical Analysis]: Optimization -- nonlinear
                 programming",
}

@Article{More:1994:LSA,
  author =       "Jorge J. Mor{\'e} and David J. Thuente",
  title =        "Line Search Algorithms With Guaranteed Sufficient
                 Decrease",
  journal =      j-TOMS,
  volume =       "20",
  number =       "3",
  pages =        "286--307",
  month =        sep,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/192115.192132",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "90C30 (65K05)",
  MRnumber =     "96k:90074",
  bibdate =      "Sat Nov 19 12:53:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p286-more/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; conjugate gradient algorithms; line search
                 algorithms; nonlinear optimization; truncated Newton
                 algorithms; variable metric algorithms",
  reviewer =     "K. Schittkowski",
  subject =      "G.1.6 [Numerical Analysis]: Optimization --
                 constrained optimization; gradient methods; nonlinear
                 programming; G.4 [Mathematics of Computing]:
                 Mathematical Software -- algorithm analysis;
                 efficiency; reliability and robustness",
}

@Article{Buckley:1994:CFC,
  author =       "A. G. Buckley",
  title =        "Conversion to {Fortran 90}: a Case Study",
  journal =      j-TOMS,
  volume =       "20",
  number =       "3",
  pages =        "308--353",
  month =        sep,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/192115.192139",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 12:53:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p308-buckley/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "conversion; Fortran 90; new features; overview",
}

@Article{Buckley:1994:AFC,
  author =       "A. G. Buckley",
  title =        "{Algorithm 734}: a {Fortran} 90 Code for Unconstrained
                 Nonlinear Minimization",
  journal =      j-TOMS,
  volume =       "20",
  number =       "3",
  pages =        "354--372",
  month =        sep,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/192115.192146",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 12:53:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p354-buckley/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; conversion; Fortran 90; limited memory;
                 new features; nonlinear optimization; quasi-Newton",
  subject =      "G.1.6 [Numerical Analysis]: Optimization -- gradient
                 methods",
}

@Article{Kim:1994:PNA,
  author =       "K. Kim and J. L. Nazareth",
  title =        "A Primal Null-Space Affine-Scaling Method",
  journal =      j-TOMS,
  volume =       "20",
  number =       "3",
  pages =        "373--392",
  month =        sep,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/192115.192153",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "90C05 (65-04 65K05)",
  MRnumber =     "1 367 801",
  bibdate =      "Sat Nov 19 12:53:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p373-kim/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; conjugate gradients; diagonal
                 preconditioning; interior-point algorithm; null-space
                 affine scaling; primal method",
  subject =      "G.1.6 [Numerical Analysis]: Optimization -- linear
                 programming",
}

@Article{Brown:1994:CAS,
  author =       "Barry W. Brown and Lawrence Levy",
  title =        "Certification of {Algorithm 708}: Significant Digit
                 Computation of the Incomplete Beta",
  journal =      j-TOMS,
  volume =       "20",
  number =       "3",
  pages =        "393--397",
  month =        sep,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/192115.192155",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 19 12:53:17 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{DiDonato:1992:ASD}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p393-brown/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; continued fractions; F-distribution",
  subject =      "G.1.2 [Numerical Analysis]: Approximation",
}

@Article{Taswell:1994:AWT,
  author =       "Carl Taswell and Kevin C. McGill",
  title =        "{Algorithm 735}: Wavelet Transform Algorithms for
                 Finite-Duration Discrete-Time Signals",
  journal =      j-TOMS,
  volume =       "20",
  number =       "3",
  pages =        "398--412",
  month =        sep,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/192115.192156",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 09:25:55 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-3/p398-taswell/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; multiresolution analysis; signal
                 processing; waveform analysis; wavelet transform;
                 wavelets",
  subject =      "G.1.2 [Numerical Analysis]: Approximations; G.4
                 [Mathematics of Computing]: Mathematical Software;
                 I.4.5 [Image Processing]: Reconstruction",
}

@Article{Dunkl:1994:CHI,
  author =       "Charles F. Dunkl and Donald E. Ramirez",
  title =        "Computing Hyperelliptic Integrals for Surface Measure
                 of Ellipsoids",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "413--426",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/198429.198430",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30",
  MRnumber =     "1 368 024",
  bibdate =      "Tue Mar 14 16:16:49 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p413-dunkl/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "elliptic integral; expected radius; Lauricella's
                 hypergeometric function; optimal designs; surface
                 measure",
  subject =      "G.1.4 [Numerical Analysis]: Quadrature and Numerical
                 Differentiation -- multiple quadrature; G.3
                 [Mathematics of Computing]: Probability and
                 Statistics",
}

@Article{Dunkl:1994:AHI,
  author =       "Charles F. Dunkl and Donald E. Ramirez",
  title =        "{Algorithm 736}: Hyperelliptic Integrals and the
                 Surface Measure of Ellipsoids",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "427--435",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/198429.198431",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D30",
  MRnumber =     "1 368 025",
  bibdate =      "Tue Mar 14 16:16:51 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p427-dunkl/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "elliptic integral; expected radius; Lauricella's
                 hypergeometric function; optimal designs; surface
                 measure",
  subject =      "G.1.4 [Numerical Analysis]: Quadrature and Numerical
                 Differentiation -- multiple quadrature; G.3
                 [Mathematics of Computing]: Probability and
                 Statistics",
}

@Article{Fruchtl:1994:NAE,
  author =       "H. Fr{\"u}chtl and P. Otto",
  title =        "A New Algorithm for the Evaluation of the Incomplete
                 Gamma Function on Vector Computers",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "436--446",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/198429.198432",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 14 16:16:52 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Incomplete Gamma Function; quantum chemistry;
                 two-electron integrals",
  subject =      "C.1.2 [Processor Architectures]: Multiple Data Stream
                 Architectures -- array and vector processors; G.1.2
                 [Numerical Analysis]: Approximation -- rational
                 approximation; G.4 [Mathematics of Computing]:
                 Mathematical Software -- efficiency; J.2 [Computer
                 Applications]: Physical Sciences and Engineering --
                 chemistry",
}

@Article{Kearfott:1994:AIP,
  author =       "R. B. Kearfott and M. Dawande and K. Du and C. Hu",
  title =        "{Algorithm 737}: {INTLIB}: a Portable {Fortran-77}
                 Elementary Function Library",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "447--459",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/198429.198433",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 29 15:22:20 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See companion interval arithmetic package
                 \cite{Kearfott:1996:IFM}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p447-kearfott/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "BLAS; Fortran 77; Fortran 90; interval arithmetic;
                 operator overloading; standard functions",
  subject =      "D.2.2 [Software Engineering]: Tools and Techniques --
                 software libraries; D.2.7 [Software Engineering]:
                 Distribution and Maintenance -- documentation;
                 portability; G.1.0 [Numerical Analysis]: General --
                 computer arithmetic; G.1.2 [Numerical Analysis]:
                 Approximation -- elementary function approximation",
}

@Article{Peters:1994:EAE,
  author =       "J{\"o}rg Peters",
  title =        "Evaluation and Approximate Evaluation of the
                 Multivariate {Bernstein--B{\'e}zier} Form on a
                 Regularly Partitioned Simplex",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "460--480",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/198429.198434",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D17 (65-04)",
  MRnumber =     "1 368 026",
  bibdate =      "Tue Mar 14 16:28:34 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p460-peters/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Bernstein--B{\'e}zier form; evaluation; multivariate;
                 power form; subdivision",
  subject =      "G.1.2 [Numerical Analysis]: Approximation; I.3.5
                 [Computer Graphics]: Computational Geometry and Object
                 Modeling",
}

@Article{Li:1994:RSA,
  author =       "Kim-Hung Li",
  title =        "Reservoir Sampling Algorithms of Time Complexity
                 {$O(n(1+\log(N/n)))$}",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "481--493",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/198429.198435",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 14 16:16:57 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p481-li/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "analysis of algorithms; random sampling; reservoir",
  subject =      "G.3 [Mathematics of Computing]: Probability and
                 Statistics -- probabilistic algorithms; random number
                 generation; statistical software; G.4 [Mathematics of
                 Computing]: Mathematical Software -- algorithm
                 analysis",
}

@Article{Bratley:1994:APG,
  author =       "Paul Bratley and Bennett L. Fox and Harald
                 Niederreiter",
  title =        "{Algorithm 738}: {Programs} to Generate
                 {Niederreiter}'s Low-discrepancy Sequences",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "494--495",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/198429.198436",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Apr 10 15:51:40 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p494-bratley/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "low-discrepancy sequences; quasi-Monte Carlo;
                 quasirandom sequences",
  subject =      "G.1.4 [Numerical Analysis]: Quadrature and Numerical
                 Differentiation; I.6 [Computing Methodologies]:
                 Simulation and Modeling",
}

@Article{Gustafsson:1994:CTT,
  author =       "Kjell Gustafsson",
  title =        "Control Theoretic Techniques for Stepsize Selection in
                 Implicit {Runge--Kutta} Methods",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "496--517",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/198429.198437",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65L06",
  MRnumber =     "1 368 027",
  bibdate =      "Tue Mar 14 16:17:00 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p496-gustafsson/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "control theory; numerical integration; Runge--Kutta
                 methods; stability; stepsize selection",
  subject =      "G.1.7 [Numerical Analysis]: Ordinary Differential
                 Equations -- initial value problems; single step
                 methods; G.4 [Mathematics of Computing]: Mathematical
                 Software -- algorithm analysis; efficiency; reliability
                 and robustness",
}

@Article{Chow:1994:ASP,
  author =       "Ta-Tung Chow and Elizabeth Eskow and Robert B.
                 Schnabel",
  title =        "{Algorithm 739}: a Software Package for Unconstrained
                 Optimization using Tensor Methods",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "518--530",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/198429.198438",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Apr 10 15:51:48 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p518-chow/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "higher-order model; tensor method; unconstrained
                 optimization",
  subject =      "G.1.6 [Numerical Analysis]: Optimization -- Gradient
                 methods; G.4 [Mathematics of Computing]: Mathematical
                 Software -- efficiency; reliability and robustness",
}

@Article{Pinar:1994:DPL,
  author =       "Mustafa Pinar and Stavros A. Zenios",
  title =        "Data-level Parallel Linear-quadratic Penalty Algorithm
                 for Multicommodity Network Flows",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "531--552",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/198429.198439",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 14 16:27:42 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1994-20-4/p531-pinar/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "massively parallel algorithms; multicommodity network
                 problems; parallel optimization",
  subject =      "D.1.3 [Programming Techniques]: Concurrent Programming
                 -- parallel programming; E.1 [Data]: Data Structures;
                 G.1.6 [Numerical Analysis]: Optimization -- constrained
                 optimization; nonlinear programming; G.2.2 [Discrete
                 Mathematics]: Graph Theory -- network problems",
}

@Article{Anonymous:1994:C,
  author =       "Anonymous",
  title =        "Corrigenda",
  journal =      j-TOMS,
  volume =       "20",
  number =       "4",
  pages =        "553--553",
  month =        dec,
  year =         "1994",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 14 16:17:03 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Hull:1994:ICE}",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  xxURL =        "Missing from ACM Digital Library",
}

@Article{Boisvert:1995:PST,
  author =       "Ronald F. Boisvert",
  title =        "Purpose and Scope: {TOMS}",
  journal =      j-TOMS,
  volume =       "21",
  number =       "1",
  pages =        "1--2",
  month =        mar,
  year =         "1995",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 14 16:17:05 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  xxURL =        "Missing from ACM Digital Library",
}

@Article{Hopkins:1995:PSC,
  author =       "Tim R. Hopkins",
  title =        "Purpose and Scope: {CALGO}",
  journal =      j-TOMS,
  volume =       "21",
  number =       "1",
  pages =        "3--3",
  month =        mar,
  year =         "1995",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 14 16:17:06 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  xxURL =        "Missing from ACM Digital Library",
}

@Article{Jones:1995:IIC,
  author =       "Mark T. Jones and Paul E. Plassmann",
  title =        "An Improved Incomplete {Cholesky} Factorization",
  journal =      j-TOMS,
  volume =       "21",
  number =       "1",
  pages =        "5--17",
  month =        mar,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/200979.200981",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F10 (65F50)",
  MRnumber =     "1 365 810",
  bibdate =      "Tue Mar 14 16:17:12 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p5-jones/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "incomplete Cholesky; incomplete factorization;
                 preconditioners; sparse matrices",
  subject =      "G.1.3 [Numerical Analysis]: Numerical Linear Algebra
                 -- linear systems; sparse and very large systems",
}

@Article{Jones:1995:AFS,
  author =       "Mark T. Jones and Paul E. Plassmann",
  title =        "{Algorithm 740}: {Fortran} Subroutines to Compute
                 Improved Incomplete {Cholesky} Factorizations",
  journal =      j-TOMS,
  volume =       "21",
  number =       "1",
  pages =        "18--19",
  month =        mar,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/200979.200986",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 14 16:17:13 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p18-jones/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "incomplete Cholesky; incomplete factorization;
                 preconditioners; sparse matrices",
  subject =      "G.1.3 [Numerical Analysis]: Numerical Linear Algebra
                 -- linear systems; sparse and very large systems",
}

@Article{Ray:1995:ALS,
  author =       "Richard D. Ray",
  title =        "{Algorithm 741}: Least Squares Solution of a Linear
                 Bordered, Block-diagonal System of Equations",
  journal =      j-TOMS,
  volume =       "21",
  number =       "1",
  pages =        "20--25",
  month =        mar,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/200979.200987",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 14 16:17:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p20-ray/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "bordered block-diagonal equations; least-squares
                 solutions; sparse systems",
  subject =      "G.1.3 [Numerical Analysis]: Numerical Linear Algebra
                 -- linear systems (direct and iterative methods); G.1.6
                 [Numerical Analysis]: Optimization -- least squares
                 methods; G.4 [Mathematics of Computing]: Mathematical
                 Software",
}

@Article{Fateman:1995:FFP,
  author =       "Richard J. Fateman and Kevin A. Broughan and Diane K.
                 Willcock and Duane Rettig",
  title =        "Fast Floating Point Processing in {Common Lisp}",
  journal =      j-TOMS,
  volume =       "21",
  number =       "1",
  pages =        "26--62",
  month =        mar,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/200979.200989",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:20:50 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Reid:1996:RFF}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p26-fateman/",
  acknowledgement = ack-nhfb # " and " # ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "C programming language; Common Lisp; compiler
                 optimization; floating-point arithmetic; Fortran; Lisp;
                 numerical algorithms; symbolic computation",
  subject =      "D.3.4 [Programming Languages]: Processors ---
                 compilers; interpreters; optimization; G.4 [Mathematics
                 of Computing]: Mathematical Software --- efficiency;
                 portability",
}

@Article{Kearfott:1995:FER,
  author =       "R. Baker Kearfott",
  title =        "A {Fortran} 90 Environment for Research and
                 Prototyping of Enclosure Algorithms for Nonlinear
                 Equations and Global Optimization",
  journal =      j-TOMS,
  volume =       "21",
  number =       "1",
  pages =        "63--78",
  month =        mar,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/200979.200991",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat May 20 15:54:41 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p63-kearfott/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "automatic differentiation; Fortran 90; global
                 optimization; nonlinear algebraic systems; symbolic
                 computation",
  subject =      "D.3.3 [Programming Languages]: Language Constructs;
                 G.1.5 [Numerical Analysis]: Roots of Nonlinear
                 Equations; G.1.6 [Numerical Analysis]: Optimization;
                 G.4 [Mathematics of Computing]: Mathematical Software",
}

@Article{Dongarra:1995:SDX,
  author =       "Jack Dongarra and Tom Rowan and Reed Wade",
  title =        "Software Distribution using {XNETLIB}",
  journal =      j-TOMS,
  volume =       "21",
  number =       "1",
  pages =        "79--88",
  month =        mar,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/200979.200995",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 14 16:17:18 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p79-dongarra/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Netlib; software repositories",
  subject =      "C.2.3 [Computer-Communication Networks]: Network
                 Operations -- public networks; D.2.2 [Software
                 Engineering]: Tools and Techniques -- software
                 libraries; user interfaces; D.2.7 [Software
                 Engineering]: Distribution and Maintenance --
                 documentation; portability; G.1.0 [Numerical Analysis]:
                 General -- numerical algorithms; G.4 [Mathematics of
                 Computing]: Mathematical Software -- portability; H.3.0
                 [Information Systems Applications]: Communications
                 Applications; H.3.3 [Information Storage and
                 Retrieval]: Information Search and Retrieval -- search
                 process; selection process; H.3.5 [Information Storage
                 and Retrieval]: Online Information Services -- databank
                 sharing; H.5.2 [Information Interfaces and
                 Presentation]: User Interfaces -- windowing systems;
                 K.6.3 [Management of Computing and Information
                 Systems]: Software Management -- software development;
                 software maintenance; software selection",
}

@Article{Grosse:1995:RM,
  author =       "Eric Grosse",
  title =        "Repository Mirroring",
  journal =      j-TOMS,
  volume =       "21",
  number =       "1",
  pages =        "89--97",
  month =        mar,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/200979.201000",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 14 16:17:20 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p89-grosse/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "C.2.4 [Computer-Communication Networks]: Distributed
                 Systems -- distributed databases",
  subject =      "archives; checksum; distributed administration;
                 electronic distribution; ftp",
}

@Article{Demetriou:1995:ALF,
  author =       "I. C. Demetriou",
  title =        "{Algorithm 742}: {L2CXFT}: {A Fortran} Subroutine for
                 Least Squares Data Fitting with Nonnegative Second
                 Divided Differences",
  journal =      j-TOMS,
  volume =       "21",
  number =       "1",
  pages =        "98--110",
  month =        mar,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/200979.201039",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 14 16:17:22 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p98-demetriou/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "B-splines; convex approximation; data fitting; divided
                 difference",
  subject =      "G.1.2 [Numerical Analysis]: Approximation -- least
                 squares approximation; G.1.6 [Numerical Analysis]:
                 Optimization -- quadratic programming",
}

@Article{Weber:1995:AIG,
  author =       "Kenneth Weber",
  title =        "The Accelerated Integer {GCD} Algorithm",
  journal =      j-TOMS,
  volume =       "21",
  number =       "1",
  pages =        "111--122",
  month =        mar,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/200979.201042",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68Q20 (68M07)",
  MRnumber =     "96h:68084",
  bibdate =      "Tue Mar 14 16:17:23 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p111-weber/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "GCD; integer greatest common divisor; number-theoretic
                 computations",
  subject =      "F.2.1 [Analysis of Algorithms and Problem Complexity]:
                 Numerical Algorithms and Problems",
}

@Article{Bongartz:1995:CCU,
  author =       "I. Bongartz and A. R. Conn and Nick Gould and Ph.L.
                 Toint",
  title =        "{CUTE}: Constrained and Unconstrained Testing
                 Environment",
  journal =      j-TOMS,
  volume =       "21",
  number =       "1",
  pages =        "123--160",
  month =        mar,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/200979.201043",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 14 16:17:24 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-1/p123-bongartz/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  subject =      "D.2.2 [Software Engineering]: Tools and Techniques --
                 modules and interfaces; G.1.6 [ Numerical Analysis]:
                 Optimization -- constrained",
}

@Article{Barry:1995:RVW,
  author =       "D. A. Barry and P. J. Culligan-Hensley and S. J.
                 Barry",
  title =        "Real Values of the {W}-Function",
  journal =      j-TOMS,
  volume =       "21",
  number =       "2",
  pages =        "161--171",
  month =        jun,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/203082.203084",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "1 342 353",
  bibdate =      "Tue Oct 10 15:50:28 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-2/p161-barry/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "W-function",
  subject =      "G.1.2 [Numerical Analysis]: Approximation -- nonlinear
                 approximation; G.1.5 [Numerical Analysis]: Roots of
                 Nonlinear Equations-iterative methods",
}

@Article{Barry:1995:AWF,
  author =       "D. A. Barry and S. J. Barry and P. J.
                 Culligan-Hensley",
  title =        "{Algorithm 743}: {WAPR}: {A Fortran} Routine for
                 Calculating Real Values of the {W}-Function",
  journal =      j-TOMS,
  volume =       "21",
  number =       "2",
  pages =        "172--181",
  month =        jun,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/203082.203088",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "1 342 354",
  bibdate =      "Tue Oct 10 15:50:30 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-2/p172-barry/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "W-function",
  subject =      "G.1.2 [Numerical Analysis]: Approximation -- nonlinear
                 approximation; G.1.5 [Numerical Analysis]: Roots of
                 Nonlinear Equations -- iterative methods",
}

@Article{Hormann:1995:RTS,
  author =       "Wolfgang H{\"o}rmann",
  title =        "A Rejection Technique for Sampling from {T}-Concave
                 Distributions",
  journal =      j-TOMS,
  volume =       "21",
  number =       "2",
  pages =        "182--193",
  month =        jun,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/203082.203089",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65D20",
  MRnumber =     "96b:65018",
  bibdate =      "Tue Oct 10 15:50:31 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-2/p182-hormann/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Log-concave distributions; rejection method; universal
                 method",
  subject =      "G.3 [Probability and Statistics]: Random Number
                 Generation",
}

@Article{Rabinowitz:1995:ASA,
  author =       "F. Michael Rabinowitz",
  title =        "{Algorithm 744}: a Stochastic Algorithm for Global
                 Optimization with Constraints",
  journal =      j-TOMS,
  volume =       "21",
  number =       "2",
  pages =        "194--213",
  month =        jun,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/203082.203090",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Oct 10 15:50:33 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-2/p194-rabinowitz/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Constrained optimization; global optimization;
                 stochastic optimization; test functions",
  subject =      "G.1.6 [Numerical Analysis]: Optimization -- nonlinear
                 programming; G.3 [Mathematics of Computing]:
                 Probability and Statistics -- probabilistic algorithms
                 (including Monte Carlo); G.4 [Mathematics of
                 Computing]: Mathematical Software -- certification and
                 testing",
}

@Article{Goano:1995:ACC,
  author =       "Michele Goano",
  title =        "{Algorithm 745}: Computation of the Complete and
                 Incomplete {Fermi--Dirac} Integral",
  journal =      j-TOMS,
  volume =       "21",
  number =       "3",
  pages =        "221--232",
  month =        sep,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210089.210090",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:19:43 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Goano:1997:RA7}",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p221-goano/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "asymptotic expansions; confluent hypergeometric
                 functions; convergence acceleration; e[k] transforms;
                 epsilon algorithm; Euler transformation; Fermi--Dirac
                 integral; incomplete Fermi--Dirac integral; incomplete
                 gamma function; Levin's u transform; Riemann's zeta
                 function",
  subject =      "G.1.2 [Mathematics of Computing]: Approximation; G.4
                 [Mathematics of Computing]: Mathematical Software; J.2
                 [Computer Applications]: Physical Sciences and
                 Engineering",
}

@Article{Dobmann:1995:APF,
  author =       "M. Dobmann and M. Liepelt and K. Schittkowski",
  title =        "{Algorithm 746}: {PCOMP}: {A Fortran} Code for
                 Automatic Differentiation",
  journal =      j-TOMS,
  volume =       "21",
  number =       "3",
  pages =        "233--266",
  month =        sep,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210089.210091",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p233-dobmann/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "automatic differentiation; forward accumulation;
                 reverse accumulation",
  subject =      "D.1.2 [Programming Techniques]: Automatic Programming;
                 D.3.4 [Programming Languages]: Processors - code
                 generation; G.1.4 [Numerical Analysis]: Quadrature and
                 Numerical Differentiation; G.4 [Mathematics of
                 Computing]: Mathematical Software",
}

@Article{Sullivan:1995:NAU,
  author =       "Stephen J. Sullivan and Benjamin G. Zorn",
  title =        "Numerical Analysis Using Nonprocedural Paradigms",
  journal =      j-TOMS,
  volume =       "21",
  number =       "3",
  pages =        "267--298",
  month =        sep,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210089.210093",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p267-sullivan/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "benchmarks; experimental languages; Gaussian
                 elimination; linear algebra; programming languages;
                 sparse matrices",
  subject =      "G.1 [Mathematics of Computing]: Numerical Analysis",
}

@Article{Miminis:1995:AFS,
  author =       "George Miminis and Helmut Roth",
  title =        "{Algorithm 747}: {A Fortran} Subroutine to Solve the
                 Eigenvalue Assignment Problem for Multiinput Systems
                 Using State Feedback",
  journal =      j-TOMS,
  volume =       "21",
  number =       "3",
  pages =        "299--326",
  month =        sep,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210089.210094",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p299-miminis/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "deflation; double steps; eigenvalue assignment;
                 numerical efficiency; pole assignment",
  subject =      "F.2.1 [Analysis of Algorithms and Problem Complexity]:
                 Numerical Algorithms and Problems - computations on
                 matrices; G.1.0 [Numerical Analysis]: General -
                 numerical algorithms; G.1.3 [Numerical Analysis]:
                 Numerical Linear Algebra - eigenvalues; J.2 [Computer
                 Applications]: Physical Sciences and Engineering -
                 aerospace; engineering; J.4 [Computer Applications]:
                 Social and Behavioral Sciences - economics",
}

@Article{Alefeld:1995:AEZ,
  author =       "G. E. Alefeld and F. A. Potra and Yixun Shi",
  title =        "{Algorithm 748}: Enclosing Zeros of Continuous
                 Functions",
  journal =      j-TOMS,
  volume =       "21",
  number =       "3",
  pages =        "327--344",
  month =        sep,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/210089.210111",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Sep 28 16:39:05 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-3/p327-alefeld/",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; asymptotic efficiency index; enclosing
                 method; inverse cubic interpolation; quadratic
                 interpolation; simple root; theory",
  subject =      "G.1.0 [Numerical Analysis]: General -- numerical
                 algorithms; G.1.5 [Numerical Analysis]: Roots of
                 Nonlinear Equations -- convergence; iterative methods",
}

@Article{Rizzardi:1995:MTM,
  author =       "Mariarosaria Rizzardi",
  title =        "A Modification of {Talbot}'s Method for the
                 Simultaneous Approximation of Several Values of the
                 Inverse {Laplace} Transform",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "347--371",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.212068",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65R10",
  MRnumber =     "96k:65084",
  bibdate =      "Sat Feb 10 08:48:51 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p347-rizzardi/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "complex inversion formula; inverse Laplace transform;
                 numerical method; Talbot; trapezoidal rule",
  reviewer =     "A. J. Rodrigues",
  subject =      "G.1.0 [Numerical Analysis]: General -- error analysis;
                 numerical algorithms; G.1.2 [Numerical Analysis]:
                 Approximation -- nonlinear approximation; G.1.4
                 [Numerical Analysis]: Quadrature and Numerical
                 Differentiation -- equal interval integration; error
                 analysis; G.1.9 [Numerical Analysis]: Integral
                 Equations -- Fredholm equations",
}

@Article{Sherlock:1995:AFD,
  author =       "Barry G. Sherlock and Donald M. Monro",
  title =        "{Algorithm 749}: Fast Discrete Cosine Transform",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "372--378",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.212071",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 14 09:58:14 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p372-sherlock/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "data compression; discrete cosine transform; fast
                 transform",
  subject =      "D.3.2 [Programming Languages]: Language
                 Classifications -- Fortran; E.4 [Data]: Coding and
                 Information Theory -- data compaction and compression;
                 F.2.1 [Analysis of Algorithms and Problem Complexity]:
                 Numerical Algorithms and Problems; G.4 [Mathematics of
                 Computing]: Mathematical Software; I.4.2 [Image
                 Processing]: Compression",
}

@Article{Bailey:1995:FBM,
  author =       "David H. Bailey",
  title =        "A {Fortran-90} Based Multiprecision System",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "379--387",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.212075",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Apr 29 15:15:44 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also extension to complex arithmetic
                 \cite{Smith:1998:AMP}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p379-bailey/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "arithmetic; Fortran 90; multiprecision",
  subject =      "D.3.2 [Programming Languages]: Language
                 Classifications -- Fortran 90; D.3.4 [Programming
                 Languages]: Processors; G.1.0 [Numerical Analysis]:
                 General; G.1.2 [Numerical Analysis]: Approximation",
}

@Article{Amos:1995:RAP,
  author =       "D. E. Amos",
  title =        "A Remark on {Algorithm 644}: a Portable Package for
                 {Bessel} Functions of a Complex Argument and
                 Nonnegative Order",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "388--393",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.212078",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:24:54 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Amos:1986:APP,Amos:1990:RPP,Kodama:2007:RA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p388-amos/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "complex Airy Functions; complex Bessel functions;
                 derivatives of Airy functions; H, I, J, K, and Y Bessel
                 functions; log gamma function",
  subject =      "G.1.0 [Numerical Analysis]: General -- numerical
                 algorithms; G.1.m [Numerical Analysis]: Miscellaneous;
                 G.m [Mathematics of Computing]: Miscellaneous",
}

@Article{Carpaneto:1995:ESL,
  author =       "G. Carpaneto and M. Dell'Amico and P. Toth",
  title =        "Exact Solution of Large Scale Asymmetric Travelling
                 Salesman Problems",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "394--409",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.212081",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "90C27 (90C35)",
  MRnumber =     "96m:90062a",
  bibdate =      "Tue Nov 14 09:58:01 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p394-carpaneto/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "assignment problem; asymmetric traveling salesman
                 problem; branch and bound; reduction procedure; subtour
                 elimination",
  reviewer =     "N. I. Yanev",
  subject =      "G.2.1 [Discrete Mathematics]: Combinatorics --
                 combinatorial algorithms; G.2.2 [Discrete Mathematics]:
                 Graph Theory -- graph algorithms; path and circuit
                 problems",
}

@Article{Carpaneto:1995:ACS,
  author =       "G. Carpaneto and M. Dell'Amico and P. Toth",
  title =        "{Algorithm 750}: {CDT}: a Subroutine for the Exact
                 Solution of Large-Scale Asymmetric Travelling Salesman
                 Problems",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "410--415",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.212084",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "90C27 (90C35)",
  MRnumber =     "96m:90062b",
  bibdate =      "Tue Nov 14 09:57:58 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p410-carpaneto/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "assignment problem; asymmetric traveling salesman
                 problem; branch and bound; reduction procedure; subtour
                 elimination",
  reviewer =     "N. I. Yanev",
  subject =      "D.3.2 [Programming Languages]: Language
                 classifications -- Fortran; G.2.1 [Discrete
                 Mathematics]: Combinatorics -- combinatorial
                 algorithms; G.2.2 [Discrete Mathematics]: Graph Theory
                 -- graph algorithms; path and circuit problems",
}

@Article{Doman:1995:SAP,
  author =       "B. G. S. Doman and C. J. Pursglove and W. M. Coen",
  title =        "A Set of {Ada} Packages for High Precision
                 Calculations",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "416--431",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.212087",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 14 09:57:55 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p416-doman/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accuracy; Ada; arithmetic elementary-function
                 evaluation; floating-point; multiple-precision portable
                 software",
  subject =      "G.1.0 [Numerical Analysis]: General -- computer
                 arithmetic; G.1.2 [Numerical Analysis]: Approximation
                 -- elementary function approximation; G.4 [Mathematics
                 of Computing]: Mathematical Software -- algorithm
                 analysis; efficiency; portability",
}

@Article{Scott:1995:ACC,
  author =       "Jennifer A. Scott",
  title =        "An {Arnoldi} Code for Computing Selected Eigenvalues
                 of Sparse, Real, Unsymmetric Matrices",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "432--475",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.212091",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65F15 65F50)",
  MRnumber =     "1 364 698",
  bibdate =      "Tue Nov 14 09:57:52 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p432-scott/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keyword =      "Arnoldi's method; Chebychev acceleration; large sparse
                 matrices; real unsymmetric matrices",
  subject =      "G.1.0 [Numerical Analysis]: General -- numerical
                 algorithms; G.1.3 [Numerical Analysis]: Numerical
                 Linear Algebra -- eigenvalues",
}

@Article{Kaufman:1995:CMD,
  author =       "Linda Kaufman",
  title =        "Computing the ${MDM}^{T}$ decomposition",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "476--489",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.212092",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 14 09:57:49 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p476-kaufman/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "block factorizations; LAPACK; linear systems (direct
                 methods); symmetric indefinite",
  subject =      "G.1.3 [Numerical Analysis]: Numerical Linear Algebra
                 -- linear systems (direct and iterative methods); G.4
                 [Mathematics of Computing]: Mathematical Software --
                 efficiency",
}

@Article{Duff:1995:CCS,
  author =       "Iain S. Duff and Jennifer A. Scott",
  title =        "Corrigendum: Computing Selected Eigenvalues of Sparse
                 Unsymmetric Matrices Using Subspace Iteration",
  journal =      j-TOMS,
  volume =       "21",
  number =       "4",
  pages =        "490--490",
  month =        dec,
  year =         "1995",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/212066.215254",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 14 09:57:46 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Duff:1993:CSE}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1995-21-4/p490-duff/",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Renka:1996:ATC,
  author =       "R. J. Renka",
  title =        "{Algorithm 751}: {TRIPACK}: a constrained
                 two-dimensional {Delaunay} triangulation package",
  journal =      j-TOMS,
  volume =       "22",
  number =       "1",
  pages =        "1--8",
  month =        mar,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/225545.225546;
                 http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p1-renka/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 15 18:58:33 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Renka:1999:RAa}.",
  abstract =     "TRIPACK is a Fortran 77 software package that employs
                 an incremental algorithm to construct a constrained
                 Delaunay triangulation of a set of points in the plane
                 (nodes). The triangulation covers the convex hull of
                 the nodes but may include polygonal constraint regions
                 whose triangles are distinguishable from those in the
                 remainder of the triangulation. This effectively allows
                 for a nonconvex or multiply connected triangulation
                 (the complement of the union of constraint regions)
                 while retaining the efficiency of searching and
                 updating a convex triangulation. The package provides a
                 wide range of capabilities including an efficient means
                 of updating the triangulation with nodal additions or
                 deletions. For $N$ nodes, the storage requirement is
                 $13N$ integer storage locations in addition to the $2N$
                 nodal coordinates.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.
                 {\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation.",
}

@Article{Renka:1996:ASS,
  author =       "R. J. Renka",
  title =        "{Algorithm 752}: {SRFPACK}: software for scattered
                 data fitting with a constrained surface under tension",
  journal =      j-TOMS,
  volume =       "22",
  number =       "1",
  pages =        "9--17",
  month =        mar,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/225545.225547;
                 http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p9-renka/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Renka:1999:RAb}.",
  abstract =     "SRFPACK is a Fortran 77 software package that
                 constructs a smooth interpolatory or approximating
                 surface to data values associated with arbitrarily
                 distributed points in the plane. It employs
                 automatically selected tension factors to preserve
                 shape properties of the data and to avoid overshoot and
                 undershoot associated with steep gradients. The domain
                 of the fitting function may be nonconvex or multiply
                 connected, and the surface may be constrained to have
                 discontinuous value or derivative across a
                 user-specified curve representing, for example, a
                 geological fault line. Although triangle based, the
                 method provides a means of avoiding the inaccuracy
                 associated with long thin triangles on the boundary of
                 the convex hull of the data abscissae.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE.
                 {\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation.",
}

@Article{Buis:1996:EVP,
  author =       "Paul E. Buis and Wayne R. Dyksen",
  title =        "Efficient vector and parallel manipulation of tensor
                 products",
  journal =      j-TOMS,
  volume =       "22",
  number =       "1",
  pages =        "18--23",
  month =        mar,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/225545.225548",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68Q40",
  MRnumber =     "1 383 183",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p18-buis/",
  abstract =     "We present efficient vector and parallel methods for
                 manipulating tensor products of matrices. We consider
                 both computing the matrix-vector product $(A_{1}
                 \otimes \cdots \otimes A_{K})x$ and solving the system
                 of linear equations $(A_{1} \otimes \cdots \otimes
                 A_{K})x=b$. The methods described are independent of
                 $K$. We accompany this article with a companion
                 algorithm which describes an implementation of a
                 complete set of tensor product routines based on LAPACK
                 and the Level 2 and 3 Basic Linear Algebra Subprograms
                 (BLAS) which provide vectorization and
                 parallelization.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra. {\bf D.1.3}:
                 Software, PROGRAMMING TECHNIQUES, Concurrent
                 Programming. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE.",
}

@Article{Buis:1996:ATL,
  author =       "Paul E. Buis and Wayne R. Dyksen",
  title =        "{Algorithm 753}: {TENPACK}: a {LAPACK-based} library
                 for the computer manipulation of tensor products",
  journal =      j-TOMS,
  volume =       "22",
  number =       "1",
  pages =        "24--29",
  month =        mar,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/225545.225549",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p24-buis/",
  abstract =     "This article presents the interface of an
                 implementation of methods to manipulate equations of
                 this form $A_1 \otimes \cdots \otimes A_m$ where
                 the $A_i$ are matrices. The methods described are
                 independent of $m$. The code is based on LAPACK and the
                 BLAS and supports virtually all of the matrix formats
                 supported by those packages. Timings of the
                 implementation on several machines are also given.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf D.1.3}: Software, PROGRAMMING TECHNIQUES,
                 Concurrent Programming. {\bf D.3.2}: Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 FORTRAN. {\bf G.1.3}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Numerical Linear Algebra. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE.",
}

@Article{Duff:1996:DNF,
  author =       "I. S. Duff and J. A. Scott",
  title =        "The design of a new frontal code for solving sparse,
                 unsymmetric systems",
  journal =      j-TOMS,
  volume =       "22",
  number =       "1",
  pages =        "30--45",
  month =        mar,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/225545.225550",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65F50)",
  MRnumber =     "1 383 184",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p30-duff/",
  abstract =     "We describe the design, implementation, and
                 performance of a frontal code for the solution of
                 large, sparse, unsymmetric systems of linear equations.
                 The resulting software package, MA42, is included in
                 Release 11 of the Harwell Subroutine Library and is
                 intended to supersede the earlier MA32 package. We
                 discuss in detail the extensive use of higher-level
                 BLAS kernels within MA42 and illustrate the performance
                 on a range of practical problems on a CRAY Y-MP, an IBM
                 3090, and an IBM RISC System/6000. We examine extending
                 the frontal solution scheme to use multiple fronts to
                 allow MA42 to be run in parallel. We indicate some
                 directions for future development.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Freund:1996:QPQ,
  author =       "Roland W. Freund and No{\"e}l M. Nachtigal",
  title =        "{QMRPACK}: a package of {QMR} algorithms",
  journal =      j-TOMS,
  volume =       "22",
  number =       "1",
  pages =        "46--77",
  month =        mar,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/225545.225551",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65F10)",
  MRnumber =     "1 383 185",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p46-freund/",
  abstract =     "The quasi-minimal residual (QMR) algorithm is a
                 Krylov-subspace method for the iterative solution of
                 large non-Hermitian linear systems. QMR is based on the
                 look-ahead Lanczos algorithm that, by itself, can also
                 be used to obtain approximate eigenvalues of large
                 non-Hermitian matrices. QMRPACK is a software package
                 with Fortran 77 implementations of the QMR algorithm
                 and variants thereof, and of the three-term and coupled
                 two-term look-ahead Lanczos algorithms. In this
                 article, we discuss some of the features of the
                 algorithms in the package, with emphasis on the issues
                 related to using the codes. We describe in some detail
                 two routines from the package, one for the solution of
                 linear systems and the other for the computation of
                 eigenvalue approximations. We present some numerical
                 examples from applications where QMRPACK was used.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; reliability; theory",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf D.3.2}: Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 FORTRAN. {\bf F.2.1}: Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness. {\bf G.1.3}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Eigenvalues. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Efficiency.",
}

@Article{Kaagstrom:1996:LAS,
  author =       "Bo K{\aa}gstr{\"o}m and Peter Poromaa",
  title =        "{LAPACK-style} algorithms and software for solving the
                 generalized {Sylvester} equation and estimating the
                 separation between regular matrix pairs",
  journal =      j-TOMS,
  volume =       "22",
  number =       "1",
  pages =        "78--103",
  month =        mar,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/225545.225552",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65-04 (65F30)",
  MRnumber =     "1 383 186",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p78-kagstrom/",
  abstract =     "Robust and fast software to solve the generalized
                 Sylvester equation ($AR - LB = C$, $DR - LE = F$) for
                 unknowns $R$ and $L$ is presented. This special linear
                 system of equations, and its transpose, arises in
                 computing error bounds for computed eigenvalues and
                 eigenspaces of the generalized eigenvalue problem
                 $S-\lambda T$, in computing deflating subspaces of the
                 same problem, and in computing certain decompositions
                 of transfer matrices arising in control theory. Our
                 contributions are twofold. First, we reorganize the
                 standard algorithm for this problem to use Level 3 BLAS
                 operations, like matrix multiplication, in its inner
                 loop. This speeds up the algorithm by a factor of 9 on
                 an IBM RS6000. Second, we develop and compare several
                 condition estimation algorithms, which inexpensively
                 but accurately estimate the sensitivity of the solution
                 of this linear system.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Algorithm analysis. {\bf F.2.1}: Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices. {\bf G.1.3}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative methods).
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Reliability and robustness. {\bf G.1.3}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Conditioning. {\bf G.1.3}: Mathematics
                 of Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Eigenvalues. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf
                 F.2.1}: Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on matrices. {\bf G.1.3}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Matrix inversion.",
}

@Article{Resende:1996:AFS,
  author =       "Mauricio G. C. Resende and Panos M. Pardalos and Yong
                 Li",
  title =        "{Algorithm 754}: {Fortran} subroutines for approximate
                 solution of dense quadratic assignment problems using
                 {GRASP}",
  journal =      j-TOMS,
  volume =       "22",
  number =       "1",
  pages =        "104--118",
  month =        mar,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/225545.225553",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p104-resende/",
  abstract =     "In the NP-complete quadratic assignment problem (QAP),
                 $n$ facilities are to be assigned to $n$ sites at
                 minimum cost. The contribution of assigning facility
                 $i$ to site $k$ and facility $j$ to site $l$ to the
                 total cost is $f_{ij} - d_{kl}$, where $f_{ij}$ is the
                 flow between facilities $i$ and $j$, and $d_{kl}$ is
                 the distance between sites $k$ and $l$. Only very small
                 ($n\le20$) instances of the QAP have been solved
                 exactly, and heuristics are therefore used to produce
                 approximate solutions. This article describes a set of
                 Fortran subroutines to find approximate solutions to
                 dense quadratic assignment problems, having at least
                 one symmetric flow or distance matrix. A greedy,
                 randomized, adaptive search procedure (GRASP) is used
                 to produce the solutions. The design and implementation
                 of the code are described in detail, and extensive
                 computational experiments are reported, illustrating
                 solution quality as a function of running time.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Integer programming. {\bf
                 D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.2.1}: Mathematics of
                 Computing, DISCRETE MATHEMATICS, Combinatorics,
                 Combinatorial algorithms.",
}

@Article{Wallace:1996:FPG,
  author =       "C. S. Wallace",
  title =        "Fast pseudorandom generators for normal and
                 exponential variates",
  journal =      j-TOMS,
  volume =       "22",
  number =       "1",
  pages =        "119--127",
  month =        mar,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/225545.225554",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See comments \cite{Brent:2008:SCC}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-1/p119-wallace/",
  abstract =     "Fast algorithms for generating pseudorandom numbers
                 from the unit-normal and unit-exponential distributions
                 are described. The methods are unusual in that they do
                 not rely on a source of uniform random numbers, but
                 generate the target distributions directly by using
                 their maximal-entropy properties. The algorithms are
                 fast. The normal generator is faster than the commonly
                 used Unix library uniform generator ``random'' when the
                 latter is used to yield real values. Their statistical
                 properties seem satisfactory, but only a limited suite
                 of tests has been conducted. They are written in C and
                 as written assume 32-bit integer arithmetic. The code
                 is publicly available as C source and can easily be
                 adopted for longer word lengths and/or vector
                 processing.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design; performance",
  remark =       "Wallace's generators produce normal and exponential
                 distributions directly, without first generation
                 numbers from a uniform distribution.",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Random number generation. {\bf G.3}:
                 Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing.",
}

@Article{Griewank:1996:AAP,
  author =       "Andreas Griewank and David Juedes and Jean Utke",
  title =        "{Algorithm 755}: {ADOL-C}: a package for the automatic
                 differentiation of algorithms written in {C\slash
                 C++}",
  journal =      j-TOMS,
  volume =       "22",
  number =       "2",
  pages =        "131--167",
  month =        jun,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/229473.229474",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-2/p131-griewank/",
  abstract =     "The C++ package ADOL-C described here facilitates the
                 evaluation of first and higher derivatives of vector
                 functions that are defined by computer programs written
                 in C or C++. The resulting derivative evaluation
                 routines may be called from C/C++, Fortran, or any
                 other language that can be linked with C. The numerical
                 values of derivative vectors are obtained free of
                 truncation errors at a small multiple of the run-time
                 and randomly accessed memory of the given function
                 evaluation program. Derivative matrices are obtained by
                 columns or rows. For solution curves defined by
                 ordinary differential equations, special routines are
                 provided that evaluate the Taylor coefficient vectors
                 and their Jacobians with respect to the current state
                 vector. The derivative calculations involve a possibly
                 substantial (but always predictable) amount of data
                 that are accessed strictly sequentially and are
                 therefore automatically paged out to external files.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.
                 {\bf I.1.2}: Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms, Analysis of algorithms. {\bf
                 I.1.2}: Computing Methodologies, ALGEBRAIC
                 MANIPULATION, Algorithms.",
}

@Article{Driscoll:1996:AMT,
  author =       "Tobin A. Driscoll",
  title =        "{Algorithm 756}: a {MATLAB} Toolbox for
                 {Schwarz--Christoffel} mapping",
  journal =      j-TOMS,
  volume =       "22",
  number =       "2",
  pages =        "168--186",
  month =        jun,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/229473.229475",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-2/p168-driscoll/",
  abstract =     "The Schwarz--Christoffel transformation and its
                 variations yield formulas for conformal maps from
                 standard regions to the interiors or exteriors of
                 possibly unbounded polygons. Computations involving
                 these maps generally require a computer, and although
                 the numerical aspects of these transformations have
                 been studied, there are few software implementations
                 that are widely available and suited for general use.
                 The Schwarz--Christoffel Toolbox for MATLAB is a new
                 implementation of Schwarz--Christoffel formulas for
                 maps from the disk, half-plane, strip, and rectangle
                 domains to polygon interiors, and from the disk to
                 polygon exteriors. The toolbox, written entirely in the
                 MATLAB script language, exploits the high-level
                 functions, interactive environment, visualization
                 tools, and graphical user interface elements supplied
                 by current versions of MATLAB, and is suitable for use
                 both as a standalone tool and as a library for
                 applications written in MATLAB, Fortran, or C. Several
                 examples and simple applications are presented to
                 demonstrate the toolbox's capabilities.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.m}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Miscellaneous. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, MATLAB. {\bf J.2}:
                 Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING.",
}

@Article{Duff:1996:DMC,
  author =       "I. S. Duff and J. K. Reid",
  title =        "The design of {MA48}: a code for the direct solution
                 of sparse unsymmetric linear systems of equations",
  journal =      j-TOMS,
  volume =       "22",
  number =       "2",
  pages =        "187--226",
  month =        jun,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/229473.229476",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-2/p187-duff/",
  abstract =     "We describe the design of a new code for the direct
                 solution of sparse unsymmetric linear systems of
                 equations. The new code utilizes a novel restructuring
                 of the symbolic and numerical phases, which increases
                 speed and saves storage without sacrifice of numerical
                 stability. Other features include switching to
                 full-matrix processing in all phases of the computation
                 enabling the use of all three levels of BLAS, treatment
                 of rectangular or rank-deficient matrices, partial
                 factorization, and integrated facilities for iterative
                 refinement and error estimation.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf G.1.3}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Sparse and very large systems.",
}

@Article{Duff:1996:EZD,
  author =       "I. S. Duff and J. K. Reid",
  title =        "Exploiting zeros on the diagonal in the direct
                 solution of indefinite sparse symmetric linear
                 systems",
  journal =      j-TOMS,
  volume =       "22",
  number =       "2",
  pages =        "227--257",
  month =        jun,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/229473.229480",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F50",
  MRnumber =     "1 408 491",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-2/p227-duff/",
  abstract =     "We describe the design of a new code for the solution
                 of sparse indefinite symmetric linear systems of
                 equations. The principal difference between this new
                 code and earlier work lies in the exploitation of the
                 additional sparsity available when the matrix has a
                 significant number of zero diagonal entries. Other new
                 features have been included to enhance the execution
                 speed, particularly on vector and parallel machines.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf G.1.3}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra, Sparse and very large systems.",
}

@Article{Price:1996:RA,
  author =       "David T. Price",
  title =        "Remark on {Algorithm 715}",
  journal =      j-TOMS,
  volume =       "22",
  number =       "2",
  pages =        "258--258",
  month =        jun,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/229473.236186",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Cody:1993:ASE}",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-2/p258-price/",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hull:1996:MBP,
  author =       "T. E. Hull and R. Mathon",
  title =        "The mathematical basis and a prototype implementation
                 of a new polynomial rootfinder with quadratic
                 convergence",
  journal =      j-TOMS,
  volume =       "22",
  number =       "3",
  pages =        "261--280",
  month =        sep,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/232826.232830",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p261-hull/",
  abstract =     "Formulas developed originally by Weierstrass have been
                 used since the 1960s by many others for the
                 simultaneous determination of all the roots of a
                 polynomial. Convergence to simple roots is quadratic,
                 but individual approximations to a multiple root
                 converge only linearly. However, it is shown here that
                 the mean of such individual approximations converges
                 quadratically to that root. This result, along with
                 some detail about the behavior of such approximations
                 in the neighborhood of the multiple root, suggests a
                 new approach to the design of polynomial rootfinders.
                 It should also be noted that the technique is well
                 suited to take advantage of a parallel environment.
                 This article first provides the relevant mathematical
                 results: a short derivation of the formulas,
                 convergence proofs, an indication of the behavior near
                 a multiple root, and some error bounds. It then
                 provides the outline of an algorithm based on these
                 results, along with some graphical and numerical
                 results to illustrate the major theoretical points.
                 Finally, a new program based on this algorithm, but
                 with a more efficient way of choosing starting values,
                 is described and then compared with corresponding
                 programs from IMSL and NAG with good results. This
                 program is available from Mathon
                 (\path=combin@cs.utoronto.ca=).",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Error analysis. {\bf G.1.0}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Numerical algorithms. {\bf G.1.5}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
                 Equations, Convergence. {\bf G.1.5}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
                 Equations, Error analysis. {\bf G.1.5}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
                 Equations, Iterative methods. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.",
}

@Article{Sosonkina:1996:NEG,
  author =       "Maria Sosonkina and Layne T. Watson and David E.
                 Stewart",
  title =        "Note on the end game in homotopy zero curve tracking",
  journal =      j-TOMS,
  volume =       "22",
  number =       "3",
  pages =        "281--287",
  month =        sep,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/232826.232843",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p281-sosonkina/",
  abstract =     "Homotopy algorithms to solve a nonlinear system of
                 equations $f(x) = 0$ involve tracking the zero curve of
                 a homotopy map $p(a, \lambda, x)$ from $\lambda = 0$
                 until $\lambda = 1$. When the algorithm nears or
                 crosses the hyperplane $\lambda = 1$, an ``end game''
                 phase is begun to compute the solution *** satisfying
                 $p(a, \lambda, ***) = f(**) = 0$. This note compares
                 several end game strategies, including the one
                 implemented in the normal flow code FIXPNF in the
                 homotopy software package HOMPACK.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.5}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Systems of
                 equations. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE.",
}

@Article{Macleod:1996:AMS,
  author =       "Allan J. Macleod",
  title =        "{Algorithm 757}: {MISCFUN}, a software package to
                 compute uncommon special functions",
  journal =      j-TOMS,
  volume =       "22",
  number =       "3",
  pages =        "288--301",
  month =        sep,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/232826.232846",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p288-macleod/",
  abstract =     "MISCFUN (MISCellaneous FUNctions) is a Fortran package
                 for the evaluation of several special functions, which
                 are not used often enough to have been included in the
                 standard libraries or packages. The package uses
                 Chebyshev expansions as the underlying method of
                 approximation, with the Chebyshev coefficients given to
                 20D. A wide variety of functions are included, and the
                 package is designed so that other functions can be
                 added in a standard manner.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev
                 approximation and theory. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Certification and
                 testing.",
}

@Article{Blom:1996:AVVa,
  author =       "J. G. Blom and R. A. Trompert and J. G. Verwer",
  title =        "{Algorithm 758}: {VLUGR2}: a vectorizable
                 adaptive-grid solver for {PDEs} in {2D}",
  journal =      j-TOMS,
  volume =       "22",
  number =       "3",
  pages =        "302--328",
  month =        sep,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/232826.232850",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p302-blom/",
  abstract =     "This article deals with an adaptive-grid
                 finite-difference solver for time-dependent
                 two-dimensional systems of partial differential
                 equations. It describes the ANSI Fortran 77 code,
                 VLUGR2, autovectorizable on the Cray Y-MP, that is
                 based on this method. The robustness and the efficiency
                 of the solver, both for vector and scalar processors,
                 are illustrated by the application of the code to two
                 example problems arising from a groundwater-flow
                 model.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.8}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Partial Differential
                 Equations. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE.",
}

@Article{Blom:1996:AVVb,
  author =       "J. G. Blom and J. G. Verwer",
  title =        "{Algorithm 759}: {VLUGR3}: a vectorizable
                 adaptive-grid solver for {PDEs} in {3D} --- {Part II}.
                 code description",
  journal =      j-TOMS,
  volume =       "22",
  number =       "3",
  pages =        "329--347",
  month =        sep,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/232826.232853",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p329-blom/",
  abstract =     "This article describes an ANSI Fortran 77 code,
                 VLUGR3, autovectorizable on the Cray Y-MP, that is
                 based on an adaptive-grid finite-difference method to
                 solve time-dependent three-dimensional systems of
                 partial differential equations.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.8}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Partial Differential
                 Equations. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE.",
}

@Article{Andersen:1996:MSM,
  author =       "Knud D. Andersen",
  title =        "A modified {Schur-complement} method for handling
                 dense columns in interior-point methods for linear
                 programming",
  journal =      j-TOMS,
  volume =       "22",
  number =       "3",
  pages =        "348--356",
  month =        sep,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/232826.232937",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p348-andersen/",
  abstract =     "The main computational work in interior-point methods
                 for linear programming (LP) is to solve a least-squares
                 problem. The normal equations are often used, but if
                 the LP constraint matrix contains a nearly dense column
                 the normal-equations matrix will be nearly dense.
                 Assuming that the nondense part of the constraint
                 matrix is of full rank, the Schur complement can be
                 used to handle dense columns. In this article we
                 propose a modified Schur-complement method that relaxes
                 this assumption. Encouraging numerical results are
                 presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf G.1.6}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Linear programming.",
}

@Article{Akima:1996:ARS,
  author =       "Hiroshi Akima",
  title =        "{Algorithm 760}: rectangular-grid-data surface fitting
                 that has the accuracy of a bicubic polynomial",
  journal =      j-TOMS,
  volume =       "22",
  number =       "3",
  pages =        "357--361",
  month =        sep,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/232826.232854",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p357-akima/",
  abstract =     "A local algorithm for smooth surface fitting for
                 rectangular-grid data has been presented. It has the
                 accuracy of a bicubic polynomial.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.1}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Interpolation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE.",
}

@Article{Akima:1996:ASS,
  author =       "Hiroshi Akima",
  title =        "{Algorithm 761}: scattered-data surface fitting that
                 has the accuracy of a cubic polynomial",
  journal =      j-TOMS,
  volume =       "22",
  number =       "3",
  pages =        "362--371",
  month =        sep,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/232826.232856",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:11:35 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remarks \cite{Renka:1998:RA,DeTisi:2000:RAS}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p362-akima/",
  abstract =     "An algorithm for smooth surface fitting for scattered
                 data has been presented. It has the accuracy of a cubic
                 polynomial in most cases and is a local, triangle-based
                 algorithm.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.1}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Interpolation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE.",
}

@Article{Brown:1996:ALL,
  author =       "Barry W. Brown and Lawrence B. Levy and James Lovato
                 and Kathy Russell and Floyd M. Spears",
  title =        "{Algorithm 762}: {LLDRLF}, log-likelihood and some
                 derivatives for {log-F} models",
  journal =      j-TOMS,
  volume =       "22",
  number =       "3",
  pages =        "372--382",
  month =        sep,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/232826.232858",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 11:11:08 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p372-brown/",
  abstract =     "The flexible statistical models incorporating the
                 log-F distribution are little used because of numeric
                 difficulties. We describe a method for calculating the
                 log-likelihood and two derivatives with respect to the
                 data argument. Fortran subroutines incorporating these
                 calculations are provided.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation.",
}

@Article{Kearfott:1996:IFM,
  author =       "R. Baker Kearfott",
  title =        "{Algorithm 763}: {INTERVAL\_ARITHMETIC}: {A Fortran
                 90} Module for an Interval Data Type",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "385--392",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235816",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Kearfott:1994:AIP}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p385-kearfott/",
  abstract =     "Interval arithmetic is useful in {\it automatically
                 verified computation}, that is, in computations in
                 which the algorithm itself rigorously proves that the
                 answer must lie within certain bounds. In addition to
                 rigor, interval arithmetic also provides a simple and
                 somewhat sharp method of bounding ranges of functions
                 for global optimization and other tasks. Convenient use
                 of interval arithmetic requires an interval data type
                 in the programming language. Although various packages
                 supply such a data type, previous ones are machine
                 specific, obsolete, and unsupported, for languages
                 other than Fortran, or commercial. The Fortran 90
                 module {INTERVAL\_ARITHMETIC} provides a portable
                 interval data type in Fortran 90. This data type is
                 based on two double-precision real Fortran storage
                 unit. Module {INTERVAL\_ARITHMETIC} uses the Fortran 77
                 library {INTLIB} (ACM TOMS {Algorithm 737}) as a
                 supporting library. The module has been employed
                 extensively in the author's own research.",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, languages",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 90. {\bf G.1.0}: Mathematics
                 of Computation, NUMERICAL ANALYSIS, General, Computer
                 arithmetic, Error analysis, Numerical algorithms.",
}

@Article{Lehoucq:1996:CEU,
  author =       "R. B. Lehoucq",
  title =        "The Computation of Elementary Unitary Matrices",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "393--400",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235817",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p393-lehoucq/",
  abstract =     "The construction of elementary unitary matrices that
                 transform a complex vector to a multiple of $e_1$, the
                 first column of the identity matrix, is studied. We
                 present four variants and their software
                 implementation, including a discussion on the {LAPACK}
                 subroutine {CLARFG}. Comparisons are also given.",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf F.2}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices. {\bf G.1.3}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis.",
}

@Article{Butcher:1996:DMS,
  author =       "J. C. Butcher and J. R. Cash and M. T. Diamantakis",
  title =        "{DESI} Methods for Stiff Initial Value Problems",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "401--422",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235818",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p401-butcher/",
  abstract =     "Recently, the so-called DESI (diagonally extended
                 singly implicit) {Runge}-{Kutta} methods were
                 introduced to overcome some of the limitations of
                 singly implicit methods. Preliminary experiments have
                 shown that these methods are usually more efficient
                 than the standard singly implicit {Runge}-{Kutta}
                 (SIRK) methods and, in many cases, are competitive with
                 backward differentiation formulae (BDF). This article
                 presents an algorithm for determining the full
                 coefficient matrix from the stability function, which
                 is already chosen to make the method {A}-stable.
                 Because of their unconventional nature, DESI methods
                 have to be implemented in a special way. In particular,
                 the effectiveness of these methods depends heavily on
                 how the starting values are chosen for the stage
                 iterations. These and other implementation questions
                 are discussed in detail, and the design choices we have
                 made form the basis of an experimental code for the
                 solution of stiff problems by DESI methods. We present
                 here a small subset of the numerical results obtained
                 with our code. Many of these results are quite
                 satisfactory and suggest that DESI methods have a
                 useful role in the solution of this type of problem.",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  subject =      "{\bf G.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS. {\bf G.1.7}: Mathematics of Computing,
                 ORDINARY DIFFERENTIAL EQUATIONS, Initial value
                 problems, Stiff equations.",
}

@Article{Eastham:1996:USP,
  author =       "Michael S. P. Eastham and Charles T. Fulton and Steven
                 Pruess",
  title =        "Using the {SLEDGE} Package on {Sturm--Liouville}
                 Problems Having Nonempty Essential Spectrum",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "423--446",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235819",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 24 15:44:41 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p423-eastham/",
  abstract =     "We describe the performance of the Sturn-Liouville
                 software package SLEDGE on a variety of problems having
                 continuous spectra. The code's output is shown to be in
                 good accord with a wide range of known theoretical
                 results.",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance",
  subject =      "{\bf G.1.7}: Mathematics of Computing, ORDINARY
                 DIFFERENTIAL EQUATIONS, Boundary value problems. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm analysis.",
}

@Article{Weerawarana:1996:PKB,
  author =       "Sanjiva Weerawarana and Elias N. Houstis and John R.
                 Rice and Anupam Joshi and Catherine E. Houstis",
  title =        "{PYTHIA}: a Knowledge Based System for Intelligent
                 Scientific Computing",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "447--468",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235820",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p447-weerawarana/",
  abstract =     "Problem-solving Environments (PSEs) interact with the
                 user in a language ``natural'' to the associated
                 discipline, and they provide a high-level abstraction
                 of the underlying, computationally complex model. The
                 knowledge-based system PYTHIA addresses the problem of
                 {\tt (parameter, algorithm)} pair selection within a
                 scientific computing domain assuming some minimum
                 user-specified computational objectives and some
                 characteristics of the given problem. PYTHIA's
                 framework and methodology are general and applicable to
                 any class of scientific problems and solvers. PYTHIA is
                 applied in the context of Parallel ELLPACK where there
                 are many alternatives for the numerical solution of
                 elliptic partial differential equations (PDEs). PYTHIA
                 matches the characteristics of the given problem with
                 those of PDEs in an existing problem population and
                 then uses performance profiles of the various solvers
                 to select the appropriate method given user-specified
                 error and solution time bounds. The profiles are
                 automatically generated for each solver of the Parallel
                 ELLPACK library.",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance",
  subject =      "{\bf G.1.8}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations. {\bf I.2.1}:
                 Computing Methodologies, ARTIFICIAL INTELLIGIENCE,
                 Applications and expert systems.",
}

@Article{Barber:1996:QAC,
  author =       "C. Bradford Barber and David P. Dobkin and Hannu
                 Huhdanpaa",
  title =        "The {Quickhull} Algorithm for Convex Hulls",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "469--483",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235821",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Nov 8 14:50:36 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/",
  abstract =     "The convex hull of a set of points is the smallest
                 convex set that contains the points. This article
                 presents a practical convex hull algorithm that
                 combines the two-dimensional Quickhull Algorithm with
                 the general-dimensional Beneath-Beyond Algorithm. It is
                 similar to the randomized, incremental algorithms for
                 convex hull and Delaunay triangulation. We provide
                 empirical evidence that the algorithm runs faster when
                 the input contains nonextreme points and that it uses
                 less memory. Computational geometry algorithms have
                 traditionally assumed that input sets are well behaved.
                 When an algorithm is implemented with floating-point
                 arithmetic, this assumption can lead to serious errors.
                 We briefly describe a solution to this problem when
                 computing the convex hull in two, three, or four
                 dimensions. The output is a set of ``thick'' facets
                 that contain all possible exact convex hulls of the
                 input. A variation is effective in five or more
                 dimensions.",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, reliability",
  subject =      "{\bf I.3.5}: Computing Methodologies, COMPUTER
                 GRAPHICS, Computational Geometry and Object Modeling,
                 Geometric algorithms, languages and systems.",
}

@Article{Sarkar:1996:CAM,
  author =       "T. K. Sarkar",
  title =        "A Composition-Alias Method for Generating Gamma
                 Variates with Shape Parameter Greater than 1",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "484--492",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235822",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p484-sarkar/",
  abstract =     "In this article the author describes a procedure for
                 generating gamma variates with shape parameter $> 1$.
                 Given a supply of ``good'' uniform $(0,1)$ variates,
                 the procedure makes use of composition method, squeeze
                 method, and aliasing to generate gamma variates.
                 Comparison with existing methods shows that the
                 author's method is faster in terms of computer time and
                 uses a smaller number of uniform $(0,1)$ variates. The
                 method is also statistically exact.",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, theory",
  subject =      "{\bf G.3}: Mathematics of Computing, PROBABILITY AND
                 STATISTICS. {\bf I.6.1}: Computing Methodologies,
                 SIMULATION AND MODELING, Simulation Theory.",
}

@Article{Koenker:1996:RBC,
  author =       "Roger W. Koenker and Pin T. Ng",
  title =        "A Remark on {Bartels} and {Conn}'s Linearly
                 Constrained, Discrete $l_1$ Problems",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "493--495",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235823",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 9 10:22:02 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Bartels:1980:APL}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p493-koenker/",
  abstract =     "Two modifications of Bartels and Conn's algorithm for
                 solving linearly constrained discrete $l_1$ problems
                 are described. The modifications are designed to
                 improve performance of the algorithm under conditions
                 of degeneracy.",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance, reliability, theory",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Constrained optimization,
                 Gradient methods, Linear programming. {\bf G.3}:
                 Mathematics of Computing, PROBABILITY AND STATISTICS,
                 Statistical computing.",
}

@Article{Reid:1996:RFF,
  author =       "J. K. Reid",
  title =        "Remark on ``{Fast Floating-Point Processing in Common
                 Lisp}''",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "496--497",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235824",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 9 10:21:08 1999",
  bibsource =    "Compendex database;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Fateman:1995:FFP}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p496-reid/",
  abstract =     "We explain why we feel that the comparison between
                 Common Lisp and Fortran in a recent article by Fateman
                 et al. in this journal is not entirely fair.",
  acknowledgement = ack-nhfb # " and " # ack-rfb,
  affiliation =  "Rutherford Appleton Lab",
  classification = "721.1; 723.1.1; 902.2; 921.6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  journalabr =   "ACM Trans Math Software",
  keywords =     "Common Lisp language; Control structures; Digital
                 arithmetic; Floating point computation; fortran
                 (programming language); Lisp (programming language);
                 Standards",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, General,
                 Standards. {\bf D.3.3}: Software, PROGRAMMING
                 LANGUAGES, Language Constructs and Features, Modules,
                 packages.",
}

@Article{Snyder:1996:RAF,
  author =       "W. Van Snyder",
  title =        "Remark on {Algorithm 723}: {Fresnel} Integrals",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "498--500",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235825",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Snyder:1993:AFI}.",
  abstract =     "{\it Algorithm 723: Fresnel Integrals} has been
                 improved to provide more precise results for $x \gg
                 0$.",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Rational
                 approximation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing.",
}

@Article{Cools:1997:ACC,
  author =       "Ronald Cools and Dirk Laurie and Luc Pluym",
  title =        "{Algorithm 764}: {Cubpack++} --- {A C++} Package for
                 Automatic Two-Dimensional Cubature",
  journal =      j-TOMS,
  volume =       "23",
  number =       "1",
  pages =        "1--15",
  month =        mar,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/244768.244770",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-1/p1-cools/",
  abstract =     "In this article, software for the numerical
                 approximation of double integrals over a variety of
                 regions is described. The software was written in C++.
                 Classes for a large number of shapes are provided. A
                 global adaptive integration algorithm is used based on
                 transformations and subdivisions of regions.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, C++. {\bf G.1.4}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation, adaptive quadrature, multiple
                 quadrature. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, efficiency, reliability and
                 robustness.",
}

@Article{Favati:1997:LEE,
  author =       "Paola Favati and Guiseppe Fiorentino and Grazia Lotti
                 and Francesco Romani",
  title =        "Local Error Estimates and Regularity Tests for the
                 Implementation of Double Adaptive Quadrature",
  journal =      j-TOMS,
  volume =       "23",
  number =       "1",
  pages =        "16--31",
  month =        mar,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/244768.244772",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-1/p16-favati/",
  abstract =     "This article presents a device which is suitable for a
                 practical and efficient implementation of Double
                 Adaptive Quadrature. The device includes local error
                 estimates and attempts to detect the presence of
                 numerical difficulties in the integrand function. If a
                 family of rules with suitable properties is chosen,
                 then this can be achieved without affecting the overall
                 computational cost. Extensive numerical testing has
                 been performed on a comprehensive set of functions
                 showing the effectiveness of the device and its
                 efficiency.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.4}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation,
                 adaptive quadrature. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, efficiency,
                 reliability and robustness.",
}

@Article{Machiels:1997:FEO,
  author =       "L. Machiels and M. O. Deville",
  title =        "{Fortran 90}: An Entry to Object-Oriented Programming
                 for Solution of Partial Differential Equations",
  journal =      j-TOMS,
  volume =       "23",
  number =       "1",
  pages =        "32--49",
  month =        mar,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/244768.244774",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-1/p32-machiels/",
  abstract =     "The aim of this work is to set up a programming model
                 suitable for numerical computing while taking benefit
                 of Fortran 90's features. The use of concepts from
                 object-oriented programming avoids the weaknesses of
                 the traditional global data programming model of
                 Fortran 77. This work supports the view that
                 object-oriented concepts are not in contradiction with
                 good Fortran 77 programming practices but complement
                 them. These concepts can be embodied in a module-based
                 programming style and result in an efficient and
                 easy-to-maintain code (maintainability means code
                 clarity, scope for further enhancements and ease of
                 debugging). After introducing the terminology
                 associated with object-oriented programming, it is
                 shown how these concepts are implemented in the
                 framework of Fortran 90. Then, we present an
                 object-oriented implementation of a spectral element
                 solver for a Poisson equation.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "design",
  subject =      "{\bf D.1.5}: Software, PROGRAMMING TECHNIQUES,
                 Object-Oriented Programming. {\bf D.3.2}: Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 FORTRAN 90. {\bf G.1.8}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Partial Differential Equations.",
}

@Article{Bruaset:1997:OOD,
  author =       "Are Magnus Bruaset and Hans Petter Langtangen",
  title =        "Object-Oriented Design of Preconditioned Iterative
                 Methods in {Diffpack}",
  journal =      j-TOMS,
  volume =       "23",
  number =       "1",
  pages =        "50--80",
  month =        mar,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/244768.244776",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-1/p50-bruaset/",
  abstract =     "As modern programming methodologies migrate from
                 computer science to scientific computing, developers of
                 numerical software are faced with new possibilities and
                 challenges. Based on experiences from an ongoing
                 project that develops C++ software for the solution of
                 partial differential equations, this article has its
                 focus on object-oriented design of iterative solvers
                 for linear systems of equations. Special attention is
                 paid to possible conflicts that have to be resolved in
                 order to achieve a flexible, yet efficient, code.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "design, performance",
  subject =      "{\bf D.2.8}: Software, SOFTWARE ENGINEERING, Tools and
                 Techniques, software libraries. {\bf D.3.2}: Software,
                 PROGRAMMING LANGUAGES, Language Classifications, C++.
                 {\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, linear systems,
                 sparse and very large systems.",
}

@Article{Bouaricha:1997:ASS,
  author =       "Ali Bouaricha",
  title =        "{Algorithm 765}: {STENMIN} --- a Software Package
                 for Large, Sparse Unconstrained Optimization Using
                 Tensor Methods",
  journal =      j-TOMS,
  volume =       "23",
  number =       "1",
  pages =        "81--90",
  month =        mar,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/244768.244788",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-1/p81-bouaricha/",
  abstract =     "We describe a new package for minimizing an
                 unconstrained nonlinear function where the Hessian is
                 large and sparse. The software allows the user to
                 select between a tensor method and a standard method
                 based upon a quadratic model. The tensor method models
                 the objective function by a fourth-order model, where
                 the third- and fourth-order terms are chosen such that
                 the extra cost of forming and solving the model is
                 small. The new contribution of this package consists of
                 the incorporation of an entirely new way of minimizing
                 the tensor model that makes it suitable for solving
                 large, sparse optimization problems efficiently. The
                 test results indicate that, in general, the tensor
                 method is often more efficient and more reliable than
                 the standard Newton method for solving large, sparse
                 unconstrained optimization problems.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Fortran. {\bf G.1.3}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, sparse and very large systems. {\bf G.1.6}:
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, unconstrained optimization. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Cabay:1997:AEW,
  author =       "S. Cabay and A. R. Jones and G. Labahn",
  title =        "{Algorithm 766}: Experiments with a Weakly Stable
                 Algorithm for Computing {Pad{\'e}} and Simultaneous
                 {Pad{\'e}} Approximants",
  journal =      j-TOMS,
  volume =       "23",
  number =       "1",
  pages =        "91--110",
  month =        mar,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/244768.244790",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-1/p91-cabay/",
  abstract =     "In a recent paper, Cabay, Jones and Labahn develop a
                 fast, iterative, lookahead algorithm for numerically
                 computing Pad{\'e}--Hermite systems and simultaneous
                 Pad{\'e} systems along a diagonal of the associated
                 Pad{\'e} tables. Included in their work is a detailed
                 error analysis showing that the algorithm is weakly
                 stable. In this article, we describe a Fortran
                 implementation, VECTOR\_PADE, of this algorithm
                 together with a number of numerical experiments. These
                 experiments show that the theoretical error bounds
                 obtained by Cabay, Jones, and Labahn reflect the
                 general behavior of the actual error, but that in
                 practice these bounds are large overestimates.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, experimentation",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Fortran. {\bf G.1}: Mathematics of
                 Computing, NUMERICAL ANALYSIS. {\bf G.1.2}: Mathematics
                 of Computing, NUMERICAL ANALYSIS, Approximation,
                 rational approximation. {\bf G.1.3}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, error analysis, linear systems, matrix
                 inversion.",
}

@Article{Geurts:1997:AFP,
  author =       "A. J. Geurts and C. Praagman",
  title =        "{Algorithm 767}: a {Fortran 77} Package for Column
                 Reduction of Polynomial Matrices",
  journal =      j-TOMS,
  volume =       "23",
  number =       "1",
  pages =        "111--129",
  month =        mar,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/244768.244791",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-1/p111-geurts/",
  abstract =     "A polynomial matrix is called column reduced if its
                 column degrees are as low as possible in some sense.
                 Two polynomial matrices $P$ and $R$ are called
                 unimodularly equivalent if there exists a unimodular
                 polynomial matrix $U$ such that $PU = R$. Every
                 polynomial matrix is unimodularly equivalent to a
                 column-reduced polynomial matrix. In this article a
                 subroutine is described that takes a polynomial matrix
                 $P$ as input and yields on output a unimodular matrix
                 $U$ and a column-reduced matrix $R$ such that $PU = R$;
                 actually, $PU - R$ is near zero. The subroutine is
                 based on an algorithm, described in a paper by Neven
                 and Praagman. The subroutine has been tested with a
                 number of examples on different computers, with
                 comparable results. The performance of the subroutine
                 on every example tried is satisfactory in the sense
                 that the magnitude of the elements of the residual
                 matrix $PU-R$ is about $\parallel P \parallel \parallel
                 U \parallel EPS$, where $EPS$ is the machine precision.
                 To obtain these results a tolerance, used to determine
                 the rank of some (sub)matrices, has to be set properly.
                 The influence of this tolerance on the performance of
                 the algorithm is discussed, from which a guideline for
                 the usage of the subroutine is derived.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, reliability",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Fortran. {\bf F.2.1}: Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems. {\bf
                 G.1.3}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Numerical Linear Algebra, linear systems. {\bf G.4}:
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 algorithm analysis.",
}

@Article{Blackford:1997:PEN,
  author =       "L. S. Blackford and A. Cleary and A. Petitet and R. C.
                 Whaley and J. Demmel and I. Dhillon and H. Ren and K.
                 Stanley and J. Dongarra and S. Hammarling",
  title =        "Practical Experience in the Numerical Dangers of
                 Heterogeneous Computing",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "133--147",
  month =        jun,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/264029.264030",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Nov 8 14:50:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p133-blackford/",
  abstract =     "Special challenges exist in writing reliable numerical
                 library software for heterogeneous computing
                 environments. Although a lot of software for
                 distributed-memory parallel computers has been written,
                 porting this software to a network of workstations
                 requires careful consideration. The symptoms of
                 heterogeneous computing failures can range from
                 erroneous results without warning to deadlock. Some of
                 the problems are straightforward to solve, but for
                 others the solutions are not so obvious, or incur an
                 unacceptable overhead. Making software robust on
                 heterogeneous systems often requires additional
                 communication. We describe and illustrate the problems
                 encountered during the development of ScaLAPACK and the
                 NAG Numerical PVM Library. Where possible, we suggest
                 ways to avoid potential pitfalls, or if that is not
                 possible, we recommend that the software not be used on
                 heterogeneous networks.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "distributed-memory systems, floating-point arithmetic,
                 heterogeneous processor networks, message passing,
                 numerical software, reliability",
  subject =      "{\bf D.1.3} Software, PROGRAMMING TECHNIQUES,
                 Concurrent Programming, Distributed programming. {\bf
                 G.1.0} Mathematics of Computing, NUMERICAL ANALYSIS,
                 General, Computer arithmetic. {\bf G.1.0} Mathematics
                 of Computing, NUMERICAL ANALYSIS, General, Parallel
                 algorithms.",
}

@Article{Ho:1997:DND,
  author =       "James K. Ho and R. P. Sundarraj",
  title =        "Distributed Nested Decomposition of Staircase Linear
                 Programs",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "148--173",
  month =        jun,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/264029.264031",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p148-ho/",
  abstract =     "This article considers the application of a primal
                 nested-decomposition method to solve staircase linear
                 programs (SLPs) on distributed-memory,
                 multiple-instruction-multiple-data computers. Due to
                 the coupling that exist among the stages of an SLP, a
                 standard parallel-decomposition algorithm for these
                 problems would allow only a subset of the subproblem
                 processes to overlap with one another at any give time.
                 We propose algorithms that seek to increase the amount
                 of overlap among the processes as well as utilize idle
                 time beneficially. Computational results testing the
                 effectiveness of our algorithms are reported, using a
                 standard set of test problems.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "computational linear programming, distributed
                 computation",
  subject =      "{\bf C.1.2} Computer Systems Organization, PROCESSOR
                 ARCHITECTURES, Multiple Data Stream Architectures
                 (Multiprocessors), Multiple-instruction-stream,
                 multiple-data-stream processors (MIMD). {\bf G.1.0}
                 Mathematics of Computing, NUMERICAL ANALYSIS, General,
                 Parallel algorithms. {\bf G.1.6} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization, Linear
                 programming.",
}

@Article{Bouaricha:1997:TSP,
  author =       "Ali Bouaricha and Robert B. Schnabel",
  title =        "{Algorithm 768}: {TENSOLVE}: a Software Package for
                 Solving Systems of Nonlinear Equations and Nonlinear
                 Least-squares Problems Using Tensor Methods",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "174--195",
  month =        jun,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/264029.264032",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p174-bouaricha/",
  abstract =     "This article describes a modular software package for
                 solving systems of nonlinear equations and nonlinear
                 problems, using a new class of methods called tensor
                 methods. It is intended for small- to medium-sized
                 problems, say with up to 100 equations and unknowns, in
                 cases where it is reasonable to calculate the Jacobian
                 matrix or to approximate it by finite differences at
                 each iteration. The software allows the user to choose
                 between a tensor method and a standard method based on
                 a linear model. The tensor method approximates F(x) by
                 a quadratic model, where the second-order term is
                 chosen so that the model is hardly more expensive to
                 form, store, or solve than the standard linear model.
                 Moreover, the software provides two different global
                 strategies: a line search approach and a
                 two-dimensional trust region approach. Test results
                 indicate that, in general, tensor methods are
                 significantly more efficient and robust than standard
                 methods on small- and medium-sized problems in
                 iterations and function evaluations.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "nonlinear equations, nonlinear least squares,
                 rank-deficient matrices, tensor methods",
  subject =      "{\bf G.1.5} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Systems of
                 equations. {\bf G.1.6} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Optimization, Least squares
                 methods. {\bf G.4} Mathematics of Computing,
                 MATHEMATICAL SOFTWARE.",
}

@Article{Pardalos:1997:AFS,
  author =       "Panos M. Pardalos and Leonidas S. Pitsolulis and
                 Mauricio G. C. Resende",
  title =        "{Algorithm 769}: {Fortran} Subroutines for Approximate
                 Solution of Sparse Quadratic Assignment Problems Using
                 {GRASP}",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "196--208",
  month =        jun,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/264029.264038",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p196-pardalos/",
  abstract =     "We describe Fortran subroutines for finding
                 approximate solutions of sparse instances of the
                 Quadratic Assignment Problem (QAP) using a Greedy
                 Randomized Adaptive Search Procedure (GRASP). The
                 design and implementation of the code are described in
                 detail. Computational results comparing the new
                 subroutines with a dense version of the code (Algorithm
                 754, ACM TOMS) show that the speedup increases with the
                 sparsity of the data.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "combinatorial optimization, Fortran subroutines,
                 GRASP, local search, quadratic assignment problem",
  subject =      "{\bf G.1.6} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Integer programming. {\bf
                 G.2.1} Mathematics of Computing, DISCRETE MATHEMATICS,
                 Combinatorics, Combinatorial algorithms. {\bf G.m}
                 Mathematics of Computing, MISCELLANEOUS.",
}

@Article{Siarry:1997:ESA,
  author =       "Patrick Siarry and G{\'e}rard Berthiau and
                 Fran\c{c}ois Durdin and Jacques Haussy",
  title =        "Enhanced Simulated Annealing for Globally Minimizing
                 Functions of Many-continuous Variables",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "209--228",
  month =        jun,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/264029.264043",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p209-siarry/",
  abstract =     "A new global optimization algorithm for functions of
                 many continuous variables is presented, derived from
                 the basic Simulated annealing method. Our main
                 contribution lies in dealing with high-dimensionality
                 minimization problems, which are often difficult to
                 solve by all known minimization methods with or without
                 gradient. In this article we take a special interest in
                 the variables discretization issue. We also develop and
                 implement several complementary stopping criteria. The
                 original Metropolis iterative random search, which
                 takes place in a Euclidean space $R_n$, is replaced by
                 another similar exploration, performed within a
                 succession of Euclidean spaces $R_p$, with $p << n$. This
                 Enhanced Simulated Annealing (ESA) algorithm was
                 validated first on classical highly multimodal
                 functions of 2 to 100 variables. We obtained
                 significant reductions in the number of function
                 evaluations compared to six other global optimization
                 algorithms, selected according to previously published
                 computational results for the same set of test
                 functions. In most cases, ESA was able to closely
                 approximate known global optima. The reduced ESA
                 computational cost helped us to refine further the
                 obtained global results, through the use of some local
                 search. We have used this new minimizing procedure to
                 solve complex circuit design problems, for which the
                 objective function evaluation can be exceedingly
                 costly.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "global optimization, stochastic optimization, test
                 functions",
  subject =      "{\bf G.1.6} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Nonlinear programming. {\bf
                 G.3} Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Probabilistic algorithms (including Monte
                 Carlo). {\bf G.4} Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing.",
}

@Article{Costantini:1997:BVS,
  author =       "P. Costantini",
  title =        "Boundary-Valued Shape-Preserving Interpolating
                 Splines",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "229--251",
  month =        jun,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/264029.264050",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p229-costantini/",
  abstract =     "This article describes a general-purpose method for
                 computing interpolating polynomial splines with
                 arbitrary constraints on their shape and satisfying
                 separable or nonseparable boundary conditions. Examples
                 of applications of the related Fortran code are
                 periodic shape-preserving spline interpolation and the
                 construction of visually pleasing closed curves.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Bernstein-B\'{e}zier polynomials, dynamic programming,
                 spline interpolation",
  subject =      "{\bf G.1.1} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation.",
}

@Article{Costantini:1997:APC,
  author =       "P. Costantini",
  title =        "{Algorithm 770}: {BVSPIS} --- a Package for Computing
                 Boundary-Valued Shape-Preserving Interpolating
                 Splines",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "252--254",
  month =        jun,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/264029.264059",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p252-costantini/",
  abstract =     "This article describes a software package for
                 computing interpolating polynomial splines with
                 arbitrary constraints on their shape and satisfying
                 separable or nonseparable boundary conditions.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Bernstein-B\'{e}zier polynomials, dynamic programming,
                 spline interpolation",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.1} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Interpolation. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Wu:1997:MCR,
  author =       "Pei-Chi Wu",
  title =        "Multiplicative, congruential random-number generators
                 with multiplier $\pm 2^{k_1} \pm 2^{k_2}$ and modulus
                 $2^p - 1$",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "255--265",
  month =        jun,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/264029.264056",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p255-wu/",
  abstract =     "The demand for random numbers in scientific
                 applications in increasing. However, the most widely
                 used multiplicative, congruential random-number
                 generators with modulus $2^31 - 1$ have a cycle length
                 of about $2.1 \times 10^9$. Moreover, developing
                 portable and efficient generators with a larger modulus
                 such as $2^61 - 1$ is more difficult than those with
                 modulus $2^31 - 1$. This article presents the
                 development of multiplicative, congruential generators
                 with modulus $m = 2p - 1$ and four forms of
                 multipliers: $2^{k_1} - 2^{k_2}, 2^{k_1} + 2^{k_2}, m -
                 2^{k_1} + 2^{k_2}$, and $m - 2^{k_1} - 2^{k_2}, {k_1} >
                 {k_2}$. The multipliers for modulus $2^{31} - 1$ and
                 $2^{61} - 1$ are measured by spectral tests, and the
                 best ones are presented. The generators with these
                 multipliers are portable and vary fast. They have also
                 passed several empirical tests, including the frequency
                 test, the urn test, and the maximum-of-$t$ test.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "cycle length, efficiency, multiplicative congruential
                 random-number generators, portability, spectral test",
  subject =      "{\bf G.3} Mathematics of Computing, PROBABILITY AND
                 STATISTICS, Random number generation.",
}

@Article{Kocis:1997:CIL,
  author =       "Ladislav Kocis and William J. Whiten",
  title =        "Computational Investigations of Low-discrepancy
                 Sequences",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "266--294",
  month =        jun,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/264029.264064",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-2/p266-kocis/",
  abstract =     "The Halton, Sobol, and Faure sequences and the
                 Braaten-Weller construction of the generalized Halton
                 sequence are studied in order to assess their
                 applicability for the quasi Monte Carlo integration
                 with large number of variates. A modification of the
                 Halton sequence (the Halton sequence leaped) and a new
                 construction of the generalized Halton sequence are
                 suggested for unrestricted number of dimensions and are
                 show to improve considerably on the original Halton
                 sequence. Problems associated with estimation of the
                 error in quasi Monte Carlo integration and with the
                 selection of test functions are identified. Then an
                 estimate of the maximum error of the quasi Monte Carlo
                 integration of nine test functions is computed for up
                 to 400 dimensions and is used to evaluate the known
                 generators mentioned above and the two new generators.
                 An empirical formula for the error of the quasi Monte
                 Carlo integration is suggested.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "discrepancy, error of numerical integration, Faure
                 sequence, generalized Halton sequence, Halton sequence,
                 low-discrepancy sequences, Monte Carlo and quasi Monte
                 Carlo integration, Sobol sequence",
  subject =      "{\bf G.1.4} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation.
                 {\bf I.6} Computing Methodologies, SIMULATION AND
                 MODELING.",
}

@Article{Goano:1997:RA7,
  author =       "Michele Goano",
  title =        "Remark on {Algorithm 745}",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "295--295",
  month =        jun,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/264029.643581",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 9 10:19:38 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Goano:1995:ACC}.",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hull:1997:ICA,
  author =       "T. E. Hull and Thomas F. Fairgrieve and Ping Tak Peter
                 Tang",
  title =        "Implementing the Complex Arcsine and Arccosine
                 Functions Using Exception Handling",
  journal =      j-TOMS,
  volume =       "23",
  number =       "3",
  pages =        "299--335",
  month =        sep,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/275323.275324",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed May 6 11:23:41 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p299-hull/",
  abstract =     "We develop efficient algorithms for reliable and
                 accurate evaluations of the complex arcsine and
                 arccosine functions. A tight error bound is derived for
                 each algorithm; the results are valid for all
                 machine-representable points in the complex plane. The
                 algorithms are presented in a pseudocode that has a
                 convenient exception-handling facility. Corresponding
                 Fortran 77 programs for an IEEE environment have also
                 been developed to illustrate the practicality of the
                 algorithms, and these programs have been tested very
                 carefully to help confirm the correctness of the
                 algorithms and their error bounds. The results of these
                 tests are included in the article, but the Fortran 77
                 programs are not (these programs are available from
                 Fairgrieve). Tests of other widely available programs
                 fail at many points in the complex plane, and otherwise
                 are slower and produce much less accurate results.",
  accepted =     "February 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, design, complex elementary functions,
                 implementation",
  subject =      "{\bf G.1.0}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, error analysis, Numerical
                 algorithms. {\bf G.1.2}: Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation, elementary function
                 approximation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, algorithm analysis, reliability
                 and robustness, verification.",
}

@Article{Carr:1997:CBD,
  author =       "Steve Carr and R. B. Lehoucq",
  title =        "Compiler Blockability of Dense Matrix Factorizations",
  journal =      j-TOMS,
  volume =       "23",
  number =       "3",
  pages =        "336--361",
  month =        sep,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/275323.275325",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed May 6 11:23:41 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p336-carr/",
  abstract =     "The goal of the LAPACK project is to provide efficient
                 and portable software for dense numerical linear
                 algebra computations. By recasting many of the
                 fundamental dense matrix computations in terms of calls
                 to an efficient implementation of the BLAS (Basic
                 Linear Algebra Subprograms), the LAPACK project has, in
                 large part, achieved its goal. Unfortunately, the
                 efficient implementation of the BLAS results often in
                 machine-specific code that is not portable across
                 multiple architectures without a significant loss in
                 performance or significant effort to reoptimize them.
                 This article examines whether most of the hand
                 optimizations performed on matrix factorization codes
                 are unnecessary because they can (and should) be
                 performed by the compiler. We believe that it is better
                 for the programmer to express algorithms in a
                 machine-independent form and allow the compiler to
                 handle the machine-dependent details. This gives the
                 algorithms portability across architectures and removes
                 the error-prone, expensive, and tedious process of hand
                 optimization. Although there currently exist no
                 production compilers that can perform all the loop
                 transformations discussed in this article, a
                 description of current research in compiler technology
                 is provided that will prove beneficial to the numerical
                 linear algebra community. We show that the Cholesky and
                 optimized automatically by a compiler to be as
                 efficient as the same hand-optimized version found in
                 LAPACK. We also show that the QR factorization may be
                 optimized by the compiler to perform comparably with
                 the hand-optimized LAPACK version on modest matrix
                 sizes. Our approach allows us to conclude that with the
                 advent of the compiler optimizations discussed in this
                 article, matrix factorizations may be efficiently
                 implemented in a BLAS-less form.",
  accepted =     "February 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "languages, performance, BLAS, cache optimization,
                 Cholesky decomposition, LAPACK, LU decomposition, QR
                 decomposition",
  subject =      "{\bf D.3.4}: Software, PROGRAMMING LANGUAGES,
                 Processors, Compilers, optimization. {\bf F.2.1}:
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices. {\bf G.1.3}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, efficiency,
                 portability.",
}

@Article{Carrig:1997:EHQ,
  author =       "James J. {Carrig Jr.} and Gerald G. L. Meyer",
  title =        "Efficient {Householder} {QR} Factorization for
                 Superscalar Processors",
  journal =      j-TOMS,
  volume =       "23",
  number =       "3",
  pages =        "362--378",
  month =        sep,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/275323.275326",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed May 6 11:23:41 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p362-carrig/",
  abstract =     "To extract the potential promised by superscalar
                 processors, algorithm designers must streamline memory
                 references and allow for efficient data reuse
                 throughout the memory hierarchy. Two parameterized
                 Householder QR factorization algorithms are presented
                 that take into account the caches and registers typical
                 of such processors. Guidelines are developed for
                 choosing parameter values that obtain near-optimal
                 cache and register utilization. The new algorithms are
                 implemented and performance-tuned on an Intel Pentium
                 Pro system, a single this POWER2 node of the IBM
                 Scalable Parallel System 2 (SP2), and a single R8000
                 processor of a Silicon Graphics POWER Challenge XL.",
  accepted =     "February 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance, cache model, Householder QR
                 factorization, register model",
  subject =      "{\bf B.3.2}: Hardware, MEMORY STRUCTURES, Design
                 Styles, Cache memories. {\bf F.2.1}: Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices. {\bf G.1.3}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, linear systems (direct and iterative methods).
                 {\bf G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, algorithm analysis, efficiency,
                 portability.",
}

@Article{Duff:1997:LBL,
  author =       "Iain S. Duff and Michele Marrone and Giuseppe Radicati
                 and Carlo Vittoli",
  title =        "{Level 3 Basic Linear Algebra Subprograms} for Sparse
                 Matrices: a User Level Interface",
  journal =      j-TOMS,
  volume =       "23",
  number =       "3",
  pages =        "379--401",
  month =        sep,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/275323.275327",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65Y15",
  MRnumber =     "MR1672168",
  bibdate =      "Mon Jan 2 09:11:24 2006",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p379-duff/",
  abstract =     "This article proposes a set of Level 3 Basic Linear
                 Algebra Subprograms and associated kernels for sparse
                 matrices. A major goal is to design and develop a
                 common framework to enable efficient, and portable,
                 implementations of iterative algorithms for sparse
                 matrices on high-performance computers. We have
                 designed the routines to shield the developer of
                 mathematical software from most of the complexities of
                 the various data structures used for sparse matrices.
                 We have kept the interface and suite of codes as simple
                 as possible while at the same time including sufficient
                 functionality to cover most sparse matrix data
                 structures. An important aspect of our framework is
                 that it can be easily extended to incorporate new
                 kernels if the need arises. We discuss the design,
                 implementation, and use of subprograms for the
                 multiplication of a full matrix by a sparse one and for
                 the solution of sparse triangular systems with one or
                 more (full) right-hand sides. We include a routine for
                 checking the input data, generating a new sparse data
                 structure from that input, and scaling a sparse matrix.
                 The new data structure for the transformation can be
                 specified by the user or can be chosen automatically by
                 vendors to be efficient on their machines. We also
                 include a routine for permuting the columns of a sparse
                 matrix and one for permuting the rows of a full
                 matrix.",
  accepted =     "March 1997",
  acknowledgement = ack-rfb # " and " # ack-kr # " and " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance, reliability, high-performance
                 computing, iterative solution, programming standards,
                 sparse BLAS, sparse data structures, sparse matrices",
  subject =      "{\bf D.2.2}: Software, SOFTWARE ENGINEERING, Tools and
                 Techniques, user interfaces. {\bf D.2.2}: Software,
                 SOFTWARE ENGINEERING, Coding, standards. {\bf F.2.1}:
                 Theory of Computation, ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, certification and
                 testing, efficiency, portability, reliability and
                 robustness, verification.",
}

@Article{Brankin:1997:ARF,
  author =       "R. W. Brankin and I. Gladwell",
  title =        "{Algorithm 771}. {\tt rksuite\_90}: {Fortran} Software
                 for Ordinary Differential Equation Initial Value
                 Problems",
  journal =      j-TOMS,
  volume =       "23",
  number =       "3",
  pages =        "402--415",
  month =        sep,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/275323.275328",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed May 6 11:23:41 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p402-brankin/",
  abstract =     "We present Fortran 90 software for the initial-value
                 problem in ordinary differential equations, including
                 the interfaces and how Fortran 90 language features
                 afford the opportunity to address different types and
                 structures of variables and to provide additional
                 functionality. A novel feature of this software is the
                 availability of Unix scripts which enable presentation
                 of the software for multiple problem types.",
  accepted =     "January 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, complex, recursion",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Fortran 90. {\bf G.1.7}: Mathematics
                 of Computing, ORDINARY DIFFERENTIAL EQUATIONS, Initial
                 value problems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE.",
}

@Article{Renka:1997:ASD,
  author =       "Robert J. Renka",
  title =        "{Algorithm 772}. {STRIPACK}: {Delaunay} Triangulation
                 and {Voronoi} Diagram on the Surface of a Sphere",
  journal =      j-TOMS,
  volume =       "23",
  number =       "3",
  pages =        "416--434",
  month =        sep,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/275323.275329",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed May 6 11:23:41 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p416-renka/",
  abstract =     "STRIPACK is a Fortran 77 software package that employs
                 an incremental algorithm to construct a Delaunay
                 triangulation and, optionally, a Voronoi diagram of a
                 set of points (nodes) on the surface of the unit
                 sphere. The triangulation covers the convex hull of the
                 nodes, which need not be the entire surface, while the
                 Voronoi diagram covers the entire surface. The package
                 provides a wide range of capabilities including an
                 efficient means of updating the triangulation with
                 nodal additions or deletions. For N nodes, the storage
                 requirement for the triangulation is 13N integer
                 storage locations in addition to 3N nodal coordinates.
                 Using an off-line algorithm and work space of size 3N,
                 the triangulation can be constructed with time
                 complexity O(NlogN).",
  accepted =     "March 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, Delaunay triangulation, Dirichlet
                 tessellation, sphere, Thiessen regions, Voronoi
                 diagram",
  subject =      "{\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE.",
}

@Article{Renka:1997:ASI,
  author =       "Robert J. Renka",
  title =        "{Algorithm 773}. {SSRFPACK}: Interpolation of
                 Scattered Data on the Surface of a Sphere with a
                 Surface under Tension",
  journal =      j-TOMS,
  volume =       "23",
  number =       "3",
  pages =        "435--442",
  month =        sep,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/275323.275330",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed May 6 11:23:41 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p435-renka/",
  abstract =     "SSRFPACK is a Fortran 77 software package that
                 constructs a smooth interpolatory or approximating
                 surface to data values associated with arbitrarily
                 distributed points on the surface of a sphere. It
                 employs automatically selected tension factors to
                 preserve shape properties of the data and avoid
                 overshoot and undershoot associated with steep
                 gradients.",
  accepted =     "March 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, scattered data fitting, smoothing, surface
                 under tension, triangle-based interpolation",
  subject =      "{\bf G.1.1}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE.",
}

@Article{Facchinei:1997:GBC,
  author =       "Francisco Facchinei and Joaquim J{\'u}dice and
                 Jo{\~a}o Soares",
  title =        "Generating Box Constrained Optimization Problems",
  journal =      j-TOMS,
  volume =       "23",
  number =       "3",
  pages =        "443--447",
  month =        sep,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/275323.275331",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed May 6 11:23:41 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p443-facchinei/",
  abstract =     "We present a method for generating box-constrained
                 nonlinear programming test problems. The technique
                 allows the user to control some properties of the
                 generated test problems that are known to influence the
                 behavior of algorithms for their solution. A
                 corresponding set of Fortran 77 routines is described
                 in a companion algorithm (774).",
  accepted =     "February 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance, verification, nonlinear
                 programming test problems, optimization, test problems
                 generation",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, certification and
                 testing, verification.",
}

@Article{Facchinei:1997:AFS,
  author =       "Francisco Facchinei and Joaquim J{\'u}dice and
                 Jo{\~a}o Soares",
  title =        "{Algorithm 774}. {FORTRAN} Subroutine for Generating
                 Box Constrained Optimization Problems",
  journal =      j-TOMS,
  volume =       "23",
  number =       "3",
  pages =        "448--450",
  month =        sep,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/275323.275332",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed May 6 11:23:41 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-3/p448-facchinei/",
  abstract =     "We describe a set of Fortran routines for generating
                 box-constrained nonlinear programming test problems.
                 The technique, as described by Facchinei et al. (this
                 issue), allows the user to control relevant properties
                 of the generated problems.",
  accepted =     "February 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance, verification, nonlinear
                 programming test problems, optimization, test problems
                 generation",
  subject =      "{\bf G.1.6}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, certification and
                 testing, verification.",
}

@Article{Greenberg:1997:ACS,
  author =       "Leon Greenberg and Marco Marletta",
  title =        "{Algorithm 775}. The Code {SLEUTH} for Solving
                 Fourth-Order {Sturm--Liouville} Problems",
  journal =      j-TOMS,
  volume =       "23",
  number =       "4",
  pages =        "453--493",
  month =        dec,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/279232.279231",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Sep 17 15:28:33 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p453-greenberg/",
  abstract =     "We describe a new code (SLEUTH) for numerical solution
                 of regular two-point fourth-order Sturm--Liouville
                 eigenvalue problems. Eigenvalues are computed according
                 to index: the user specifies an integer $k \geq 0$, and
                 the code computes an approximation to the $k$th
                 eigenvalue. Eigenfunctions are also available through
                 an auxiliary routine, called after the eigenvalue has
                 been determined. The code will be made available
                 through netlib.",
  accepted =     "March 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, SLEUTH",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Fortran 77. {\bf G.1.7}: Mathematics
                 of Computing, ORDINARY DIFFERENTIAL EQUATIONS, Boundary
                 value problems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE.",
}

@Article{Bai:1997:ASF,
  author =       "Z. Bai and G. W. Stewart",
  title =        "{Algorithm 776}. {SRRIT} --- a {FORTRAN} Subroutine
                 to Calculate the Dominant Invariant Subspace of a
                 Nonsymmetric Matrix",
  journal =      j-TOMS,
  volume =       "23",
  number =       "4",
  pages =        "494--513",
  month =        dec,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/279232.279234;
                 http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p494-bai/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "SRRIT is a Fortran program to calculate an approximate
                 orthonormal basis for a dominant invariant subspace of
                 a real matrix $A$ by the method of simultaneous
                 iteration. Specifically, given an integer $m$, SRRIT
                 computes a matrix $Q$ with $m$ orthonormal columns and
                 real quasi-triangular matrix $T$ of order $m$ such that
                 the equation $AQ = QT$ is satisfied up to a tolerance
                 specified by the user. The eigenvalues of $T$ are
                 approximations to the $m$ eigenvalues of largest
                 absolute magnitude of $A$, and the columns of $Q$ span
                 the invariant subspace corresponding to those
                 eigenvalues. SRRIT references $A$ only through a
                 user-provided subroutine to form the product $AQ$;
                 hence it is suitable for large sparse problems.",
  accepted =     "March 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, invariant subspace, nonsymmetric
                 eigenvalue problem, project method",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Fortran. {\bf F.2.1}: Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices. {\bf G.1.3}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, eigenvalues. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, certification and
                 testing.",
}

@Article{Watson:1997:ASF,
  author =       "Layne T. Watson and Robert C. Melville and Alexander
                 P. Morgan and Homer F. Walker",
  title =        "{Algorithm 777}. {HOMPACK90}: a Suite of {Fortran} 90
                 Codes for Globally Convergent Homotopy Algorithms",
  journal =      j-TOMS,
  volume =       "23",
  number =       "4",
  pages =        "514--549",
  month =        dec,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/279232.279235;
                 http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p514-watson/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "HOMPACK90 is a Fortran 90 version of the Fortran 77
                 package HOMPACK (Algorithm 652), a collection of codes
                 for finding zeros of fixed points of nonlinear systems
                 using globally convergent probability-one homotopy
                 algorithms. Three qualitatively different algorithms
                 --- ordinary differential equation based, normal flow,
                 quasi-Newton augmented Jacobian matrix --- are provided
                 for tracking homotopy zero curves, as well as separate
                 routine for dense and sparse Jacobian matrices. A high
                 level driver for the special case of polynomial systems
                 is also provided. Changes to HOMPACK include numerous
                 minor improvements, simpler and more elegant
                 interfaces, use of modules, new end games, support for
                 several sparse matrix data structures, and new
                 iterative algorithms for large sparse Jacobian
                 matrices.",
  accepted =     "April 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, Chow-Yorke algorithm, curve tracking,
                 fixed point, globally convergent, homotopy methods,
                 polynomial systems, probability-one, zero.",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Fortran. {\bf G.1.5}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Roots of Nonlinear
                 Equations, Systems of equations. {\bf G.4}: Mathematics
                 of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Zhu:1997:ALF,
  author =       "Ciyou Zhu and Richard H. Byrd and Peihuang Lu and
                 Jorge Nocedal",
  title =        "{Algorithm 778}. {L-BFGS-B}: {Fortran} Subroutines for
                 {Large-Scale} Bound Constrained Optimization",
  journal =      j-TOMS,
  volume =       "23",
  number =       "4",
  pages =        "550--560",
  month =        dec,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/279232.279236;
                 http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p550-zhu/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Morales:2011:RAB}.",
  abstract =     "L-BFGS-B is a limited-memory algorithm for solving
                 large nonlinear optimization problems subject to simple
                 bounds on the variables. It is intended for problems in
                 which information on the Hessian matrix is difficult to
                 obtain, or for large dense problems. L-BFGS-B can also
                 be user for unconstrained problems and in this case
                 performs similarly to its predecessor, algorithm L-BFGS
                 (Harwell routine VA15). The algorithm is implemented in
                 Fortran 77.",
  accepted =     "April 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, large-scale optimization, limited-memory
                 method, nonlinear optimization, variable metric
                 method.",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Fortran. G.1.6 [Numerical Analysis]:
                 Optimization -- constrained optimization; gradient
                 methods; nonlinear programming; G.4 [Mathematics of
                 Computing]: Mathematical Software",
}

@Article{Karp:1997:HPD,
  author =       "Alan H. Karp and Peter Markstein",
  title =        "High-Precision Division and Square Root",
  journal =      j-TOMS,
  volume =       "23",
  number =       "4",
  pages =        "561--589",
  month =        dec,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/279232.279237",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Nov 8 14:50:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/articles/journals/toms/forthcoming/a0-karp/a0-karp.ps;
                 http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p561-karp/",
  abstract =     "We present division and square root algorithms for
                 calculation with more bits than are handled by the
                 floating-point hardware. These algorithms avoid the
                 need to multiply two high-precision numbers, speeding
                 up the last iteration by as much as a factor of 10. We
                 also show how to produce the floating-point number
                 closest to the exact result with relatively few
                 additional operations.",
  accepted =     "June 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance, division, quad precision,
                 square root.",
  subject =      "G.1.0 [Numerical Analysis]: General -- computer
                 arithmetic. G.4 [Mathematics of Computing]:
                 Mathematical Software.",
}

@Article{MacLeod:1998:AFD,
  author =       "Allan J. MacLeod",
  title =        "{Algorithm 779}: {Fermi--Dirac} Functions of Order
                 $-1/2, 1/2, 3/2, 5/2$",
  journal =      j-TOMS,
  volume =       "24",
  number =       "1",
  pages =        "1--12",
  month =        mar,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/285861.285862;
                 http://www.acm.org/pubs/citations/journals/toms/1998-24-1/p1-macleod/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The computations of Fermi--Dirac ${\cal F}_k$
                 integrals is discussed for the values $k = -1, 1/2,
                 3/2, 5/2$. We derive Chebyshev polynomial expansions
                 which allow the computation of these functions to
                 double precision IEEE accuracy.",
  accepted =     "May 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, Chebyshev polynomials, collocation,
                 Fermi--Dirac, floating-point arithmetic.",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf F.2.1}: Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems. {\bf
                 G.1.2}: Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation.",
}

@Article{Sharp:1998:GHO,
  author =       "P. W. Sharp and J. H. Verner",
  title =        "Generation of High-order Interpolants for Explicit
                 {Runge--Kutta} Pairs",
  journal =      j-TOMS,
  volume =       "24",
  number =       "1",
  pages =        "13--29",
  month =        mar,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/285861.285863;
                 http://www.acm.org/pubs/citations/journals/toms/1998-24-1/p13-sharp/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Explicit Runge--Kutta pairs can be enhanced by
                 providing them with interpolants. Enhancements include
                 the ability to estimate and control the defect, to
                 produce dense output, and to calculate past values in
                 delay differential equations. The coefficients of an
                 interpolant are easily generated by bootstrapping on
                 the order conditions. However, the generation of
                 high-order interpolants requires a large number of
                 arithmetic operations. We describe an efficient
                 algorithm for the generation of high-order interpolants
                 and illustrate the use of the algorithm with three
                 applications.",
  accepted =     "June 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, explicit, generation, high order,
                 interpolants, pairs, Runge--Kutta.",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations.",
}

@Article{Houstis:1998:PPS,
  author =       "E. N. Houstis and J. R. Rice and S. Weerawarana and A.
                 C. Catlin and P. Papachiou and K.-Y. Wang and M.
                 Gaitatzes",
  title =        "{PELLPACK}: a Problem Solving Environment for {PDE}
                 Based Applications on Multicomputer Platforms",
  journal =      j-TOMS,
  volume =       "24",
  number =       "1",
  pages =        "30--73",
  month =        mar,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/285861.285864;
                 http://www.acm.org/pubs/citations/journals/toms/1998-24-1/p30-houstis/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article presents the software architecture and
                 implementation of the problem-solving environment (PSE)
                 PELLPACK for modeling physical objects described by
                 partial differential equations (PDEs). The scope of
                 this PDE is broad, as PELLPACK incorporates many PDE
                 solving systems, and some of these, in turn, include
                 several specific PDE solving methods. Its coverage for
                 1D, 2D, and 3D elliptic or parabolic problems is quite
                 broad, and it handles some hyperbolic problems. Since a
                 PSE should provide complete support for the
                 problem-solving process, PELLPACK also contains a large
                 amount of code to support graphical user interfaces,
                 analytic tools, user help, domain or mesh partitioning,
                 machine and data selection, visualization, and various
                 other tasks. Its total size is well over 1 million
                 lines of code. Its open-ended software architecture
                 consists of several software layers. The top layer is
                 an interactive graphical interface for specifying the
                 PDE model and its solution framework. This interface
                 saves the results of the user specification in the form
                 of a very high level PDE language which is an alternate
                 interface to the PELLPACK system. This language also
                 allows a user to specify the PDE problem and its
                 solution framework textually in a natural form. The
                 PELLPACK language preprocessor generates a Fortran
                 control program with the interfaces, calls to specified
                 components and libraries of the PDE solution framework,
                 and functions defining the PDE problem. The PELLPACK
                 program execution is supported by a high-level tool
                 where the virtual parallel system is defined, where the
                 execution mode, file system, and hardware resources are
                 selected, and where the compilation, loading, and
                 execution are controlled. Finally, the PELLPACK PSE
                 integrates several PDE libraries and PDE systems
                 available in the public domain. The system employs
                 several parallel reuse methodologies based on the
                 decomposition of discrete geometric data to map sparse
                 PDE computations to parallel machines. An instance of
                 the system is available as a Web server (WebPELLPACK)
                 for public use at http://pellpack.cs.purdue.edu.",
  accepted =     "June 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, design, languages, management,
                 performance, execution models, knowledge bases,
                 libraries, parallel reuse methodologies, PDE language,
                 problem-solving environments, programming-in-the-large,
                 software bus.",
  subject =      "{\bf C.3}: Computer Systems Organization,
                 SPECIAL-PURPOSE AND APPLICATION-BASED SYSTEMS. {\bf
                 D.2.6}: Software, SOFTWARE ENGINEERING, Programming
                 Environments, Graphical environments, interactive
                 environments and integrated environments. {\bf D.2.11}:
                 Software, SOFTWARE ENGINEERING, Software Architectures,
                 Domain-specific architectures. {\bf D.3.2}: Software,
                 PROGRAMMING LANGUAGES, Language Classifications, Very
                 high-level languages. {\bf G.1.8}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Partial Differential
                 Equations, Domain decomposition methods, elliptic
                 equations, hyperbolic equations, iterative solution
                 techniques, multigrid and multilevel methods, and
                 parabolic equations. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Parallel and vector
                 implementations. {\bf I.2.5}: Computing Methodologies,
                 ARTIFICIAL INTELLIGENCE, Programming Languages and
                 Software, Expert system tools and techniques. {\bf
                 J.2}: Computer Applications, PHYSICAL SCIENCES AND
                 ENGINEERING, Engineering, and mathematics and
                 statistics.",
}

@Article{Gupta:1998:DIE,
  author =       "Anshul Gupta and Fred G. Gustavson and Mahesh Joshi
                 and Sivan Toledo",
  title =        "The Design, Implementation and Evaluation of a
                 Symmetric Banded Linear Solver for Distributed-Memory
                 Parallel Computers",
  journal =      j-TOMS,
  volume =       "24",
  number =       "1",
  pages =        "74--101",
  month =        mar,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/285861.285865;
                 http://www.acm.org/pubs/citations/journals/toms/1998-24-1/p74-gupta/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article describes the design, implementation, and
                 evaluation of a parallel algorithm for the Cholesky
                 factorization of symmetric banded matrices. The
                 algorithm is part of IBM's parallel engineering and
                 scientific subroutine library version 1.2 and is
                 compatible with ScaLAPACK's banded solver. Analysis, as
                 well as experiments on an IBM SP2 distributed-memory
                 parallel computer, shows that the algorithm efficiently
                 factors banded matrices with wide bandwidth. For
                 example, a 31-mode SP2 factors a large matrix more than
                 16 times faster than a single node would factor it
                 using the best sequential algorithm, and more than 20
                 times faster than a single node would using LAPACK's
                 DPBTRF. The algorithm uses novel ideas in the area of
                 distributed dense-matrix computations that include the
                 use of a dynamic schedule for a blocked systolic-like
                 algorithm and the separation of the input and output
                 layouts from the layout the algorithm uses internally.
                 The algorithm alson uses known techniques such as
                 blocking to improve its communication-to-computation
                 ratio and its data-cache behavior.",
  accepted =     "June 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithms, performance, banded matrices, Cholesky
                 factorization, distributed memory, parallel
                 algorithms.",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf G.4}: Mathematics
                 of Computing, MATHEMATICAL SOFTWARE, Algorithm design
                 and analysis, and efficiency.",
}

@Article{Hamilton:1998:AEP,
  author =       "K. G. Hamilton",
  title =        "{Algorithm 780}: Exponential Pseudorandom
                 Distribution",
  journal =      j-TOMS,
  volume =       "24",
  number =       "1",
  pages =        "102--106",
  month =        mar,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/285861.285866;
                 http://www.acm.org/pubs/citations/journals/toms/1998-24-1/p102-hamilton/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "An algorithm is presented for the calculation of
                 exponentially distributed random numbers. It is based
                 on mathematics that was published by Ahrend and Dieter,
                 but some errors have been corrected.",
  accepted =     "June 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, exponential distribution, random numbers,
                 pseudorandom numbers.",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Fortran 90. {\bf G.3}: Mathematics of
                 Computing, PROBABILITY AND STATISTICS, Random number
                 generation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing. {\bf
                 I.6.0}: Computing Methodologies, SIMULATION AND
                 MODELING, General.",
}

@Article{Fulton:1998:CSD,
  author =       "Charles T. Fulton and Steven Pruess",
  title =        "The Computation of Spectral Density Functions for
                 Singular {Sturm--Liouville} Problems Involving Simple
                 Continuous Spectra",
  journal =      j-TOMS,
  volume =       "24",
  number =       "1",
  pages =        "107--129",
  month =        mar,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/285861.285867;
                 http://www.acm.org/pubs/citations/journals/toms/1998-24-1/p107-fulton/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The software package SLEDGE has as one of its options
                 the estimation of spectral density functions $p(t)$ for
                 a wide class of singular Sturm--Liouville problems. In
                 this article the underlying theory and implementation
                 issues are discussed. Several examples exhibiting quite
                 varied asymptotic behavior in $p$ are presented.",
  accepted =     "June 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithms, performance, continuous spectrum,
                 eigenfunction norm, eigenvalue, limit circle, limit
                 point, oscillatory, singular endpoints, spectral
                 density functions, Sturm--Liouville problems.",
  subject =      "{\bf G.1.7}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Boundary
                 value problems. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm design and analysis.",
}

@Article{Sidje:1998:ESP,
  author =       "Roger B. Sidje",
  title =        "{EXPOKIT}: Software Package for Computing Matrix
                 Exponentials",
  journal =      j-TOMS,
  volume =       "24",
  number =       "1",
  pages =        "130--156",
  month =        mar,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/285861.285868;
                 http://www.acm.org/pubs/citations/journals/toms/1998-24-1/p130-sidje/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Expokit provides a set of routines aimed at computing
                 matrix exponentials. More precisely, it computes either
                 a small matrix exponential in full, the action of a
                 large sparse matrix exponential on an operand vector,
                 or the solution of a system of linear ODEs with
                 constant inhomogeneity. The backbone of the sparse
                 routines consists of matrix-free Krylov subspace
                 projection methods (Arnoldi and Lanczos processes), and
                 that is why the toolkit is capable of coping with
                 sparse matrices of large dimension. The software
                 handles real and complex matrices and provides specific
                 routines for symmetric and Hermitian matrices. The
                 computation of matrix exponentials is a numerical issue
                 of critical importance in the area of Markov chains and
                 furthermore, the computed solution is subject to
                 probabilistic constraints. In addition to addressing
                 general matrix exponentials, a distinct attention is
                 assigned to the computation of transient states of
                 Markov chains.",
  accepted =     "June 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithms, Krylov methods, Markov chains, matrix
                 exponential.",
  subject =      "{\bf G.1.3}: Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra. {\bf G.1.7}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Ordinary
                 Differential Equations, Initial value problems. {\bf
                 G.4}: Mathematics of Computing, MATHEMATICAL
                 SOFTWARE.",
}

@Article{Chow:1998:OFB,
  author =       "Edmond Chow and Michael A. Heroux",
  title =        "An object-oriented framework for block
                 preconditioning",
  journal =      j-TOMS,
  volume =       "24",
  number =       "2",
  pages =        "159--183",
  month =        jun,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/290200.287639",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-2/p159-chow/",
  abstract =     "General software for preconditioning the iterative
                 solution of linear systems is greatly lagging behind
                 the literature. This is partly because specific
                 problems and specific matrix and preconditioner data
                 structures in order to be solved efficiently, i.e.,
                 multiple implementations of a preconditioner with
                 specialized data structures are required. This article
                 presents a framework to support preconditioning with
                 various, possibly user-defined, data structures for
                 matrices that are partitioned into blocks. The main
                 idea is to define data structures for the blocks, and
                 an upper layer of software which uses these blocks
                 transparently of their data structure. This
                 transparency can be accomplished by using an
                 object-oriented language. Thus, various
                 preconditioners, such as block relaxations and
                 block-incomplete factorizations, only need to be
                 defined once and will work with any block type. In
                 addition, it is possible to transparently interchange
                 various approximate or exact techniques for inverting
                 pivot blocks, or solving systems whose coefficient
                 matrices are diagonal blocks. This leads to a rich
                 variety of preconditioners that can be selected.
                 Operations with the blocks are performed with optimized
                 libraries or fundamental data types. Comparisons with
                 an optimized Fortran 77 code on both workstations and
                 Cray supercomputers show that this framework can
                 approach the efficiency of Fortran 77, as long as
                 suitable block sized and block types are chosen.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "design",
  subject =      "{\bf G.1.3} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf G.1.3} Mathematics
                 of Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Sparse, structured, and very large systems
                 (direct and iterative methods). {\bf G.4} Mathematics
                 of Computing, MATHEMATICAL SOFTWARE. {\bf F.2.1} Theory
                 of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices.",
}

@Article{Breinholt:1998:AGH,
  author =       "Greg Breinholt and Christoph Schierz",
  title =        "{Algorithm 781}: generating {Hilbert}'s space-filling
                 curve by recursion",
  journal =      j-TOMS,
  volume =       "24",
  number =       "2",
  pages =        "184--189",
  month =        jun,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/290200.290219",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-2/p184-breinholt/",
  abstract =     "An efficient algorithm for the generation of Hilbert's
                 space-filling curve is given. The algorithm implements
                 a recursive procedure that involves simple integer
                 operations and quickly converges to the set of points
                 that make the Hilbert curve. The algorithm is elegant,
                 short, and considerably easier to implement than
                 previous recursive and nonrecursive algorithms and can
                 be efficiently implemented in all programming languages
                 that have integer operations and allow recursion. The
                 fundamental Hilbert shape (a line joining the four
                 corners of a square) is represented by two variables
                 with values of either 0 or 1. This coding technique
                 could be successfully applied to the generation of
                 other regular space-filling curves, such as the Peano
                 curve.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf F.2.2} Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical
                 Algorithms and Problems, Geometrical problems and
                 computations. {\bf I.3.3} Computing Methodologies,
                 COMPUTER GRAPHICS, Picture/Image Generation, Line and
                 curve generation. {\bf I.3.5} Computing Methodologies,
                 COMPUTER GRAPHICS, Computational Geometry and Object
                 Modeling, Curve, surface, solid, and object
                 representations.",
}

@Article{Bik:1998:AGS,
  author =       "Aart J. C. Bik and Peter J. H. Brinkhaus and Peter M.
                 W. Knijnenburg and Harry A. G. Wijshoff",
  title =        "The automatic generation of sparse primitives",
  journal =      j-TOMS,
  volume =       "24",
  number =       "2",
  pages =        "190--225",
  month =        jun,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/290200.287636",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-2/p190-bik/",
  abstract =     "Primitives in mathematical software are usually
                 written and optimized by hand. With the implementation
                 of a ``sparse compiler'' that is capable of
                 automatically converting a dense program into sparse
                 code, however, a completely different approach to the
                 generation of sparse primitives can be taken. A {\em
                 dense\/} implementation of a particular primitive is
                 supplied to the sparse compiler, after which it can be
                 converted into many different {\em sparse\/} versions
                 of this primitive. Each version is specifically
                 tailored to a class of sparse matrices having a
                 specific nonzero structure. In this article, we discuss
                 some of our experiences with this new approach.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; experimentation; performance",
  subject =      "{\bf G.1.3} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Sparse, structured,
                 and very large systems (direct and iterative methods).
                 {\bf D.1.2} Software, PROGRAMMING TECHNIQUES, Automatic
                 Programming. {\bf D.3.4} Software, PROGRAMMING
                 LANGUAGES, Processors, Compilers. {\bf E.2} Data, DATA
                 STORAGE REPRESENTATIONS. {\bf G.1.3} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Matrix inversion. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices.",
}

@Article{Bischof:1998:CRQ,
  author =       "Christian H. Bischof and G. Quintana--Ort{\'\i}",
  title =        "Computing rank-revealing {$QR$} factorizations of
                 dense matrices",
  journal =      j-TOMS,
  volume =       "24",
  number =       "2",
  pages =        "226--253",
  month =        jun,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/290200.287637",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-2/p226-bischof/",
  abstract =     "We develop algorithms and implementations for
                 computing rank-revealing QR (RRQR) factorizations of
                 dense matrices. First, we develop an efficient block
                 algorithm for approximating an RRQR factorization,
                 employing a windowed version of the commonly used Golub
                 pivoting strategy, aided by incremental condition
                 estimation. Second, we develop efficiently
                 implementable variants of guaranteed reliable RRQR
                 algorithms for triangular matrices originally suggested
                 by Chandrasekaran and Ipsen and by Pan and Tang. We
                 suggest algorithmic improvements with respect to
                 condition estimation, termination criteria, and Givens
                 updating. By combining the block algorithm with one of
                 the triangular postprocessing steps, we arrive at an
                 efficient and reliable algorithm for computing an RRQR
                 factorization of a dense matrix. Experimental results
                 on IBM RS/6000 SGI R8000 platforms show that this
                 approach performs up to three times faster that the
                 less reliable QR factorization with column pivoting as
                 it is currently implemented in LAPACK, and comes within
                 15\% of the performance of the LAPACK block algorithm
                 for computing a QR factorization without any column
                 exchanges. Thus, we expect this routine to be useful in
                 may circumstances where numerical rank deficiency
                 cannot be ruled out, but currently has been ignored
                 because of the computational cost of dealing with it.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.3} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE. {\bf
                 F.2.1} Theory of Computation, ANALYSIS OF ALGORITHMS
                 AND PROBLEM COMPLEXITY, Numerical Algorithms and
                 Problems, Computations on matrices.",
}

@Article{Bischof:1998:ACR,
  author =       "C. H. Bischof and G. Quintana-Ort{\'\i}",
  title =        "{Algorithm 782}: {Codes} for rank-revealing {$QR$}
                 factorizations of dense matrices",
  journal =      j-TOMS,
  volume =       "24",
  number =       "2",
  pages =        "254--257",
  month =        jun,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/290200.287638",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-2/p254-bischof/",
  abstract =     "This article describes a suite of codes as well as
                 associated testing and timing drivers for computing
                 rank-revealing QR (RRQR) factorizations of dense
                 matrices. The main contribution is an efficient block
                 algorithm for approximating an RRQR factorization,
                 employing a windowed version of the commonly used Golub
                 pivoting strategy and improved versions of the RRQR
                 algorithms for triangular matrices originally suggested
                 by Chandrasekaran and Ipsen and by Pan and Tang,
                 respectively, We highlight usage and features of these
                 codes.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77. {\bf G.1.3} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra. {\bf G.4} Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Mathematica.",
}

@Article{Peters:1998:APF,
  author =       "J{\"o}rg Peters",
  title =        "{Algorithm 783}: {Pcp2Nurb} --- smooth free-form
                 surfacing with linearly trimmed bicubic {B}-splines",
  journal =      j-TOMS,
  volume =       "24",
  number =       "3",
  pages =        "261--267",
  month =        sep,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/292395.292399",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p261-peters/",
  abstract =     "Unrestricted control polyhedra facilitate modeling
                 free-form surfaces of arbitrary topology and local
                 patch-layout by allowing {\em n\/}-sided, possibly
                 nonplanar, facets and {\em m\/}-valent vertices. By
                 cutting off edges and corners, the smoothing of an
                 unrestricted control polyhedron can be reduced to the
                 smoothing of a {\em planar-cut polyhedron\/}. A
                 planar-cut polyhedron is a generalization of the
                 well-known tensor-product control structure. The
                 routine Pcp2Nurb in turn translates planar-cut
                 polyhedra to a collection of four-sided linearly
                 trimmed bicubic B-splines and untrimmed biquadratic
                 B-splines. The routine can thus serve as central
                 building block for overcoming topological constraints
                 in the mathematical modeling of smooth surfaces that
                 are stored, transmitted, and rendered using only the
                 standard representation in industry. Specifically, on
                 input of a nine-point subnet of a planar-cut
                 polyhedron, the routine outputs a trimmed bicubic NURBS
                 patch. If the subnet does not have geometrically
                 redundant edges, this patch joins smoothly with patches
                 from adjacent subnets as a four-sided piece of a
                 regular {\em C1\/} surface. The patch integrates
                 smoothly with untrimmed biquadratic tensor-product
                 surfaces derived from subnets with tensor-product
                 structure. Sharp features can be retained in this
                 representation by using geometrically redundant edges
                 in the planar-cut polyhedron. The resulting surface
                 follows the outlines of the planar-cut polyhedron in
                 the manner traditional tensor-product splines follow
                 the outline of their rectilinear control polyhedron. In
                 particular, it stays in the local convex hull of the
                 planar-cut polyhedron.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf I.3.5} Computing Methodologies, COMPUTER
                 GRAPHICS, Computational Geometry and Object Modeling,
                 Splines. {\bf D.3.2} Software, PROGRAMMING LANGUAGES,
                 Language Classifications, C. {\bf G.1.1} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Interpolation, Spline
                 and piecewise polynomial interpolation. {\bf G.1.2}
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Spline and piecewise polynomial
                 approximation. {\bf I.3.5} Computing Methodologies,
                 COMPUTER GRAPHICS, Computational Geometry and Object
                 Modeling, Boundary representations.",
}

@Article{Kaagstrom:1998:GLB,
  author =       "Bo K{\aa}gstr{\"o}m and Per Ling and Charles {Van
                 Loan}",
  title =        "{GEMM-based} level 3 {BLAS}: high-performance model
                 implementations and performance evaluation benchmark",
  journal =      j-TOMS,
  volume =       "24",
  number =       "3",
  pages =        "268--302",
  month =        sep,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/292395.292412",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p268-kagstrom/",
  abstract =     "The level 3 Basic Linear Algebra Subprograms (BLAS)
                 are designed to perform various matrix multiply and
                 triangular system solving computations. Due to the
                 complex hardware organization of advanced computer
                 architectures the development of optimal level 3 BLAS
                 code is costly and time consuming. However, it is
                 possible to develop a portable and high-performance
                 level 3 BLAS library mainly relying on a highly
                 optimized GEMM, the routine for the general matrix
                 multiply and add operation. With suitable partitioning,
                 all the other level 3 BLAS can be defined in terms of
                 GEMM and a small amount of level 1 and level 2
                 computations. Our contribution is twofold. First, the
                 model implementations in Fortran 77 of the GEMM-based
                 level 3 BLAS are structured to reduced effectively data
                 traffic in a memory hierarchy. Second, the GEMM-based
                 level 3 BLAS performance evaluation benchmark is a tool
                 for evaluating and comparing different implementations
                 of the level 3 BLAS with the GEMM-based model
                 implementations.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance",
  subject =      "{\bf G.1.3} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf D.3.2} Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 FORTRAN 77. {\bf F.2.1} Theory of Computation, ANALYSIS
                 OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical
                 Algorithms and Problems, Computations on matrices. {\bf
                 G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing. {\bf G.4} Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Portability**. {\bf G.4} Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Reliability and robustness. {\bf
                 G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Verification**.",
}

@Article{Kaagstrom:1998:AGL,
  author =       "Bo K{\aa}gstr{\"o}m and Per Ling and Charles {Van
                 Loan}",
  title =        "{Algorithm 784}: {GEMM-based} level 3 {BLAS}:
                 portability and optimization issues",
  journal =      j-TOMS,
  volume =       "24",
  number =       "3",
  pages =        "303--316",
  month =        sep,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/292395.292426",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p303-kagstrom/",
  abstract =     "This companion article discusses portability and
                 optimization issues of the GEMM-based level 3 BLAS
                 model implementations and the performance evaluation
                 benchmark. All software comes in all four data types
                 (single- and double-precision, real and complex) and
                 are designed to be easy to implement and use on
                 different platforms. Each of the GEMM-based routines
                 has a few machine-dependent parameters that specify
                 internal block sizes, cache characteristics, and branch
                 points for alternative code sections. These parameters
                 provide means for adjustment to the characteristics of
                 a memory hierarchy.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; measurement; performance",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77. {\bf F.2.1} Theory of
                 Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
                 COMPLEXITY, Numerical Algorithms and Problems,
                 Computations on matrices. {\bf G.1.3} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Linear systems (direct and iterative methods).
                 {\bf G.4} Mathematics of Computing, MATHEMATICAL
                 SOFTWARE, Certification and testing. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency. {\bf G.4} Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Portability**. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness. {\bf G.4} Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Verification**.",
}

@Article{Hu:1998:ASP,
  author =       "Chenglie Hu",
  title =        "{Algorithm 785}: a software package for computing
                 {Schwarz--Christoffel} conformal transformation for
                 doubly connected polygonal regions",
  journal =      j-TOMS,
  volume =       "24",
  number =       "3",
  pages =        "317--333",
  month =        sep,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/292395.291204",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p317-hu/",
  abstract =     "A software package implementing Schwarz--Christoffel
                 Conformal transformation (or mapping) of doubly
                 connected polygonal regions is fully described in this
                 article from mathematical, numerical, and practical
                 perspectives. The package solves the so-called
                 accessory parameter problem associated with the mapping
                 function as well as evaluates forward and inverse maps.
                 The robustness of the package is reflected by the
                 flexibility in choosing the accuracy of the parameters
                 to be computed, the speed of computation, the ability
                 of mapping ``difficult'' regions (to be specified in
                 Section 2), and being user friendly. Several examples
                 are presented to demonstrate the capabilities of the
                 package.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.m} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Miscellaneous. {\bf G.4} Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Reliability and robustness.",
}

@Article{Espelid:1998:RAD,
  author =       "Terje O. Espelid",
  title =        "Remark on {Algorithm 706}: {DCUTRI} --- an algorithm
                 for adaptive cubature over a collection of triangles",
  journal =      j-TOMS,
  volume =       "24",
  number =       "3",
  pages =        "334--335",
  month =        sep,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/292395.291205",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:18:39 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Berntsen:1992:ADA}.",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p334-espelid/",
  abstract =     "We present corrections to {Algorithm 706} ({\em ACM
                 Trans. Math. Softw.\/} 18, 3, Sept. 1992, pages
                 329-342; CALGO supplement 123).",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; reliability",
  subject =      "{\bf G.1.4} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Quadrature and Numerical Differentiation,
                 Adaptive and iterative quadrature. {\bf G.1.4}
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Quadrature and Numerical Differentiation,
                 Multidimensional (multiple) quadrature. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Efficiency. {\bf G.4} Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Reliability and robustness.",
}

@Article{Levin:1998:RAS,
  author =       "Stewart A. Levin",
  title =        "Remark on {Algorithm 622}: a simple macroprocessor",
  journal =      j-TOMS,
  volume =       "24",
  number =       "3",
  pages =        "336--340",
  month =        sep,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/292395.292448",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:17:52 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Rice:1984:ASM}.",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p336-levin/",
  abstract =     "A number of updates to the macroprocessor are
                 described that bring the code into line with the
                 Fortran 77 standard. This is followed by an outline of
                 how the macroprocessor was used for the rapid porting
                 of geophysical software from a 64-bit supercomputer
                 environment to a number of different Unix workstations.
                 Finally a number of deficiencies remaining in the
                 macroprocessor are noted and workarounds suggested
                 where possible.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Macro and assembly languages. {\bf
                 D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77. {\bf D.3.4} Software,
                 PROGRAMMING LANGUAGES, Processors, Preprocessors.",
}

@Article{Marsaglia:1998:MPM,
  author =       "George Marsaglia and Wai Wan Tsang",
  title =        "The {Monty Python} method for generating random
                 variables",
  journal =      j-TOMS,
  volume =       "24",
  number =       "3",
  pages =        "341--350",
  month =        sep,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/292395.292453;
                 http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p341-marsaglia/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  ZMnumber =     "0930.65002",
  abstract =     "We suggest an interesting and fast method for
                 generating normal, exponential, $t$, von Mises, and
                 certain other important random variables used in Monte
                 Carlo studies. The right half of a symmetric density is
                 cut into pieces, then, using simple area-preserving
                 transformations, reassembled into a rectangle from
                 which the $x$-coordinate---or a linear function of the
                 $x$-coordinate---of a random point provides the
                 required variate. To illustrate the speed and
                 simplicity of the Monty Python method, we provide a
                 small C program, self-contained, for rapid generation
                 of normal (Gaussian) variables. It is self-contained in
                 the sense that required uniform variates are generated
                 in-line, as pairs of 16-bit integers by means of the
                 remarkable new multiply-with-carry method.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "$t$ variates; algorithms; Monte Carlo studies; Monty
                 Python method; normal variates; random variable
                 generation; theory; von Mises variates",
  subject =      "{\bf G.3} Mathematics of Computing, PROBABILITY AND
                 STATISTICS. {\bf I.6.1} Computing Methodologies,
                 SIMULATION AND MODELING, Simulation Theory.",
  ZMclass =      "*65C10 Random number generation 65C05 Monte Carlo
                 methods",
}

@Article{Hopkins:1998:CAF,
  author =       "Tim Hopkins",
  title =        "Certification of {Algorithm 734}: a {Fortran 90} code
                 for unconstrained nonlinear minimization",
  journal =      j-TOMS,
  volume =       "24",
  number =       "3",
  pages =        "351--354",
  month =        sep,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/292395.292460",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p351-hopkins/",
  abstract =     "A Fortran 90 Code for Unconstrained Nonlinear
                 Minimization ({\em ACM Trans. Math. Softw. 20\/}, 3
                 (Sept. 1994), pages 354-372; CALGO Supplement 131) was
                 ported to a number of compiler-platform combinations.
                 The necessary changes to the code are given along with
                 some comparative timings.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Fortran 90. {\bf G.4} Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Certification and
                 testing. {\bf G.1.6} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Optimization, Gradient methods.",
}

@Article{Gautschi:1998:RAO,
  author =       "Walter Gautschi",
  title =        "Remark on {Algorithm 726}: {ORTHPOL} --- a package
                 of routines for generating orthogonal polynomials and
                 {Gauss}-type quadrature rules",
  journal =      j-TOMS,
  volume =       "24",
  number =       "3",
  pages =        "355--355",
  month =        sep,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/292395.292467",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:16:21 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Gautschi:1994:ACP}.",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p355-gautschi/",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.2} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation. {\bf G.1.4} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation. {\bf G.4} Mathematics of Computing,
                 MATHEMATICAL SOFTWARE.",
}

@Article{Smith:1998:AMP,
  author =       "David M. Smith",
  title =        "{Algorithm 786}: Multiple-Precision Complex Arithmetic
                 and Functions",
  journal =      j-TOMS,
  volume =       "24",
  number =       "4",
  pages =        "359--367",
  month =        dec,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/293686.293687",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:09:51 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also
                 \cite{Bailey:1995:FBM,Brent:1978:AMF,Brent:1979:RMF,Brent:1980:AIB}.",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p359-smith/",
  abstract =     "The article describes a collection of Fortran routines
                 for multiple-precision complex arithmetic and
                 elementary functions. The package provides good
                 exception handling, flexible input and output, trace
                 features, and results that are almost always correctly
                 rounded. For best efficiency on different machines, the
                 user can change the arithmetic type used to represent
                 the multiple-precision numbers.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance; reliability",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Computer arithmetic. {\bf G.1.2}
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation, Elementary function approximation. {\bf
                 G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Algorithm design and analysis. {\bf G.4} Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Efficiency. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Portability**.",
}

@Article{Ekeland:1998:SDE,
  author =       "Kersti Ekeland and Brynjulf Owren and Eivor {\O}ines",
  title =        "Stiffness Detection and Estimation of Dominant Spectra
                 with Explicit {Runge--Kutta} Methods",
  journal =      j-TOMS,
  volume =       "24",
  number =       "4",
  pages =        "368--382",
  month =        dec,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/293686.287641",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-3/p368-ekeland/",
  abstract =     "A new stiffness detection scheme based on explicit
                 Runge--Kutta methods is proposed. It uses a Krylov
                 subspace approximation to estimate the eigenvalues of
                 the Jacobian of the differential system. The numerical
                 examples indicate that this technique is a worthwhile
                 alternative to other known stiffness detection schemes,
                 especially when the systems are large and when it is
                 desirable to know more about the spectrum of the
                 Jacobian than just the spectral radius.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.7} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Ordinary Differential Equations, Initial
                 value problems. {\bf G.1.7} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Ordinary Differential Equations,
                 One-step (single step) methods. {\bf G.1.7} Mathematics
                 of Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations, Stiff equations.",
}

@Article{Renka:1998:RA,
  author =       "Robert J. Renka and Ron Brown",
  title =        "Remark on {Algorithm 761}",
  journal =      j-TOMS,
  volume =       "24",
  number =       "4",
  pages =        "383--385",
  month =        dec,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/293686.293689;
                 http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p383-renka/",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:12:24 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Akima:1996:ASS,DeTisi:2000:RAS}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.1} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Interpolation,
                 Interpolation formulas. {\bf G.4} Mathematics of
                 Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Resende:1998:AFS,
  author =       "Mauricio G. C. Resende and Thomas A. Feo and Stuart H.
                 Smith",
  title =        "{Algorithm 787}: {Fortran} Subroutines for Approximate
                 Solution of Maximum Independent Set Problems Using
                 {GRASP}",
  journal =      j-TOMS,
  volume =       "24",
  number =       "4",
  pages =        "386--394",
  month =        dec,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/293686.293690",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 10:13:13 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p386-resende/",
  abstract =     "Let $G=(V, E)$ be an undirected graph where $V$ and
                 $E$ are the sets of vertices and edges of $G$,
                 respectively. A subset of the vertices $S \subseteq V$
                 is independent if all of its members are pairwise
                 nonadjacent, i.e., have no edge between them. A
                 solution to the NP-hard maximum independent set problem
                 is an independent set of maximum cardinality. This
                 article describes gmis, a set of Fortran subroutines to
                 find an approximate solution of a maximum independent
                 set problem. A greedy randomized adaptive search
                 procedure (GRASP) is used to produce the solutions. The
                 algorithm is described in detail. Implementation and
                 usage of the package is outlined, and computational
                 experiments are reported, illustrating solution quality
                 as a function of running time.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.6} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Optimization, Integer
                 programming. {\bf G.2.1} Mathematics of Computing,
                 DISCRETE MATHEMATICS, Combinatorics, Combinatorial
                 algorithms. {\bf G.m} Mathematics of Computing,
                 MISCELLANEOUS.",
}

@Article{Atkinson:1998:AAB,
  author =       "Kendall Atkinson and Youngmok Jeon",
  title =        "{Algorithm 787}: {Automatic} Boundary Integral
                 Equation Programs for the Planar {Laplace} Equation",
  journal =      j-TOMS,
  volume =       "24",
  number =       "4",
  pages =        "395--417",
  month =        dec,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/293686.293692",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p395-atkinson/",
  abstract =     "Algorithms with automatic error control are described
                 for the solution of Laplace's equation on both interior
                 and exterior regions, with both Dirichlet and Neumann
                 boundary conditions. The algorithms are based on
                 standard reformulations of each boundary value problem
                 as a boundary integral equation of the second kind. The
                 Nystr{\"o}m method is used to solve the integral
                 equations, and convergence of arbitrary high order is
                 observed when the boundary data are analytic. The
                 Kelvin transformation is introduced to allow a simple
                 conversion between internal and external problems. Two
                 Fortran program implementations, DRCHLT and NEUMAN, are
                 defined, analyzed, and illustrated.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.8} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Partial Differential
                 Equations. {\bf G.1.9} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Integral Equations.",
}

@Article{Govaerts:1998:IHD,
  author =       "W. Govaerts and F. W. O. Kuznetsov and B. Sijnave",
  title =        "Implementation of {Hopf} and Double-{Hopf}
                 Continuation Using Bordering Methods",
  journal =      j-TOMS,
  volume =       "24",
  number =       "4",
  pages =        "418--436",
  month =        dec,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/293686.293693",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p418-govaerts/",
  abstract =     "We discuss the computational study of curves of Hopf
                 and double-Hopf points in the software package CONTENT
                 developed at CWI, Amsterdam. These are important points
                 in the numerical study of dynamical systems
                 characterized by the occurrence of one or two conjugate
                 pairs of pure imaginary eigenvalues in the spectrum of
                 the Jacobian matrix. The bialternate product of
                 matrices is extensively used in three codes for the
                 numerical continuation of curves of Hopf points and in
                 one for the continuation of curves of double-Hopf
                 points. In the double-Hopf and two of the single-Hopf
                 cases this is combined with a bordered matrix method.
                 We use this software to find special points on a Hopf
                 curve in a model of chemical oscillations and by
                 computing a Hopf and a double-Hopf curve in a realistic
                 model of a neuron.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; design",
  subject =      "{\bf D.2.6} Software, SOFTWARE ENGINEERING,
                 Programming Environments. {\bf G.1.7} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations. {\bf G.4} Mathematics of Computing,
                 MATHEMATICAL SOFTWARE.",
}

@Article{Giering:1998:RAC,
  author =       "Ralf Giering and Thomas Kaminski",
  title =        "Recipes for Adjoint Code Construction",
  journal =      j-TOMS,
  volume =       "24",
  number =       "4",
  pages =        "437--474",
  month =        dec,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/293686.293695",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p437-giering/",
  abstract =     "Adjoint models are increasingly being developed for
                 use in meteorology and oceanography. Typical
                 applications are data assimilation, model tuning,
                 sensitivity analysis, and determination of singular
                 vectors. The adjoint model computes the gradient of a
                 cost function with respect to control variables.
                 Generation of adjoint code may be seen as the special
                 case of differentiation of algorithms in reverse mode,
                 where the dependent function is a scalar. The described
                 method for adjoint code generation is based on a few
                 basic principles, which permits the establishment of
                 simple construction rules for adjoint statements and
                 complete adjoint subprograms. These rules are presented
                 and illustrated with some examples. Conflicts that
                 occur due to loops and redefinition of variables are
                 also discussed. Direct coding of the adjoint of a more
                 sophisticated model is extremely time consuming and
                 subject to errors. Hence, automatic generation of
                 adjoint code represents a distinct advantage. An
                 implementation of the method, described in this
                 article, is the tangent linear and adjoint model
                 compiler (TAMC).",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; theory",
  subject =      "{\bf D.3.4} Software, PROGRAMMING LANGUAGES,
                 Processors, Preprocessors. {\bf G.1.4} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Quadrature and Numerical
                 Differentiation, Automatic differentiation. {\bf G.1.6}
                 Mathematics of Computing, NUMERICAL ANALYSIS,
                 Optimization, Gradient methods. {\bf I.2.2} Computing
                 Methodologies, ARTIFICIAL INTELLIGENCE, Automatic
                 Programming, Program transformation.",
}

@Article{Berzins:1998:SAS,
  author =       "M. Berzins and R. Fairlie and S. V. Pennington and J.
                 M. Ware and L. E. Scales",
  title =        "{SPRINT2D}: adaptive software for {PDEs}",
  journal =      j-TOMS,
  volume =       "24",
  number =       "4",
  pages =        "475--499",
  month =        dec,
  year =         "1998",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/293686.293696",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Feb 8 17:51:43 MST 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1998-24/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1998-24-4/p475-berzins/",
  abstract =     "SPRINT2D is a set of software tools for solving both
                 steady and unstea dy partial differential equations in
                 two-space variables. The software consists of a set of
                 coupled modules for mesh generation, spatial
                 discretization, time integration, nonlinear equations,
                 linear algebra, spatial adaptivity, and visualization.
                 The software uses unstructured triangular meshes and
                 adaptive local error control in both space and time.
                 the class of problems solved includes systems of
                 parabolic, elliptic, and hyperbolic equations; for the
                 latter by use of Riemann-solve-based methods. This
                 article describes the software and show how the
                 adaptive techniques may be used to increase the
                 reliability of the solution for a Burgers' equations
                 problem, an electrostatics problem from
                 elastohydrodynamic lubrication, and a challenging gas
                 jet problem.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.8} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations, Method of
                 lines. {\bf G.1.8} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Partial Differential Equations, Hyperbolic
                 equations. {\bf G.1.8} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Partial Differential Equations,
                 Elliptic equations. {\bf G.4} Mathematics of Computing,
                 MATHEMATICAL SOFTWARE.",
}

@Article{Anonymous:1998:AI,
  author =       "Anonymous",
  title =        "1998 Author Index",
  journal =      j-TOMS,
  volume =       "24",
  number =       "4",
  pages =        "500--502",
  month =        dec,
  year =         "1998",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 09 17:22:53 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  xxURL =        "Missing from ACM Digital Library",
}

@Article{Davis:1999:CUM,
  author =       "Timothy A. Davis and Iain S. Duff",
  title =        "Combined Unifrontal\slash Multifrontal Method for
                 Unsymmetric Sparse Matrices",
  journal =      j-TOMS,
  volume =       "25",
  number =       "1",
  pages =        "1--20",
  month =        mar,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/305658.287640",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 15 19:01:02 1999",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/1999-25/;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p1-davis/",
  abstract =     "We discuss the organization of frontal matrices in
                 multifrontal methods for the solution of large sparse
                 sets of unsymmetric linear equations. In the
                 multifrontal method, work on a frontal matrix can be
                 suspended, the frontal matrix can be stored for later
                 reuse, and a new frontal matrix can be generated. There
                 are thus several frontal matrices stored during the
                 factorization, and one or more of these are assembled
                 (summed) when creating a new frontal matrix. Although
                 this means that arbitrary sparsity patterns can be
                 handled efficiently, extra work is required to sum the
                 frontal matrices together and can be costly because
                 indirect addressing is required. The (uni)frontal
                 method avoids this extra work by factorizing the matrix
                 with a single frontal matrix. Rows and columns are
                 added to the frontal matrix, and pivot rows and columns
                 are removed. Data movement is simpler, but higher
                 fill-in can result if the matrix cannot be permuted
                 into a variable-band form with small profile. We
                 consider a combined unifrontal/multifrontal algorithm
                 to enable general fill-in reduction orderings to be
                 applied without the data movement of previous
                 multifrontal approaches. We discuss this technique in
                 the context of a code designed for the solution of
                 sparse systems with unsymmetric pattern.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; experimentation; performance",
  subject =      "{\bf G.1.3} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Numerical Linear Algebra, Linear systems
                 (direct and iterative methods). {\bf G.1.3} Mathematics
                 of Computing, NUMERICAL ANALYSIS, Numerical Linear
                 Algebra, Sparse, structured, and very large systems
                 (direct and iterative methods). {\bf G.4} Mathematics
                 of Computing, MATHEMATICAL SOFTWARE, Algorithm design
                 and analysis.",
}

@Article{Pryce:1999:TPS,
  author =       "J. D. Pryce",
  title =        "A Test Package for {Sturm--Liouville} Solvers",
  journal =      j-TOMS,
  volume =       "25",
  number =       "1",
  pages =        "21--57",
  month =        mar,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/305658.287651",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 15 19:01:02 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p21-pryce/p21-pryce/",
  abstract =     "The author and colleagues have produced a collection
                 of 60 test problems which offer a realistic performance
                 test of the currently available automatic codes for
                 eigenvalues of the classical Sturm--Liouville problem.
                 We describe a Fortran implementation and the
                 considerations that went into its design. A novel
                 feature is that (almost) all the code defining one
                 problem is textually contiguous in the Fortran text,
                 unlike for example the DETEST package for ODE
                 initial-value solvers where the definition of a problem
                 is spread over several routines. The described
                 implementation forms the infrastructure of the SLDRVER
                 interactive package which supports exploration of a set
                 of Sturm--Liouville problems with the four SL-solvers
                 SLEIGN, SLEDGE, SL02F, and SLEIGN2. A ``standard'' set
                 of 60 problems is provided, but it is simple to replace
                 this by another one.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.2.5} Software, SOFTWARE ENGINEERING, Testing
                 and Debugging. {\bf D.3.2} Software, PROGRAMMING
                 LANGUAGES, Language Classifications, FORTRAN 77. {\bf
                 G.1.7} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Ordinary Differential Equations, Boundary value
                 problems. {/bf G.4} Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing. {/bf
                 I.2.4} Computing Methodologies, ARTIFICIAL
                 INTELLIGENCE, Knowledge Representation Formalisms and
                 Methods.",
}

@Article{Pryce:1999:AST,
  author =       "J. D. Pryce",
  title =        "{Algorithm 789}: {SLTSTPAK}: a Test Package for
                 {Sturm--Liouville} Solvers",
  journal =      j-TOMS,
  volume =       "25",
  number =       "1",
  pages =        "58--69",
  month =        mar,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/305658.287652",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 15 19:01:02 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "ftp://netlib.bell-labs.com/netlib/toms/789.gz;
                 http://phase.etl.go.jp/netlib/toms/789;
                 http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p58-pryce/;
                 http://www.hensa.ac.uk/netlib/toms/789.gz;
                 http://www.netlib.no/netlib/toms/789;
                 http://www.netlib.org/toms/789",
  abstract =     "We give technical details of the Sturm--Liouville test
                 package SLTSTPAK, complementing the companion article
                 (this issue) on its design. SLTSTPAK comprises the
                 following: a specification of how to write a routine
                 TSTSET containing a set of Sturm--Liouville problems; a
                 number of routines that act as a harness between a
                 TSTSET, written to this specification, and a driver
                 program. A set of 60 standard problems is provided, but
                 it is simple to replace this by another one.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{/bf D.2.5} Software, SOFTWARE ENGINEERING, Testing
                 and Debugging. {\bf D.3.2} Software, PROGRAMMING
                 LANGUAGES, Language Classifications, FORTRAN 77. {\bf
                 D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, Fortran 90. {\bf G.1.7} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Ordinary Differential
                 Equations, Boundary value problems. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE,
                 Certification and testing.",
}

@Article{Renka:1999:ACC,
  author =       "R. J. Renka",
  title =        "{Algorithm 790}: {CSHEP2D}: Cubic {Shepard} Method for
                 Bivariate Interpolation of Scattered Data",
  journal =      j-TOMS,
  volume =       "25",
  number =       "1",
  pages =        "70--73",
  month =        mar,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/305658.305737",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 15 19:01:02 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "ftp://netlib.bell-labs.com/netlib/toms/790.gz;
                 http://phase.etl.go.jp/netlib/toms/790;
                 http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p70-renka/;
                 http://www.hensa.ac.uk/netlib/toms/790.gz;
                 http://www.netlib.no/netlib/toms/790;
                 http://www.netlib.org/toms/790",
  abstract =     "We describe a new algorithm for scattered data
                 interpolation. The method is similar to that of
                 Algorithm 660 but achieves cubic precision and C2
                 continuity at very little additional cost. An
                 accompanying article presents test results that show
                 the method to be among the most accurate available.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.1} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation. {\bf D.3.2} Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 FORTRAN 77. {\bf G.1.2} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Renka:1999:ATC,
  author =       "R. J. Renka and Ron Brown",
  title =        "{Algorithm 791}: {TSHEP2D}: Cosine series {Shepard}
                 Method for Bivariate Interpolation of Scattered Data",
  journal =      j-TOMS,
  volume =       "25",
  number =       "1",
  pages =        "74--77",
  month =        mar,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/305658.305754",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 15 19:01:02 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "ftp://netlib.bell-labs.com/netlib/toms/791.gz;
                 http://phase.etl.go.jp/netlib/toms/791;
                 http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p74-renka/;
                 http://www.hensa.ac.uk/netlib/toms/791.gz;
                 http://www.netlib.no/netlib/toms/791;
                 http://www.netlib.org/toms/791",
  abstract =     "We describe a new algorithm for scattered data
                 interpolation. It is based on a modified Shepard method
                 similar to that of Algorithm 660 but uses 10-parameter
                 cosine series nodal functions in place of quadratic
                 polynomials. Also, the interpolant has continuous
                 second partial derivatives. An accompanying survey
                 article presents test results that show the method to
                 be more accurate that polynomial-based methods in terms
                 of reproducing test functions with large variations and
                 steep gradients.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.1} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation. {\bf D.3.2} Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 FORTRAN 77. {\bf G.1.2} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Renka:1999:AAT,
  author =       "R. J. Renka and Ron Brown",
  title =        "{Algorithm 792}: Accuracy Tests of {ACM} Algorithms
                 for Interpolation of Scattered Data in the Plane",
  journal =      j-TOMS,
  volume =       "25",
  number =       "1",
  pages =        "78--94",
  month =        mar,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/305658.305745",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 15 19:01:02 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "ftp://netlib.bell-labs.com/netlib/toms/792.gz;
                 http://phase.etl.go.jp/netlib/toms/792;
                 http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p78-renka/;
                 http://www.hensa.ac.uk/netlib/toms/792.gz;
                 http://www.netlib.no/netlib/toms/792;
                 http://www.netlib.org/toms/792",
  abstract =     "We present results of accuracy tests on scattered-data
                 fitting methods that have been published as ACM
                 algorithms. The algorithms include seven
                 triangulation-based methods and three modified Shepard
                 methods, two of which are new algorithms. Our purpose
                 is twofold: to guide potential users in the selection
                 of an appropriate algorithm and to provide a test suite
                 for assessing the accuracy of new methods (or existing
                 methods that are not included in this survey). Our test
                 suite consists of five sets of nodes, with nodes counts
                 ranging from 25 to 100, and 10 test functions. These
                 are made available in the form of three Fortran
                 subroutines: TESTDT returns one of the node sets;
                 TSTFN1 returns a value and, optionally, a gradient
                 value, of one of the test function; and TSTFN2 returns
                 a value, first partials, and second partial derivatives
                 of one of the test functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.1} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation. {\bf D.3.2} Software,
                 PROGRAMMING LANGUAGES, Language Classifications,
                 FORTRAN 77. {\bf G.1.2} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Testa:1999:RA,
  author =       "F. J. Testa and R. J. Renka",
  title =        "Remark on {Algorithm 716}",
  journal =      j-TOMS,
  volume =       "25",
  number =       "1",
  pages =        "95--96",
  month =        mar,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/305658.287656",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 15 19:01:02 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Renka:1993:ATT}.",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p95-testa/",
  abstract =     "The curve-fitting package TSPACK has been converted to
                 double precision. Also, portability has been improved
                 by eliminating some potential errors.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.1} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation. {\bf G.1.2} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Renka:1999:RAa,
  author =       "R. J. Renka",
  title =        "Remark on {Algorithm 751}",
  journal =      j-TOMS,
  volume =       "25",
  number =       "1",
  pages =        "97--98",
  month =        mar,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/305658.305726",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 15 19:01:02 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Renka:1996:ATC}.",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p97-renka/",
  abstract =     "The triangulation package TRIPACK has been revised to
                 run more efficiently and to eliminate some potential
                 errors. Also, a portable triangulation plotting routine
                 was added.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.1} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation. {\bf G.1.2} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Renka:1999:RAb,
  author =       "R. J. Renka",
  title =        "Remark on {Algorithm 752}",
  journal =      j-TOMS,
  volume =       "25",
  number =       "1",
  pages =        "99--100",
  month =        mar,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/305658.305731",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 15 19:01:02 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Renka:1996:ASS}.",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p99-renka/",
  abstract =     "The triangulation-based scattered-data fitting package
                 SRFPACK was updated for (a) compatibility with a
                 revised interface to the triangulation package TRIPACK,
                 (b) the elimination of potential errors in the
                 treatment of tension factors and in the extrapolation
                 procedure, and (c) the addition of a more accurate
                 local gradient-estimation procedure and a simple but
                 portable contour-plotting capability.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf G.1.1} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Interpolation. {\bf G.1.2} Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation. {\bf G.4}
                 Mathematics of Computing, MATHEMATICAL SOFTWARE.",
}

@Article{Gautschi:1999:NRC,
  author =       "Walter Gautschi",
  title =        "A Note on the Recursive Calculation of Incomplete
                 Gamma Functions",
  journal =      j-TOMS,
  volume =       "25",
  number =       "1",
  pages =        "101--107",
  month =        mar,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/305658.305717",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 15 19:01:02 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p101-gautschi/",
  abstract =     "It is known that the recurrence relation for
                 incomplete gamma functions $\Gamma(a + n, x), 0 \le a <
                 1$, $n = 0, 1, 2 \ldots$, when $x$ is positive, is
                 unstable---more so the larger $x$. Nevertheless, the
                 recursion can be used in the range $0 \le n \le x$
                 practically without error growth, and in larger ranges
                 $0 \le n \le N$ with a loss of accuracy that can be
                 controlled by suitably limiting $N$.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; reliability",
  subject =      "{\bf G.1.0} Mathematics of Computing, NUMERICAL
                 ANALYSIS, General, Stability (and instability). {\bf
                 G.1.2} Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation.",
}

@Article{Xie:1999:RAU,
  author =       "Dexuan Xie and Tamar Schlick",
  title =        "Remark on {Algorithm 702}: The Updated Truncated
                 {Newton} Minimization Package",
  journal =      j-TOMS,
  volume =       "25",
  number =       "1",
  pages =        "108--122",
  month =        mar,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/305658.305698",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 15 19:01:02 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Schlick:1992:ATE}.",
  URL =          "http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p108-xie/",
  abstract =     "A truncated Newton minimization package, TNPACK, was
                 described in ACM Transactions on Mathematical Software
                 14, 1 (Mar. 1992), pp.46-111. Modifications to enhance
                 performance, especially for large-scale minimization of
                 molecular potential functions, are described here. They
                 involve three program segments of TNPACK: negative
                 curvature test, modified Cholesky factorization, and
                 line-search stopping rule.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; performance",
  subject =      "{\bf G.1.6} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Optimization, Nonlinear programming. {\bf
                 G.4} Mathematics of Computing, MATHEMATICAL SOFTWARE.
                 {\bf J.3} Computer Applications, LIFE AND MEDICAL
                 SCIENCES.",
}

@Article{Gay:1999:SAF,
  author =       "David M. Gay and Eric Grosse",
  title =        "Self-adapting {Fortran 77} Machine Constants: Comment
                 on {Algorithm 528}",
  journal =      j-TOMS,
  volume =       "25",
  number =       "1",
  pages =        "123--126",
  month =        mar,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/305658.305711",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 20 12:38:08 1999",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/gay-david-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib;
                 https://www.math.utah.edu/pub/tex/bib/unix.bib",
  note =         "See \cite{Fox:1978:AFP}.",
  URL =          "http://cm.bell-labs.com/who/ehg/mach/d1mach.ps;
                 http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMSbibget?Gay:1999:SAF;
                 http://www.acm.org/pubs/citations/journals/toms/cgi-bin/TOMScitation?Fox:1978:AFP;
                 http://www.acm.org:80/pubs/citations/journals/toms/1999-25-1/p123-gay/",
  abstract =     "This note discusses user dissatisfaction with the need
                 to uncomment data statements in Algorithm 528, comments
                 on alternative approaches tried by the community, and
                 proposes a solution that is both automatic and safe.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; d1mach; languages; machine environment
                 parameters",
  subject =      "{\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN 77. {\bf G.1.0} Mathematics of
                 Computing, NUMERICAL ANALYSIS, General, Computer
                 arithmetic.",
}

@Article{Flores:1999:CFR,
  author =       "Juan Flores",
  title =        "Complex Fans: a Representation for Vectors in Polar
                 Form with Interval Attributes",
  journal =      j-TOMS,
  volume =       "25",
  number =       "2",
  pages =        "129--156",
  month =        jun,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/317275.317277",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 20 18:21:35 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p129-flores/",
  abstract =     "If we allow the magnitude and angle of a complex
                 number (expressed in polar form) to range over an
                 interval, it describes a semicircular region, similar
                 to a fan; these regions are what we call complex fans.
                 Complex numbers are a special case of complex fans,
                 where the magnitude and angle are point intervals.
                 Operations (especially addition) with complex numbers
                 in polar form are complicated. What most applications
                 do is to convert them to rectangular form, perform
                 operations, and return the result to polar form.
                 However, if the complex number is a Complex Fan, that
                 transformation increases ambiguity in the result. That
                 is, the resulting Fan is not the smallest Fan that
                 contains all possible results. The need for minimal
                 results took us to develop algorithms to perform the
                 basic arithmetic operations with complex fans, ensuring
                 the result will always be the smallest possible complex
                 fan. We have developed the arithmetic operations of
                 addition, negation, subtraction, product, and division
                 of complex fans. The algorithms presented in this
                 article are written in pseudocode, and the programs in
                 Common Lisp, making use of CLOS (Common Lisp Object
                 System). Translation to any other high-level
                 programming language should be straightforward.",
  accepted =     "March 1999",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "abstract data type; complex fans; complex numbers;
                 interval computation; qualitative reasoning",
  subject =      "Mathematics of Computing - Mathematical Software ({\bf
                 G.4}): Algorithm design and analysis; Computing
                 Methodologies -Artificial Intelligence - Knowledge
                 Representation Formalisms and Methods ({\bf I.2});
                 Computer Applications - Physical Sciences and
                 Engineering ({\bf J.2}): Engineering",
}

@Article{Heinkenschloss:1999:IBO,
  author =       "Matthias Heinkenschloss and Luis N. Vicente",
  title =        "An Interface Between Optimization and Application for
                 the Numerical Solution of Optimal Control Problems",
  journal =      j-TOMS,
  volume =       "25",
  number =       "2",
  pages =        "157--190",
  month =        jun,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/317275.317278",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 20 18:21:35 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p157-heinkenschloss/",
  abstract =     "An interface between the application problem and the
                 nonlinear optimization algorithm is proposed for the
                 numerical solution of distributed optimal control
                 problems. By using this interface, numerical
                 optimization algorithms can be designed to take
                 advantage of inherent problem features like the
                 splitting of the variables into states and controls and
                 the scaling inherited from the functional scalar
                 products. Further, the interface allows the
                 optimization algorithm to make efficient use of
                 user-provided function evaluations and derivative
                 calculations.",
  accepted =     "February 1999",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "optimal control; optimization; simulation",
  subject =      "Mathematics of Computing --- Mathematical Software
                 (G.4); Mathematics of Computing --- Numerical Analysis
                 --- Optimization (G.1.6): Constrained optimization;
                 General Terms: Algorithms, Design",
}

@Article{Gockenbach:1999:CCL,
  author =       "Mark S. Gockenbach and Matthew J. Petro and William W.
                 Symes",
  title =        "{C++} Classes for Linking Optimization with Complex
                 Simulations",
  journal =      j-TOMS,
  volume =       "25",
  number =       "2",
  pages =        "191--212",
  month =        jun,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/317275.317280",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 20 18:21:35 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p191-gockenbach/",
  abstract =     "The object-oriented programming paradigm can be used
                 to overcome the incompatibilities between off-the-shelf
                 optimization software and application software. The
                 Hilbert Class Library (HCL) defines the fundamental
                 mathematical objects arising in optimization problems,
                 such as vectors, linear operators, and so forth, as C++
                 classes, making it possible to write optimization code
                 in a natural fashion, while allowing application
                 software such as simulators to use the most convenient
                 data structures and programming style. In spite of the
                 poor reputation C++ has for runtime performance, the
                 use of mixed-language programming allows performance
                 equal to that achieved by standard Fortran packages, as
                 comparisons with the popular code LBFGS and ARPACK
                 demonstrate.",
  accepted =     "April 1999",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "object-oriented design; optimization; simulation",
  subject =      "Software --- Programming Techniques ---
                 Object-oriented Programming (D.1.5); General Terms:
                 Algorithms, Languages, Performance",
}

@Article{Gautschi:1999:AGG,
  author =       "Walter Gautschi",
  title =        "{Algorithm 793}: {GQRAT} --- {Gauss} Quadrature for
                 Rational Functions",
  journal =      j-TOMS,
  volume =       "25",
  number =       "2",
  pages =        "213--239",
  month =        jun,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/317275.317282",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 20 18:21:35 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "ftp://netlib.bell-labs.com/netlib/toms/793.gz;
                 http://phase.etl.go.jp/netlib/toms/793;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p213-gautschi/;
                 http://www.hensa.ac.uk/netlib/toms/793.gz;
                 http://www.netlib.no/netlib/toms/793;
                 http://www.netlib.org/toms/793",
  abstract =     "The concern here is with Gauss-type quadrature rules
                 that are exact for a mixture of polynomials and
                 rational functions, the latter being selected so as to
                 simulate poles that may be present in the integrand.
                 The underlying theory is presented as well as methods
                 for constructing such rational Gauss formulae. Relevant
                 computer routines are provided and applied to a number
                 examples, including Fermi--Dirac and Bose--Einstein
                 integrals of interest in solid state physics.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "construction of quadrature rules; Gaussian quadrature
                 exact for rational functions; generalized Fermi--Dirac
                 and Bose Einstein integrals",
  subject =      "Software --- Programming Languages --- Language
                 Classifications (D.3.2): FORTRAN 77; Mathematics of
                 Computing --- Numerical Analysis --- Quadrature and
                 Numerical Differentiation (G.1.4); General Terms:
                 Algorithms",
}

@Article{Wieder:1999:ANH,
  author =       "Thomas Wieder",
  title =        "{Algorithm 794}: Numerical {Hankel} transform by the
                 {Fortran} program {HANKEL}",
  journal =      j-TOMS,
  volume =       "25",
  number =       "2",
  pages =        "240--250",
  month =        jun,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/317275.317284;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p240-wieder/;
                 http://www.netlib.org/toms/794;
                 ftp://netlib.bell-labs.com/netlib/toms/794.gz;
                 http://www.netlib.no/netlib/toms/794;
                 http://www.hensa.ac.uk/netlib/toms/794.gz;
                 http://phase.etl.go.jp/netlib/toms/794",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 20 18:21:35 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The numerical evaluation of the Hankel transform poses
                 the problems of both infinite integration and Bessel
                 function calculation. Using the corresponding numerical
                 program routines from the literature, a Fortran program
                 has been written to perform the Hankel transform for
                 real functions, given either in analytical form as
                 subroutines or in discrete form as tabulated data.",
  accepted =     "February 1999",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Hankel transform; numerical analysis",
  subject =      "Software --- Programming Languages --- Language
                 Classifications (D.3.2): FORTRAN 77; Theory of
                 Computation --- Analysis of Algorithms and Problem
                 Complexity --- Numerical Algorithms and Problems
                 (F.2.1): Computation of transforms",
}

@Article{Verschelde:1999:APG,
  author =       "Jan Verschelde",
  title =        "{Algorithm 795}: {PHCPACK}: a general-purpose solver
                 for polynomial systems by homotopy continuation",
  journal =      j-TOMS,
  volume =       "25",
  number =       "2",
  pages =        "251--276",
  month =        jun,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/317275.317286;
                 http://phase.etl.go.jp/netlib/toms/795;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-2/p251-verschelde/;
                 http://www.hensa.ac.uk/netlib/toms/795.gz;
                 http://www.netlib.no/netlib/toms/795;
                 http://www.netlib.org/toms/795",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 20 18:21:35 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "ftp://netlib.bell-labs.com/netlib/toms/795.gz",
  abstract =     "Polynomial systems occur in a wide variety of
                 application domains. Homotopy continuation methods are
                 reliable and powerful methods to compute numerically
                 approximations to all isolated complex solutions.
                 During the last decade considerable progress has been
                 accomplished on exploiting structure in a polynomial
                 system, in particular its sparsity. In this article the
                 structure and design of the software package PHC is
                 described. The main program operates in several modes,
                 is menu driven, and is file oriented. This package
                 features great variety of root-counting methods among
                 its tools. The outline of one black-box solver is
                 sketched, and a report is given on its performance on a
                 large database of test problems. The software has been
                 developed on four different machine architectures. Its
                 portability is ensured by the gnu-ada compiler.",
  accepted =     "15 feb 1999",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Bernshtein's theorem; B{\'e}zout number; B{\'e}zout's
                 theorem; enumerative geometry; homotopy continuation;
                 mixed volume; polyhedral homotopy; polynomial systems;
                 root count; Schubert calculus; start system",
  subject =      "Software --- Programming Languages --- Language
                 Classifications (D.3.2): Ada; Mathematics of Computing
                 --- Numerical Analysis --- Roots of Nonlinear Equations
                 (G.1.5): Systems of equations; Mathematics of Computing
                 --- Numerical Analysis --- Roots of Nonlinear Equations
                 (G.1.5): Polynomials, methods for; Mathematics of
                 Computing --- Discrete Mathematics --- Combinatorics
                 (G.2.1): Counting problems; Mathematics of Computing
                 --- Mathematical Software (G)",
}

@Article{DAmore:1999:IFS,
  author =       "Luisa D'Amore and Giuliano Laccetti and Almerico
                 Murli",
  title =        "An Implementation of a {Fourier} Series Method for the
                 Numerical Inversion of the {Laplace} Transform",
  journal =      j-TOMS,
  volume =       "25",
  number =       "3",
  pages =        "279--305",
  month =        sep,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/326147.326148;
                 http://www.acm.org/pubs/articles/journals/toms/1999-25-3/p279-d_amore/p279-d_amore.pdf;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p279-d_amore/;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p279-d_amore/#abstract;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p279-d_amore/#indterms",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 4 16:36:33 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Our method is based on the numerical evaluation of the
                 integral which occurs in the Riemann Inversion formula.
                 The trapezoidal rule approximation to this integral
                 reduces to a Fourier series. We analyze the
                 corresponding discretization error and demonstrate how
                 this expression can be used in the development of an
                 {\em automatic routine}, one in which the user needs to
                 specify only the required accuracy",
  accepted =     "10 feb 1999",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "automatic stopping criterion; Fourier series methods;
                 Laplace transform inversion",
  subject =      "Software --- Programming Languages --- Language
                 Classifications (D.3.2): FORTRAN 77; Mathematics of
                 Computing --- Numerical Analysis --- General (G.1.0):
                 Numerical algorithms; Mathematics of Computing ---
                 Numerical Analysis --- Integral Equations (G.1.9);
                 Mathematics of Computing --- Numerical Analysis ---
                 Approximation (G.1.2): Nonlinear approximation; General
                 Terms: Algorithms",
}

@Article{DAmore:1999:AFS,
  author =       "Luisa D'Amore and Guiliano Laccetti and Almerico
                 Murli",
  title =        "{Algorithm 796}: a {Fortran} Software Package for the
                 Numerical Inversion of the {Laplace} Transform Based on
                 a {Fourier} Series Method",
  journal =      j-TOMS,
  volume =       "25",
  number =       "3",
  pages =        "306--315",
  month =        sep,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/326147.326149;
                 http://www.acm.org/pubs/articles/journals/toms/1999-25-3/p306-d_amore/p306-d_amore.pdf;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p306-d_amore/;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p306-d_amore/#abstract;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p306-d_amore/#indterms",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 4 16:36:33 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A software package for the numerical inversion of a
                 Laplace Transform function is described. Besides
                 function values of $F(z)$ for complex and real $z$, the
                 user has only to provide the numerical value of the
                 Laplace convergence abscissa or, failing this, an upper
                 bound to this quantity, and the accuracy he or she
                 requires in the computed value of the inverse
                 Transform. The method implemented is based on a Fourier
                 series expansion of the inverse transform, and it is
                 especially suitable when such inverse Laplace Transform
                 is sectionally continuous.",
  accepted =     "10 feb 1999",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "automatic stopping criterion; Fourier series methods;
                 Laplace transform inversion",
  subject =      "Software --- Programming Languages --- Language
                 Classifications (D.3.2): FORTRAN 77; Mathematics of
                 Computing --- Numerical Analysis --- Integral Equations
                 (G.1.9); Mathematics of Computing --- Numerical
                 Analysis --- Approximation (G.1.2): Nonlinear
                 approximation; General Terms: Algorithms",
}

@Article{Dayde:1999:RBB,
  author =       "Michel J. Dayd{\'e} and Iain S. Duff",
  title =        "The {RISC BLAS}: a Blocked Implementation of {Level 3
                 BLAS} for {RISC} Processors",
  journal =      j-TOMS,
  volume =       "25",
  number =       "3",
  pages =        "316--340",
  month =        sep,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/326147.326150;
                 http://www.acm.org/pubs/articles/journals/toms/1999-25-3/p316-dayde/p316-dayde.pdf;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p316-dayde/;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p316-dayde/#abstract;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p316-dayde/#indterms",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 4 16:36:33 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe a version of the Level 3 BLAS which is
                 designed to be efficient on RISC processors. This is an
                 extension of previous studies by the authors and
                 colleagues on a similar approach for efficient serial
                 and parallel implementations on virtual-memory and
                 shared-memory multiprocessors. All our codes are
                 written in Fortran and use loop-unrolling, blocking,
                 and copying to improve the performance. A blocking
                 technique is used to express the BLAS in terms of
                 operations involving triangular blocks and calls to the
                 matrix-matrix multiplication kernel (GEMM). No
                 manufacturer-supplied or assembler code is used. This
                 blocked implementation uses the same blocking ideas as
                 in our implementation for vector machines except that
                 the ordering of loops is designed for efficient reuse
                 of date held in cache and not necessarily for
                 parallelization. All the codes are specifically tuned
                 for RISC processors. The software also includes a tuned
                 version of GEMM. A parameter which controls the
                 blocking allows efficient exploitation of the memory
                 hierarchy on the various target computers. We present
                 results on a range of RISC-based workstations and
                 multiprocessors: CRAY T3D, DEC 8400 5/300, HP 715/64,
                 IBM SP2, MEIKO CS2-HA, SGI Power Challenge 10000, and
                 SUN UltraSPARC-1 model 140. This implementation of the
                 Level 3 BLAS is available on anonymous FTP, and we
                 welcome input from users to improve and extend our BLAS
                 implementation.",
  accepted =     "April 1999",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "blocking; level 3 BLAS; loop-unrolling; matrix-matrix
                 kernels; RISC processors",
  subject =      "Mathematics of Computing --- Mathematical Software
                 (G.4); Theory of Computation --- Analysis of Algorithms
                 and Problem Complexity --- Numerical Algorithms and
                 Problems (F.2.1): Computations on matrices; Mathematics
                 of Computing --- Numerical Analysis --- General
                 (G.1.0): Numerical algorithms; Mathematics of Computing
                 --- Numerical Analysis --- Numerical Linear Algebra
                 (G.1.3): Linear systems (direct and iterative methods);
                 General Terms: Algorithms, Measurement, Performance",
}

@Article{Ribeiro:1999:AFS,
  author =       "Celso C. Ribeiro and Mauricio G. C. Resende",
  title =        "{Algorithm 797}: {Fortran} subroutines for approximate
                 solution of graph planarization problems using
                 {GRASP}",
  journal =      j-TOMS,
  volume =       "25",
  number =       "3",
  pages =        "341--352",
  month =        sep,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/326147.326153",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 4 16:36:33 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/articles/journals/toms/1999-25-3/p341-ribeiro/p341-ribeiro.pdf;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p341-ribeiro/;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p341-ribeiro/#abstract;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p341-ribeiro/#indterms",
  abstract =     "We describe Fortran subroutines for finding
                 approximate solutions of the maximum planar subgraph
                 problem (graph planarization) using a Greedy Randomized
                 Adaptive Search Procedure (GRASP). The design and
                 implementation of the code are described in detail.
                 Computational results with the subroutines illustrate
                 the quality of solutions found as a function of number
                 of GRASP iterations.",
  accepted =     "5 may 1999",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "automatic graph drawing; combinatorial optimization;
                 graph planarization; GRASP; local search",
  subject =      "Software --- Programming Languages --- Language
                 Classifications (D.3.2): FORTRAN 77; Mathematics of
                 Computing --- Discrete Mathematics --- Combinatorics
                 (G.2.1): Combinatorial algorithms; Mathematics of
                 Computing --- Miscellaneous (G.m); General Terms:
                 Algorithms, Performance",
}

@Article{Berry:1999:AHD,
  author =       "Michael W. Berry and Karen S. Minser",
  title =        "{Algorithm 798}: High-Dimensional Interpolation Using
                 the Modified {Shepard} Method",
  journal =      j-TOMS,
  volume =       "25",
  number =       "3",
  pages =        "353--366",
  month =        sep,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/326147.326154;
                 http://www.acm.org/pubs/articles/journals/toms/1999-25-3/p353-berry/p353-berry.pdf;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p353-berry/;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p353-berry/#abstract;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p353-berry/#indterms",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 4 16:36:33 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A new implementation of the Modified Quadratic Shepard
                 Method for the interpolation of scattered data is
                 presented. QSHEP5D is a C++ translation of the original
                 Fortran-77 program QSHEP3D developed by Renka (for 2-D
                 and 3-D interpolation) which has been upgraded for 5-D
                 interpolation. This software development was motivated
                 by the need for interpolated 5-D hypervolumes of
                 environmental response variables produced by forest
                 growth and production models.",
  accepted =     "3 jun 1999",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "C++ implementation, modified Shepard method,
                 multivariate interpolation, netCDF file format",
  subject =      "Mathematics of Computing --- Mathematical Software
                 (G.4): Algorithm design and analysis; Mathematics of
                 Computing --- Numerical Analysis --- Interpolation
                 (G.1.1); General Terms: Algorithms, Measurement,
                 Performance",
}

@Article{LEcuyer:1999:BLC,
  author =       "Pierre L'Ecuyer and Richard Simard",
  title =        "Beware of Linear Congruential Generators with
                 Multipliers of the Form $a = \pm 2^q \pm 2^r$",
  journal =      j-TOMS,
  volume =       "25",
  number =       "3",
  pages =        "367--374",
  month =        sep,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/326147.326156",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 09:42:41 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p367-l_ecuyer/;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-3/p367-l_ecuyer/p367-l_ecuyer.pdf",
  abstract =     "Linear congruential random-number generators with
                 Mersenne prime modulus and multipliers of the form $a =
                 \pm 2^q \pm 2^r$ have been proposed recently. Their
                 main advantage is the availability of a simple and fast
                 implementation algorithm for such multipliers. This
                 note generalizes this algorithm, points out statistical
                 weaknesses of these multipliers when used in a
                 straightforward manner, and suggests in what context
                 they could be used safely.",
  accepted =     "24 Aug 1999",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "correlation test; linear congruential generators;
                 random number generation",
  subject =      "Mathematics of Computing --- Mathematical Software
                 (G.4): {\bf Algorithm design and analysis}; Computing
                 Methodologies --- Simulation and Modeling (I.6);
                 Mathematics of Computing --- Probability and Statistics
                 (G.3): {\bf Random number generation}; General Terms:
                 Algorithms, Experimentation, Measurement, Performance",
}

@Article{Kees:1999:CIN,
  author =       "Christopher E. Kees and Cass T. Miller",
  title =        "{C++} implementations of numerical methods for solving
                 differential-algebraic equations: design and
                 optimization considerations",
  journal =      j-TOMS,
  volume =       "25",
  number =       "4",
  pages =        "377--403",
  month =        dec,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/332242.334001",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 09:42:41 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/articles/journals/toms/1999-25-4/p377-kees/p377-kees.pdf;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-4/p377-kees/",
  abstract =     "Object-oriented programming can produce improved
                 implementations of complex numerical methods, but it
                 can also introduce a performance penalty. Since
                 computational simulation often requires intricate and
                 highly efficient codes, the performance penalty of
                 high-level techniques must always be weighed against
                 the improvements they enable. These issues are
                 addressed in a general object-oriented (OO) toolkit for
                 the numerical solution of differential-algebraic
                 equations (DAEs). The toolkit can be configured in
                 several different ways to solve DAE initial-value
                 problems with an adaptive multistep method. It contains
                 a wrapped version of the Fortran 77 code DASPK and a
                 translation of this to C++. Two C++ constructs for
                 assembling the tools are provided, as are two
                 implementations an important DAE test problem. Multiple
                 configurations of the toolkit for DAE test problems are
                 compared in order to assess the performance penalties
                 of C++. The mathematical methods and implementation
                 techniques are discussed in detail in order to provide
                 heuristics for efficient OO scientific programming and
                 to demonstrate the effectiveness of OO techniques in
                 managing complexity and producing better code. The
                 codes were tested on a variety of problems using
                 publicly available Fortran 77 and C++ compilers.
                 Extensive efficiency comparisons are presented in order
                 to isolate computationally inefficient OO techniques.
                 Techniques that caused difficulty in implementation and
                 maintenance are also highlighted. The comparisons
                 demonstrate that the majority of C++'s built-in support
                 for OO programming has a negligible effect on
                 performance, when used at sufficiently high levels, and
                 provides flexible and extensible software for numerical
                 methods.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithms, design, experimentation, languages,
                 performance, differential-algebraic equations",
  subject =      "Software --- Programming Languages --- Language
                 Classifications (D.3.2): {\bf C++}; Software ---
                 Programming Languages --- Language Classifications
                 (D.3.2): {\bf FORTRAN 77}; Mathematics of Computing ---
                 Numerical Analysis --- Ordinary Differential Equations
                 (G.1.7): {\bf Differential-algebraic equations};
                 Software --- Programming Techniques --- Object-oriented
                 Programming (D.1.5); Software --- Software Engineering
                 --- Coding Tools and Techniques (D.2.3): {\bf
                 Object-oriented programming}",
}

@Article{Duff:1999:FCS,
  author =       "Iain S. Duff and Jennifer A. Scott",
  title =        "A frontal code for the solution of sparse
                 positive-definite symmetric systems arising from
                 finite-element applications",
  journal =      j-TOMS,
  volume =       "25",
  number =       "4",
  pages =        "404--424",
  month =        dec,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/332242.332243;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-4/p404-duff/;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-4/p404-duff/p404-duff.pdf",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 09:42:41 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe the design, implementation, and
                 performance of a frontal code for the solution of large
                 sparse symmetric systems of linear finite-element
                 equations. The code is intended primarily for
                 positive-definite systems, since numerical pivoting is
                 not performed. The resulting software package, MA62,
                 will be included in the Harwell Subroutine Library. We
                 illustrate the performance of our new code on a range
                 of problems arising from real engineering and
                 industrial applications. The performance of the code is
                 compared with that of the Harwell Subroutine Library
                 general frontal solver MA42 and with other
                 positive-definite codes from the Harwell Subroutine
                 Library.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithms; finite-element equations; Gaussian
                 elimination; Level 3 BLAS; performance; sparse
                 symmetric linear equations; symmetric frontal method",
  subject =      "Mathematics of Computing --- Numerical Analysis ---
                 General (G.1.0): {\bf Numerical algorithms};
                 Mathematics of Computing --- Numerical Analysis ---
                 Numerical Linear Algebra (G.1.3); Mathematics of
                 Computing --- Numerical Analysis --- Numerical Linear
                 Algebra (G.1.3): {\bf Sparse, structured, and very
                 large systems (direct and iterative methods)}",
}

@Article{Dackland:1999:BAS,
  author =       "Krister Dackland and Bo K{\aa}gstr{\"{o}}m",
  title =        "Blocked algorithms and software for reduction of a
                 regular matrix pair to generalized {Schur} form",
  journal =      j-TOMS,
  volume =       "25",
  number =       "4",
  pages =        "425--454",
  month =        dec,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/332242.332244;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-4/p425-dackland/;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-4/p425-dackland/p425-dackland.pdf",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 09:42:41 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A two-stage blocked algorithm for reduction of a
                 regular matrix pair $(A,B)$ to upper
                 Hessenberg-triangular form is presented. In stage 1
                 $(A,B)$ is reduced to block upper Hessenberg-triangular
                 form using mainly level 3 (matrix-matrix) operations
                 that permit data reuse in the higher levels of a memory
                 hierarchy. In the second stage all but one of the $r$
                 subdiagonals of the block Hessenberg $A$-part are set
                 to zero using Givens rotations. The algorithm proceeds
                 in a sequence of supersweeps, each reducing $m$
                 columns. The updates with respect to row and column
                 rotations are organized to reference consecutive
                 columns of $A$ and $B$. To further improve the data
                 locality, all rotations produced in a supersweep are
                 stored to enable a left-looking reference pattern,
                 i.e., all updates are delayed until they are required
                 for the continuation of the supersweep. Moreover, we
                 present a blocked variant of the single-diagonal
                 double-shift QZ method for computing the generalized
                 Schur form of $(A,B)$ in upper Hessenberg-triangular
                 form. The blocking for improved data locality is done
                 similarly, now by restructuring the reference pattern
                 of the updates associated with the bulge chasing in the
                 QZ iteration. Timing results show that our new blocked
                 variants outperform the current LAPACK routines,
                 including drivers for the generalized eigenvalue
                 problem, by a factor 2--5 for sufficiently large
                 problems.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; blocked algorithms; generalized Schur
                 form; Hessenberg-triangular reduction; LAPACK; memory
                 hierarchy; parallelization; performance; QZ-algorithm",
  subject =      "Theory of Computation --- Analysis of Algorithms and
                 Problem Complexity --- Numerical Algorithms and
                 Problems (F.2.1); Mathematics of Computing ---
                 Numerical Analysis --- Numerical Linear Algebra
                 (G.1.3); Mathematics of Computing --- Mathematical
                 Software (G.4): {\bf Certification and testing};
                 Mathematics of Computing --- Mathematical Software
                 (G.4): {\bf Efficiency}; Mathematics of Computing ---
                 Mathematical Software (G.4): {\bf Portability**};
                 Mathematics of Computing --- Mathematical Software
                 (G.4): {\bf Reliability and robustness}",
}

@Article{Edwards:1999:CSC,
  author =       "John A. Edwards",
  title =        "Characteristic Spectra of the Curvature Functional:
                 a Numerical Study in Bifurcation",
  journal =      j-TOMS,
  volume =       "25",
  number =       "4",
  pages =        "455--475",
  month =        dec,
  year =         "1999",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/332242.332245;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-4/p455-edwards/;
                 http://www.acm.org/pubs/citations/journals/toms/1999-25-4/p455-edwards/p455-edwards.pdf",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 09:42:41 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A method is described for the eigenvalues of piecewise
                 smooth $C^2$ extremum-energy curves. Typical
                 interpolants are investigated within the framework of
                 their eigensystems, and conclusions are presented
                 concerning their natural modes of vibration, stability
                 state, and limits of existence. In the present
                 discussion the word ``spline'' means exclusively an
                 interpolating elastica.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "acoustics; algorithms; buckling; catastrophes;
                 degenerate critical points; deterministic chaos;
                 dynamical systems; eigenanalysis; elastica; elasticity;
                 energy extrema; generalized coordinates; modal
                 analysis; Morse theory; structural stability; theory;
                 variational methods; vibrations",
  subject =      "Mathematics of Computing --- Numerical Analysis ---
                 Interpolation (G.1.1): {\bf Spline and piecewise
                 polynomial interpolation}; Mathematics of Computing ---
                 Numerical Analysis --- Numerical Linear Algebra
                 (G.1.3): {\bf Determinants**}; Mathematics of Computing
                 --- Numerical Analysis --- Numerical Linear Algebra
                 (G.1.3): {\bf Eigenvalues and eigenvectors (direct and
                 iterative methods)}; Mathematics of Computing ---
                 Numerical Analysis --- Optimization (G.1.6): {\bf
                 Constrained optimization}; Mathematics of Computing ---
                 Numerical Analysis --- Ordinary Differential Equations
                 (G.1.7): {\bf Boundary value problems}; Computing
                 Methodologies --- Symbolic and Algebraic Manipulation
                 --- Algorithms (I.1.2): {\bf Algebraic algorithms};
                 Computer Applications --- Physical Sciences and
                 Engineering (J.2): {\bf Engineering}; Computer
                 Applications --- Physical Sciences and Engineering
                 (J.2): {\bf Physics}; Computer Applications ---
                 Computer-Aided Engineering (J.6): {\bf Computer-aided
                 design (CAD)}; Computer Applications --- Computer-Aided
                 Engineering (J.6): {\bf Computer-aided manufacturing
                 (CAM)}",
}

@Article{Ferris:2000:NCS,
  author =       "Michael C. Ferris and Michael P. Mesnier and Jorge J.
                 Mor{\'e}",
  title =        "{NEOS} and {Condor}: solving optimization problems
                 over the {Internet}",
  journal =      j-TOMS,
  volume =       "26",
  number =       "1",
  pages =        "1--18",
  month =        mar,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/347837.347842;
                 http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p1-ferris/;
                 http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p1-ferris/p1-ferris.pdf",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 09:42:41 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We discuss the use of Condor, a distributed resource
                 management system, as a provider of computational
                 resources for NEOS, an environment for solving
                 optimization problems over the Internet. We also
                 describe how problems are submitted and processed by
                 NEOS, and then scheduled and solved by Condor on
                 available (idle) workstations",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "automatic differentiation; complementarity problems;
                 computational servers; network computing; resource
                 management",
  subject =      "Mathematics of Computing --- Mathematical Software
                 (G.4); Computer Systems Organization ---
                 Computer-Communication Networks --- General (C.2.0);
                 Software --- Software Engineering --- General (D.2.0)",
}

@Article{Griewank:2000:ARI,
  author =       "Andreas Griewank and Andrea Walther",
  title =        "{Algorithm 799}: {Revolve}: an implementation of
                 checkpointing for the reverse or adjoint mode of
                 computational differentiation",
  journal =      j-TOMS,
  volume =       "26",
  number =       "1",
  pages =        "19--45",
  month =        mar,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/347837.347846",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 09:42:41 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p19-griewank/;
                 http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p19-griewank/p19-griewank.pdf",
  abstract =     "In its basic form, the reverse mode of computational
                 differentiation yields the gradient of a scalar-valued
                 function at a cost that is a small multiple of the
                 computational work needed to evaluate the function
                 itself. However, the corresponding memory requirement
                 is proportional to the run-time of the evaluation
                 program. Therefore, the practical applicability of the
                 reverse mode in its original formulation is limited
                 despite the availability of ever larger memory systems.
                 This observation leads to the development of
                 checkpointing schedules to reduce the storage
                 requirements. This article presents the function {\tt
                 revolve}, which generates checkpointing schedules that
                 are provably optimal with regard to a primary and a
                 secondary criterion. This routine is intended to be
                 used as an explicit ``controller'' for running a
                 time-dependent applications program.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{DeTisi:2000:RAS,
  author =       "Flavia {De Tisi} and Alba Valtulina",
  title =        "Remark on {Algorithm 761}: scattered-data surface
                 fitting that has the accuracy of a cubic polynomial",
  journal =      j-TOMS,
  volume =       "26",
  number =       "1",
  pages =        "46--48",
  month =        mar,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/347837.349795",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 09:42:41 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Akima:1996:ASS,Renka:1998:RA}.",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p46-de_tisi/;
                 http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p46-de_tisi/p46-de_tisi.pdf",
  abstract =     "Several improvements to the estimation of partial
                 derivatives in Algorithm 761 are presented. The
                 problems corrected are (1) in the calculation of the
                 probability weight in subroutine {\tt SDPD3P} which may
                 result in overflow, (2) in the calculation of final
                 weight in subroutine {\tt SDPD3P} which may result in
                 overflow, (3) in the computation of a determinant in
                 subroutine {\tt SDLEQN} which is not necessary, and (4)
                 in the computation of the condition number of a matrix
                 in subroutine {\tt SDLEQN} which generates very
                 different results for matrices that differ only in row
                 order.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "bivariate interpolation; interpolation; local
                 interpolation",
  subject =      "Software --- Programming Languages --- Language
                 Classifications (D.3.2): {\bf FORTRAN 77}; Mathematics
                 of Computing --- Numerical Analysis --- Interpolation
                 (G.1.1): {\bf Interpolation formulas}; Mathematics of
                 Computing --- Mathematical Software (G.4)",
}

@Article{Benner:2000:AFS,
  author =       "Peter Benner and Ralph Byers and Eric Barth",
  title =        "{Algorithm 800}: {Fortran 77} subroutines for
                 computing the eigenvalues of {Hamiltonian} matrices
                 {I}: the square-reduced method",
  journal =      j-TOMS,
  volume =       "26",
  number =       "1",
  pages =        "49--77",
  month =        mar,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/347837.347852",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 09:42:41 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p49-benner/;
                 http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p49-benner/p49-benner.pdf",
  abstract =     "This article describes LAPACK-based Fortran 77
                 subroutines for the reduction of a Hamiltonian matrix
                 to square-reduced form and the approximation of all its
                 eigenvalues using the implicit version of Van Loan's
                 method. The transformation of the Hamiltonian matrix to
                 a square-reduced form transforms a Hamiltonian
                 eigenvalue problem of order $ 2 n $ to a Hessenberg
                 eigenvalue problem of order $n$. The eigenvalues of the
                 Hamiltonian matrix are the square roots of those of the
                 Hessenberg matrix. Symplectic scaling and norm scaling
                 are provided, which, in some cases, improve the
                 accuracy of the computed eigenvalues. We demonstrate
                 the performance of the subroutines for several examples
                 and show how they can be used to solve some
                 control-theoretic problems.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "(square-reduced) algebraic Riccati equation;
                 eigenvalues; Hamiltonian matrix; skew-Hamiltonian
                 matrix",
  subject =      "Software --- Programming Languages --- Language
                 Classifications (D.3.2): {\bf FORTRAN 77}; Theory of
                 Computation --- Analysis of Algorithms and Problem
                 Complexity --- Numerical Algorithms and Problems
                 (F.2.1): {\bf Computations on matrices}; Mathematics of
                 Computing --- Numerical Analysis --- Numerical Linear
                 Algebra (G.1.3): {\bf Eigenvalues and eigenvectors
                 (direct and iterative methods)}; Mathematics of
                 Computing --- Mathematical Software (G.4): {\bf
                 Algorithm design and analysis}; Mathematics of
                 Computing --- Mathematical Software (G.4): {\bf
                 Certification and testing}; Mathematics of Computing
                 --- Mathematical Software (G.4): {\bf Documentation};
                 Mathematics of Computing --- Mathematical Software
                 (G.4): {\bf Efficiency}; Mathematics of Computing ---
                 Mathematical Software (G.4): {\bf Reliability and
                 robustness}",
}

@Article{Leydold:2000:ASR,
  author =       "Josef Leydold",
  title =        "Automatic Sampling with the Ratio-of-Uniforms Method",
  journal =      j-TOMS,
  volume =       "26",
  number =       "1",
  pages =        "78--98",
  month =        mar,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/347837.347863",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 09:42:41 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p78-leydold/;
                 http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p78-leydold/p78-leydold.pdf",
  abstract =     "Applying the ratio-of-uniforms method for generating
                 random variates results in very efficient, fast, and
                 easy-to-implement algorithms. However parameters for
                 every particular type of density must be precalculated
                 analytically. In this article we show, that the
                 ratio-of-uniforms method is also useful for the design
                 of a black-box algorithm suitable for a large class of
                 distributions, including all with log-concave
                 densities. Using polygonal envelopes and squeezes
                 results in an algorithm that is extremely fast. In
                 opposition to any other ratio-of-uniforms algorithm the
                 expected number of uniform random numbers is less than
                 two. Furthermore, we show that this method is in some
                 sense equivalent to transformed density rejection.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "adaptive method; log-concave; nonuniform;
                 random-number generation; ratio of uniforms; rejection
                 method; T-concave; universal method",
  subject =      "Mathematics of Computing --- Probability and
                 Statistics (G.3): {\bf Random number generation}",
}

@Article{Hu:2000:HHP,
  author =       "Y. Charlie Hu and Guohua Jin and S. Lennart Johnsson
                 and Dimitris Kehagias and Nadia Shalaby",
  title =        "{HPFBench}: a {High Performance Fortran} benchmark
                 suite",
  journal =      j-TOMS,
  volume =       "26",
  number =       "1",
  pages =        "99--149",
  month =        mar,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/347837.347872",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 09:42:41 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p99-hu/;
                 http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p99-hu/p99-hu.pdf",
  abstract =     "The High Performance Fortran (HPF) benchmark suite
                 HPFBench is designed for evaluating the HPF language
                 and compilers on scalable architectures. The
                 functionality of the benchmarks covers scientific
                 software library functions and application kernels that
                 reflect the computational structure and communication
                 patterns in fluid dynamic simulations, fundamental
                 physics, and molecular studies in chemistry and
                 biology. The benchmarks are characterized in terms of
                 FLOP count, memory usage, communication pattern, local
                 memory accesses, array allocation mechanism, as well as
                 operation and communication counts per iteration. The
                 benchmarks output performance evaluation metrics in the
                 form of elapsed times, FLOP rates, and communication
                 time breakdowns. We also provide a benchmark guide to
                 aid the choice of subsets of the benchmarks for
                 evaluating particular aspects of an HPF compiler.
                 Furthermore, we report an evaluation of an
                 industry-leading HPF compiler from the Portland Group
                 Inc. using the HPFBench benchmarks on the
                 distributed-memory IBM SP2",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "benchmarks; compilers; high performance Fortran",
  subject =      "Software --- Programming Languages --- Language
                 Classifications (D.3.2): {\bf Concurrent, distributed,
                 and parallel languages}; Mathematics of Computing ---
                 Numerical Analysis --- Numerical Linear Algebra
                 (G.1.3): {\bf Linear systems (direct and iterative
                 methods)}; Mathematics of Computing --- Mathematical
                 Software (G.4): {\bf Efficiency}; Mathematics of
                 Computing --- Mathematical Software (G.4): {\bf
                 Parallel and vector implementations}; Computing
                 Methodologies --- Simulation and Modeling ---
                 Applications (I.6.3); Computer Applications ---
                 Physical Sciences and Engineering (J.2): {\bf
                 Astronomy}; Computer Applications --- Physical Sciences
                 and Engineering (J.2): {\bf Chemistry}; Computer
                 Applications --- Life and Medical Sciences (J.3): {\bf
                 Biology and genetics}",
}

@Article{Coleman:2000:AAD,
  author =       "Thomas F. Coleman and Arun Verma",
  title =        "{ADMIT-1}: Automatic Differentiation and {MATLAB}
                 Interface Toolbox",
  journal =      j-TOMS,
  volume =       "26",
  number =       "1",
  pages =        "150--175",
  month =        mar,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/347837.347879;
                 http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p150-coleman/;
                 http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p150-coleman/p150-coleman.pdf",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 09:42:41 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "ADMIT-1 enables the computation of {\em sparse}
                 Jacobian and Hessian matrices, using automatic
                 differentiation technology, from a MATLAB environment.
                 Given a function to be differentiated, ADMIT-1 will
                 exploit sparsity if present to yield sparse derivative
                 matrices (in sparse MATLAB form). A generic automatic
                 differentiation tool, subject to some functionality
                 requirements, can be plugged into ADMIT-1; examples
                 include ADOL-C (C/C++ target functions) and ADMAT
                 (MATLAB target functions). ADMIT-1 also allows for the
                 calculation of gradients and has several other related
                 functions. This article provides an introduction to the
                 design and usage of ADMIT-1.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "automatic differentiation; computational
                 differentiation; efficient computation of gradient;
                 graph coloring; Jacobians and Hessians; user
                 interface",
  subject =      "Mathematics of Computing --- Numerical Analysis ---
                 General (G.1.0): {\bf Numerical algorithms};
                 Mathematics of Computing --- Numerical Analysis ---
                 Roots of Nonlinear Equations (G.1.5): {\bf Systems of
                 equations}; Mathematics of Computing --- Numerical
                 Analysis --- Optimization (G.1.6): {\bf Unconstrained
                 optimization}; Mathematics of Computing ---
                 Mathematical Software (G.4): {\bf MATLAB}",
}

@Article{Wise:2000:APP,
  author =       "Steven M. Wise and Andrew J. Sommese and Layne T.
                 Watson",
  title =        "{Algorithm 801}: {POLSYS\_PLP}: a partitioned linear
                 product homotopy code for solving polynomial systems of
                 equations",
  journal =      j-TOMS,
  volume =       "26",
  number =       "1",
  pages =        "176--200",
  month =        mar,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/347837.347885",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 09:42:41 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p176-wise/;
                 http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p176-wise/p176-wise.pdf",
  abstract =     "Globally convergent, probability-one homotopy methods
                 have proven to be very effective for finding all the
                 isolated solutions to polynomial systems of equations.
                 After many years of development, homotopy path trackers
                 based on probability-one homotopy methods are reliable
                 and fast. Now, theoretical advances reducing the number
                 of homotopy paths that must be tracked, and in the
                 handling of singular solutions, have made
                 probability-one homotopy methods even more practical.
                 POLSYS\_PLP consists of Fortran 90 modules for finding
                 all isolated solutions of a complex coefficient
                 polynomial system of equations. The package is intended
                 to be used in conjunction with HOMPACK90 (Algorithm
                 777), and makes extensive use of Fortran 90 derived
                 data types to support a partitioned linear product
                 (PLP) polynomial system structure. PLP structure is a
                 generalization of $m$-homogeneous structure, whereby
                 each component of the system can have a different
                 $m$-homogeneous structure. The code requires a PLP
                 structure as input, and although finding the optimal
                 PLP structure is a difficult combinatorial problem,
                 generally physical or engineering intuition about a
                 problem yields a very good structure. POLSYS\_PLP
                 employs a sophisticated power series end game for
                 handling singular solutions, and provides support for
                 problem definition both at a high level and via
                 hand-crafted code. Different PLP structures and their
                 corresponding B{\'e}zout numbers can be systematically
                 explored before committing to root finding.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "$m$-homogeneous; Chow-Yorke algorithm; curve tracking;
                 fixed point; globally convergent; homotopy methods;
                 partitioned linear product; probability-one; zero",
  subject =      "Software --- Programming Languages --- Language
                 Classifications (D.3.2): {\bf Fortran 90}; Mathematics
                 of Computing --- Numerical Analysis --- Roots of
                 Nonlinear Equations (G.1.5): {\bf Continuation
                 (homotopy) methods}; Mathematics of Computing ---
                 Numerical Analysis --- Roots of Nonlinear Equations
                 (G.1.5): {\bf Polynomials, methods for}; Mathematics of
                 Computing --- Numerical Analysis --- Roots of Nonlinear
                 Equations (G.1.5): {\bf Systems of equations};
                 Mathematics of Computing --- Mathematical Software
                 (G.4)",
}

@Article{Hormann:2000:AAG,
  author =       "Wolfgang H{\"o}rmann",
  title =        "{Algorithm 802}: an automatic generator for bivariate
                 log-concave distributions",
  journal =      j-TOMS,
  volume =       "26",
  number =       "1",
  pages =        "201--219",
  month =        mar,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/347837.347908",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 09:42:41 MDT 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p201-hormann/;
                 http://www.acm.org/pubs/citations/journals/toms/2000-26-1/p201-hormann/p201-hormann.pdf",
  abstract =     "Different automatic (also called universal or
                 black-box) methods have been suggested to sample from
                 univariate log-concave distributions. Our new automatic
                 algorithm for bivariate log-concave distributions is
                 based on the method of transformed density rejection.
                 In order to construct a hat function for a rejection
                 algorithm the bivariate density is transformed by the
                 logarithm into a concave function. Then it is possible
                 to construct a dominating function by taking the
                 minimum of several tangent planes, which are by
                 exponentiation transformed back into the original
                 scale. The choice of the points of contact is automated
                 using adaptive rejection sampling. This means that
                 points that are rejected by the rejection algorithm can
                 be used as additional points of contact. The article
                 describes the details how this main idea can be used to
                 construct Algorithm ALC2D that can generate random
                 pairs from all bivariate log-concave distributions with
                 known domain, computable density, and computable
                 partial derivatives.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "automatic generator; bivariate log-concave
                 distributions; rejection method; universal generator",
  subject =      "Software --- Programming Languages --- Language
                 Classifications (D.3.2); Mathematics of Computing ---
                 Probability and Statistics (G.3): {\bf Random number
                 generation}",
}

@Article{Boisvert:2000:ESI,
  author =       "Ronald F. Boisvert and Wayne R. Dyksen and Elias N.
                 Houstis",
  title =        "Editorial: special issue in honor of {John Rice}'s
                 65th birthday",
  journal =      j-TOMS,
  volume =       "26",
  number =       "2",
  pages =        "223--223",
  month =        jun,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/353474.354094",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:41 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  for =          "Special issue dedicated to John Rice on his 65th
                 birthday.",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Anonymous:2000:JRR,
  author =       "Anonymous",
  title =        "{John R. Rice}: biographical and professional notes",
  journal =      j-TOMS,
  volume =       "26",
  number =       "2",
  pages =        "225--226",
  month =        jun,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/353474.354105",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:41 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Houstis:2000:PIK,
  author =       "Elias N. Houstis and Ann C. Catlin and John R. Rice
                 and Vassilios S. Verykios and Naren Ramakrishnan and
                 Catherine E. Houstis",
  title =        "{PYTHIA-II}: a knowledge\slash database system for
                 managing performance data and recommending scientific
                 software",
  journal =      j-TOMS,
  volume =       "26",
  number =       "2",
  pages =        "227--253",
  month =        jun,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/353474.353475",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:41 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Often scientists need to locate appropriate software
                 for their problems and then select from among many
                 alternatives. We have previously proposed an approach
                 for dealing with this task by processing performance
                 data of the targeted software. This approach has been
                 tested using a customized implementation referred to as
                 PYTHIA. This experience made us realize the complexity
                 of the algorithmic discovery of knowledge from
                 performance data and of the management of these data
                 together with the discovered knowledge. To address this
                 issue, we created PYTHIA-II--a modular framework and
                 system which combines a general knowledge discovery in
                 databases (KDD) methodology and recommender system
                 technologies to provide advice about scientific
                 software/hardware artifacts. The functionality and
                 effectiveness of the system is demonstrated for two
                 existing performance studies using sets of software for
                 solving partial differential equations. From the
                 end-user perspective, PYTHIA-II allows users to specify
                 the problem to be solved and their computational
                 objectives. In turn, PYTHIA-II (i) selects the software
                 available for the user's problem (ii) suggests
                 parameter values, and (iii) assesses the recommendation
                 provided. PYTHIA-II provides all the necessary
                 facilities to set up database schemas for testing
                 suites and associated performance data in order to test
                 sets of software. Moreover, it allows easy interfacing
                 of alternative data mining and recommendation
                 facilities. PYTHIA-II is an open-ended system
                 implemented on public domain software and has been used
                 for performance evaluation in several different problem
                 domains.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  for =          "Special issue dedicated to John Rice on his 65th
                 birthday.",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ramakrishnan:2000:MVR,
  author =       "Naren Ramakrishnan and Calvin J. Ribbens",
  title =        "Mining and visualizing recommendation spaces for
                 elliptic {PDEs} with continuous attributes",
  journal =      j-TOMS,
  volume =       "26",
  number =       "2",
  pages =        "254--273",
  month =        jun,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/353474.353481",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:41 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this paper we extend previous work in mining
                 recommendation spaces based on symbolic problem
                 features to PDE problems with continuous-valued
                 attributes. We identify the research issues in mining
                 such spaces, present a dynamic programming algorithm
                 form the data-mining literature, and describe how a
                 priori domain metaknowledge can be used to control the
                 complexity of induction. A visualization aid for
                 continuous-valued recommendation spaces is also
                 outlined. Two case studies are presented to illustrate
                 our approach and tools: (i) a comparison of an
                 iterative and a direct linear system solver on nearly
                 singular problems, and (ii) a comparison of two
                 iterative solvers on problems posed on nonrectangular
                 domains. Both case studies involve continuously varying
                 problem and method parameters which strongly influence
                 the choice of best algorithm in particular cases. By
                 mining the results from thousands of PDE solves, we can
                 gain valuable insight into the relative performance of
                 these methods on similar problems.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  for =          "Special issue dedicated to John Rice on his 65th
                 birthday.",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Enright:2000:AAS,
  author =       "W. H. Enright",
  title =        "Accurate Approximate Solution of Partial Differential
                 Equations at Off-mesh Points",
  journal =      j-TOMS,
  volume =       "26",
  number =       "2",
  pages =        "274--292",
  month =        jun,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/353474.353482",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:41 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Numerical methods for partial differential equations
                 often determine approximations that are more accurate
                 at the set of discrete meshpoints than they are at the
                 ``off-mesh'' points in the domain of interest. These
                 methods are generally most effective if they are
                 allowed to adjust the location of the mesh points to
                 match the local behavior of the solution. Different
                 methods will typically generate their respective
                 approximations on incompatible, unstructured meshes,
                 and it can be difficult to evaluate the quality of a
                 particular solution, or to visualize important
                 properties of a solution. In this paper we will
                 introduce a generic approach which can be used to
                 generate approximate solution values at arbitrary
                 points in the domain of interest for any method that
                 determines approximations to the solution and low-order
                 derivatives at meshpoints. This approach is based on
                 associating a set of ``collocation'' points with each
                 mesh element and requiring that the local approximation
                 interpolate the meshpoint data and almost satisfy the
                 partial differential equation at the collocation
                 points. The accuracy associated with this
                 interpolation/collocation approach is consistent with
                 the ``meshpoint accuracy'' of the underlying method.
                 The approach that we develop applies to a large class
                 of methods and problems. It uses local information only
                 and is therefore particularly suitable for
                 implementation in a parallel or network computing
                 environment. Numerical examples are given for some
                 second-order problems in two and three dimensions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  for =          "Special issue dedicated to John Rice on his 65th
                 birthday.",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Grosz:2000:HVA,
  author =       "Lutz Grosz",
  title =        "How to Vectorize the Algebraic Multi-level Iteration",
  journal =      j-TOMS,
  volume =       "26",
  number =       "2",
  pages =        "293--309",
  month =        jun,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/353474.353483",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:41 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We consider the algebraic multilevel iteration (AMLI)
                 for the solution of systems of linear equations as they
                 arise form a finite-difference discretization on a
                 rectangular grid. Key operation is the matrix-vector
                 product, which can efficiently be executed on vector
                 and parallel-vector computer architectures if the
                 nonzero entries of the matrix are concentrated in a few
                 diagonals. In order to maintain this structure for all
                 matrices on all levels coarsening in alternating
                 directions is used. In some cases it is necessary to
                 introduce additional dummy grid hyperplanes. The data
                 movements in the restriction and prolongation are
                 crucial, as they produce massive memory conflicts on
                 vector architectures. By using a simple performance
                 model the best of the possible vectorization strategies
                 is automatically selected at runtime. Examples show
                 that on a Fujitsu VPP300 the presented implementation
                 of AMLI reaches about 85\% of the useful performance,
                 and scalability with respect to computing time can be
                 achieved.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  for =          "Special issue dedicated to John Rice on his 65th
                 birthday.",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ward:2000:ASM,
  author =       "William A. {Ward, Jr.}",
  title =        "{Algorithm 803}: a Simpler Macro Processor",
  journal =      j-TOMS,
  volume =       "26",
  number =       "2",
  pages =        "310--319",
  month =        jun,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/353474.353484",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:41 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Macro processors have been in the computing tool chest
                 since the late 1950's. Their use, though perhaps not
                 what it was in the heyday of assembly language
                 programming, is still widespread. In the past,
                 producing a full-featured macro processor has required
                 significant effort, similar to that required to
                 implement the front-end to a compiler augmented by
                 appropriate text substitution capabilities. The tool
                 described here adopts a different approach. The text
                 containing macro definitions and substitutions is, in a
                 sense, ``compiled'' to produce a program, and this
                 program must then be executed to produce the final
                 output.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  for =          "Special issue dedicated to John Rice on his 65th
                 birthday.",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Enright:2000:SIC,
  author =       "Wayne H. Enright and Ramanan Sivasothinathan",
  title =        "Superconvergent interpolants for collocation methods
                 applied to mixed-order {BVODEs}",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "323--351",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/358407.358410",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Continuous approximations to boundary value problems
                 in ordinary differential equations (BVODEs),
                 constructed using collocation at Gauss points, are more
                 accurate at the mesh points than at off-mesh points.
                 From these approximations, it is possible to construct
                 improved continuous approximations by extending the
                 high accuracy that is available at the mesh points to
                 off-mesh points. One possibility is the bootstrap
                 approach, which improves the accuracy of the
                 approximate solution at the off-mesh points in a
                 sequence of steps until the accuracy at the mesh points
                 and off-mesh points is consistent. A bootstrap approach
                 for systems of mixed-order BVODEs is developed to
                 improve approximate solutions produced by COLNEW, a
                 Gauss-collocation-based software package. An
                 implementation of this approach is discussed and
                 numerical results presented which confirm that the
                 improved approximations satisfy the predicted error
                 bounds and are relatively inexpensive to construct.",
  accepted =     "24 Nov 1999",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Liepelt:2000:RAN,
  author =       "Michael Liepelt and Klaus Schittkowski",
  title =        "Remark on Algorithm 746: new features of {PCOMP}: a
                 {Fortran} Code for Automatic Differentiation",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "352--362",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/358407.358412",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The software system PCOMP uses automatic
                 differentiation to calculate derivatives of functions
                 that are defined by the user in a modeling language
                 similar to Fortran. This symbolical representation is
                 converted into an intermediate code, which can be
                 interpreted to calculate function and derivative values
                 at run-time within machine accuracy. Furthermore, it is
                 possible to generate Fortran code for function and
                 gradient evaluation, which has to be compiled and
                 linked separately. The first version of PCOMP was
                 introduced in Dobmann et al. [1995]. In this article,
                 we describe a series of extensions and additional
                 features that have been implemented in the meantime.",
  accepted =     "20 dec 1999",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Marsaglia:2000:SMG,
  author =       "George Marsaglia and Wai Wan Tsang",
  title =        "A Simple Method for Generating Gamma Variables",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "363--372",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/358407.358414",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We offer a procedure for generating a gamma variate as
                 the cube of a suitably scaled normal variate. It is
                 fast and simple, assuming one has a fast way to
                 generate normal variables. In brief: generate a normal
                 variate $x$ and a uniform variate $U$ until $\ln(U) <
                 0.5x^2 + d - dv + d\ln(v)$, then return $dv$. Here, the
                 gamma parameter is $\alpha \geq 1$, and $v = (1 +
                 x/\sqrt{9d})^3$ with $d = \alpha - 1/3$. The efficiency
                 is high, exceeding 0.951, 0.981, 0.992, 0.996 at
                 $\alpha = 1,2,4,8$. The procedure can be made to run
                 faster by means of a simple squeeze that avoids the two
                 logarithms most of the time; return $dv$ if $U < 1 -
                 0.0331x^4$. We give a short C program for any $\alpha
                 \geq 1$, and show how to boost an $\alpha < 1$ into an
                 $\alpha > 1$. The gamma procedure is particularly fast
                 for C implementation if the normal variate is generated
                 in-line, via the {\tt \#define} feature. We include
                 such an inline version, based on our ziggurat method.
                 With it, and an inline uniform generator, gamma
                 variates can be produced in 400MHz CPUs at better than
                 1.3 million per second, with the parameter $\alpha$
                 changing from call to call.",
  accepted =     "14 Jan 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kearfott:2000:SCV,
  author =       "R. B. Kearfott and G. W. Walster",
  title =        "On Stopping Criteria in Verified Nonlinear Systems or
                 Optimization Algorithms",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "373--389",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/358407.358418",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Traditionally, iterative methods for nonlinear systems
                 use heuristic domain and range stopping criteria to
                 determine when accuracy tolerances have been met.
                 However, such heuristics can cause stopping at points
                 far from actual solutions, and can be unreliable due to
                 the effects of roundoff error or inaccuracies in
                 data.\par

                 In verified computations, rigorous determination of
                 when a set of bounds has met a tolerance can be done
                 analogously to the traditional approximate setting.
                 Nonetheless, the range tolerance possibly cannot be
                 met. If the criteria are used to determine when to stop
                 subdivision of $n$-dimensional bounds into subregions,
                 then failure of a range tolerance results in excessive,
                 unnecessary subdivision, and could make the algorithm
                 impractical.\par

                 On the other hand, interval techniques can detect when
                 inaccuracies or roundoff will not permit residual
                 bounds to be narrowed. These techniques can be
                 incorporated into {\it range thickness\/} stopping
                 criteria that complement the range stopping criteria.
                 In this note, the issue is first introduced and
                 illustrated with a simple example. The thickness
                 stopping criterion is then formally introduced and
                 analyzed. Third, inclusion of the criterion within a
                 general verified global optimization algorithm is
                 studied. An industrial example is presented. Finally,
                 consequences and implications are discussed.",
  accepted =     "21 Mar 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Alhargan:2000:ACA,
  author =       "Fayez A. Alhargan",
  title =        "Algorithms for the Computation of all {Mathieu}
                 Functions of Integer Orders",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "390--407",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/358407.358420",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The paper presents methods for the computation of all
                 Mathieu functions of integer order, which cover a large
                 range of $n$ and $h$; previous algorithms were limited
                 to small values of $n$. The algorithms are given in
                 sufficient details to enable straightforward
                 implementation. The algorithms can handle a large range
                 of the order $n$ (0-200) and the parameter $h$
                 (0-4$n$).",
  accepted =     "19 May 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Alhargan:2000:ASC,
  author =       "Fayez A. Alhargan",
  title =        "{Algorithm 804}: subroutines for the computation of
                 {Mathieu} functions of integer orders",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "408--414",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/358407.358422",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Computer subroutines in C++ for computing Mathieu
                 functions of integer orders are described. The core
                 routines for computing Mathieu characteristic numbers
                 and Mathieu coefficients are described in details, the
                 rest of the subroutines are standard implementation of
                 the series summations for each function. The routines
                 can handle a large range of the order $n$ and the
                 parameter $h$.",
  accepted =     "19 May 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kolda:2000:ACU,
  author =       "Tamara G. Kolda and Dianne P. O'Leary",
  title =        "{Algorithm 805}: computation and uses of the
                 semidiscrete matrix decomposition",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "415--435",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/358407.358424",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We derive algorithms for computing a semidiscrete
                 approximation to a matrix in the Frobenius and weighted
                 norms. The approximation is formed as a weighted sum of
                 outer products of vectors whose elements are $\pm 1$ or
                 0, so the storage required by the approximation is
                 quite small. We also present a related algorithm for
                 approximation of a tensor. Applications of the
                 algorithms are presented to data compression, and
                 information retrieval, and software is provided in C
                 and in Matlab.",
  accepted =     "18 May 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Mascagni:2000:ASS,
  author =       "Michael Mascagni and Ashok Srinivasan",
  title =        "{Algorithm 806}: {SPRNG}: a scalable library for
                 pseudorandom number generation",
  journal =      j-TOMS,
  volume =       "26",
  number =       "3",
  pages =        "436--461",
  month =        sep,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/358407.358427",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See correction \cite{Mascagni:2000:CAS}.",
  abstract =     "In this article we present background, rationale, and
                 a description of the Scalable Parallel Random Number
                 Generators (SPRNG) library. We begin by briefly
                 presenting some methods for parallel pseudorandom
                 number generation. We will focus on methods based on
                 parameterization, meaning that we will not consider
                 splitting methods. We describe parameterized versions
                 of the following pseudorandom number generators: (i)
                 linear congruential generators, (ii) shift-register
                 generators, and (iii) lagged-Fibonacci generators. We
                 briefly describe the methods, detail some advantages
                 and disadvantages of each method and recount results
                 from number theory that impact our understanding of
                 their quality in parallel applications. SPRNG was
                 designed around the uniform implementation of different
                 families of parameterized random number generators. We
                 then present a short description of SPRNG. The
                 description contained within this document is meant
                 only to outline the rationale behind and the
                 capabilities of SPRNG. Much more information, including
                 examples and detailed documentation aimed at helping
                 users with installing and using SPRNG on scalable
                 systems is available at the URL
                 \path=http://www.ncsa.uiuc.edu/Apps/SPRNG=. In our
                 description of SPRNG we discuss the random number
                 library as well as the suite of tests of randomness
                 that is an integral part of SPRNG. Random number tools
                 for parallel Monte Carlo applications must be subjected
                 to classical as well as new types of empirical tests of
                 randomness to eliminate generators that show defects
                 when used in scalable environments.",
  accepted =     "26 may 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Weideman:2000:MDM,
  author =       "J. A. C. Weideman and S. C. Reddy",
  title =        "A {MATLAB} Differentiation Matrix Suite",
  journal =      j-TOMS,
  volume =       "26",
  number =       "4",
  pages =        "465--519",
  month =        dec,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/365723.365727",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A software suite consisting of 17 MATLAB functions for
                 solving differential equations by the spectral
                 collocation (i.e., pseudospectral) method is presented.
                 It includes functions for computing derivatives of
                 arbitrary order corresponding to Chebyshev, Hermite,
                 Laguerre, Fourier, and sinc interpolants. Auxiliary
                 functions are included for incorporating boundary
                 conditions, performing interpolation using barycentric
                 formulas, and computing roots of orthogonal
                 polynomials. It is demonstrated how to use the package
                 for solving eigenvalue, boundary value, and initial
                 value problems arising in the fields of special
                 functions, quantum mechanics, nonlinear waves, and
                 hydrodynamic stability.",
  accepted =     "15 March 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kaufman:2000:OBS,
  author =       "Linda Kaufman",
  title =        "An Observation on Bisection Software for the Symmetric
                 Tridiagonal Eigenvalue Problem",
  journal =      j-TOMS,
  volume =       "26",
  number =       "4",
  pages =        "520--526",
  month =        dec,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/365723.365728",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this paper we discuss a small modification of the
                 bisection routines in EISPACK and LAPACK for finding a
                 few of the eigenvalues of a symmetric tridiagonal
                 matrix A. When the principal minors of the matrix A
                 yield good approximations to the desired eigenvalues,
                 these modifications can yield about 30 percent
                 reduction in the computation times.",
  accepted =     "27 June 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Filippone:2000:PLP,
  author =       "Salvatore Filippone and Michele Colajanni",
  title =        "{PSBLAS}: a Library for Parallel Linear Algebra
                 Computation on Sparse Matrices",
  journal =      j-TOMS,
  volume =       "26",
  number =       "4",
  pages =        "527--550",
  month =        dec,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/365723.365732",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Many computationally intensive problems in engineering
                 and science give rise to the solution of large, sparse,
                 linear systems of equations. Fast and efficient methods
                 for their solution are very important because these
                 systems usually occur in the innermost loop of the
                 computational scheme. Parallelization is often
                 necessary to achieve an acceptable level of
                 performance. This paper presents the design,
                 implementation, and interface of a library of Basic
                 Linear Algebra Subroutines for sparse matrices (PSBLAS)
                 which is specifically tailored to distributed memory
                 computers. PSBLAS enables easy, efficient and portable
                 implementations of parallel iterative solvers for
                 linear systems. The interface keeps in view a Single
                 Program Multiple Data programming model on distributed
                 memory machines. However, the architecture of the
                 library does not exclude an implementation in different
                 paradigms, such as those based on the shared memory
                 model.",
  accepted =     "5 July 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kaufman:2000:BRA,
  author =       "Linda Kaufman",
  title =        "Band Reduction Algorithms Revisited",
  journal =      j-TOMS,
  volume =       "26",
  number =       "4",
  pages =        "551--567",
  month =        dec,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/365723.365733",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this paper we explain some of the changes that have
                 been incorporated in the latest version of the LAPACK
                 subroutine for reducing a symmetric banded matrix to
                 tridiagonal form. These modifications improve the
                 performance for larger-bandwidth problems and reduce
                 the number of operations when accumulating the
                 transformations onto the identity matrix, by taking
                 advantage of the structure of the initial matrix. We
                 show that similar modifications can be made to the
                 LAPACK subroutines for reducing a symmetric positive
                 definite generalized eigenvalue problem to a standard
                 symmetric banded eigenvalue problem and for reducing a
                 general banded matrix to bidiagonal form to facilitate
                 the computation of the singular values of the matrix.",
  accepted =     "3 Aug 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ramakrishnan:2000:NGE,
  author =       "Naren Ramakrishnan and Ra{\'u}l E.
                 Vald{\'e}s-P{\'e}rez",
  title =        "Note on Generalization in Experimental Algorithmics",
  journal =      j-TOMS,
  volume =       "26",
  number =       "4",
  pages =        "568--580",
  month =        dec,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/365723.365734",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A recurring theme in mathematical software evaluation
                 is the generalization of rankings of algorithms on test
                 problems to build knowledge-based recommender systems
                 for algorithm selection. A key issue is to {\em
                 profile} algorithms in terms of the qualitative
                 characteristics of benchmark problems. In this
                 methodological note, we adapt a novel all-pairs
                 algorithm for the profiling task --- Given performance
                 rankings for $m$ algorithms on $n$ problem instances,
                 each described with $p$ features, identify a (minimal)
                 subset of $p$ that is useful for assessing the
                 selective superiority of an algorithm over another, for
                 all pairs of the $m$ algorithms. We show how techniques
                 presented in the mathematical software literature are
                 inadequate for such profiling purposes. In conclusion,
                 we also address various statistical issues underlying
                 the effective application of this technique.",
  accepted =     "3 Aug 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bischof:2000:FSB,
  author =       "Christian H. Bischof and Bruno Lang and Xiaobai Sun",
  title =        "A Framework for Symmetric Band Reduction",
  journal =      j-TOMS,
  volume =       "26",
  number =       "4",
  pages =        "581--601",
  month =        dec,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/365723.365735",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We develop an algorithmic framework for reducing the
                 bandwidth of symmetric matrices via orthogonal
                 similarity transformations. This framework includes the
                 reduction of full matrices to banded or tridiagonal
                 form and the reduction of banded matrices to narrower
                 banded or tridiagonal form, possibly in multiple steps.
                 Our framework leads to algorithms that require fewer
                 floating-point operations than do standard algorithms,
                 if only the eigenvalues are required. In addition, it
                 allows for space--time tradeoffs and enables or
                 increases the use of blocked transformations.",
  accepted =     "29 May 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bischof:2000:AST,
  author =       "Christian H. Bischof and Bruno Lang and Xiaobai Sun",
  title =        "{Algorithm 807}: {The SBR Toolbox}---software for
                 successive band reduction",
  journal =      j-TOMS,
  volume =       "26",
  number =       "4",
  pages =        "602--616",
  month =        dec,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/365723.365736",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a software toolbox for symmetric band
                 reduction via orthogonal transformations, together with
                 a testing and timing program. The toolbox contains
                 drivers and computational routines for the reduction of
                 full symmetric matrices to banded form and the
                 reduction of banded matrices to narrower banded or
                 tridiagonal form, with optional accumulation of the
                 orthogonal transformations, as well as repacking
                 routines for storage rearrangement. The functionality
                 and the calling sequences of the routines are
                 described, with a detailed discussion of the
                 ``control'' parameters that allow adaptation of the
                 codes to particular machine and matrix characteristics.
                 We also briefly describe the testing and timing program
                 included in the toolbox.",
  accepted =     "29 May 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Anderson:2000:RAF,
  author =       "Stuart Anderson",
  title =        "Remark on {Algorithm 723}: {Fresnel} integrals",
  journal =      j-TOMS,
  volume =       "26",
  number =       "4",
  pages =        "617--617",
  month =        dec,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/365723.365737",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  accepted =     "16 October 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Mascagni:2000:CAS,
  author =       "Michael Mascagni and Ashok Srinivasan",
  title =        "Corrigendum: {Algorithm 806}: {SPRNG}: a scalable
                 library for pseudorandom number generation",
  journal =      j-TOMS,
  volume =       "26",
  number =       "4",
  pages =        "618--619",
  month =        dec,
  year =         "2000",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/365723.365738",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Mascagni:2000:ASS}.",
  abstract =     "In this article we present background, rationale, and
                 a description of the Scalable Parallel Random Number
                 Generators (SPRNG) library. We begin by presenting some
                 methods for parallel pseudorandom number generation. We
                 will focus on methods based on parameterization,
                 meaning that we will not consider splitting methods
                 such as the leap-frog or blocking methods. We describe,
                 in detail, parameterized versions of the following
                 pseudorandom number generators: (i) linear congruential
                 generators, (ii) shift-register generators, and (iii)
                 lagged-Fibonacci generators. We briefly describe the
                 methods, detail some advantages and disadvantages of
                 each method, and recount results from number theory
                 that impact our understanding of their quality of
                 parallel applications. SPRNG was designed around the
                 uniform implementation of different families of
                 parameterized random number generators. We then present
                 a short description of SPRNG. The description contained
                 within this document is meant only to outline the
                 rationale behind and the capabilities of SPRNG. Much
                 more information, including examples and detailed
                 documentation aimed at helping users with putting and
                 using SPRNG on scalable systems is available at
                 http://sprng.cs.fsu.edu. In this description of SPRNG
                 we discuss the random-number generator library as well
                 as the suite of tests of randomness that is an integral
                 part of SPRNG. Random-number tools for parallel Monte
                 Carlo applications must be subjected to classical as
                 well as new types of empirical tests of randomness to
                 eliminate generators that show defects when used in
                 scalable environments.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithms; Design; Documentation; Experimentation;
                 lagged-Fibonacci generator; linear congruential
                 generator; parallel random-number generators;
                 Performance; random-number software; random-number
                 tests; Reliability; Standardization",
  subject =      "Primary Classification: D. Software D.3 PROGRAMMING
                 LANGUAGES

                 Additional Classification: D. Software D.3 PROGRAMMING
                 LANGUAGES D.3.2 Language Classifications

                 Nouns: FORTRAN; C++

                 G. Mathematics of Computing G.4 MATHEMATICAL SOFTWARE
                 Subjects: Efficiency; Documentation; Parallel and
                 vector implementations; Algorithm design and analysis;
                 Reliability and robustness",
}

@Article{Langtangen:2001:SSP,
  author =       "Hans Petter Langtangen and Otto Munthe",
  title =        "Solving Systems of Partial Differential Equations
                 using Object-Oriented Programming Techniques with
                 Coupled Heat and Fluid Flow as Example",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "1--26",
  month =        mar,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/382043.382045",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This paper exploits object-oriented implementation
                 techniques to facilitate the development of computer
                 codes for solving systems of coupled partial
                 differential equations. We show how to build a
                 simulator for equation systems by merging independent
                 solvers for each equation that enters the system. The
                 main goal is to obtain a rapid, robust, and reliable
                 software development process with extensive reuse of
                 implemented code. Coupled heat and fluid flow in pipes
                 is used as example for illustrating the implementation
                 techniques. We also present some results for the
                 particular case of temperature-dependent generalized
                 Newtonian fluid flow between two nonconcentric
                 cylinders. The general applicability of the approach is
                 discussed.",
  accepted =     "5 July 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "C++; coupled heat-fluid; diffpack; finite elements;
                 Languages, Measurement, Performance, Theory;
                 non-Newtonian fluids; object-oriented programming;
                 software development; systems of partial differential
                 equations",
  subject =      "Primary Classification: G. Mathematics of Computing
                 G.1 NUMERICAL ANALYSIS G.1.8 Partial Differential
                 Equations Subjects: Finite element methods

                 Additional Classification: D. Software D.1 PROGRAMMING
                 TECHNIQUES D.3 PROGRAMMING LANGUAGES D.3.2 Language
                 Classifications

                 Nouns: C++

                 I. Computing Methodologies I.6 SIMULATION AND
                 MODELING

                 K. Computing Milieux K.6 MANAGEMENT OF COMPUTING AND
                 INFORMATION SYSTEMS K.6.3 Software Management Subjects:
                 Software development",
}

@Article{Neumaier:2001:EPE,
  author =       "Arnold Neumaier and Tapio Schneider",
  title =        "Estimation of Parameters and Eigenmodes of
                 Multivariate Autoregressive Models",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "27--57",
  month =        mar,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/382043.382304",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Dynamical characteristics of a complex system can
                 often be inferred from analyses of a stochastic time
                 series model fitted to observations of the system.
                 Oscillations in geophysical systems, for example, are
                 sometimes characterized by principal oscillation
                 patterns, eigenmodes of estimated autoregressive (AR)
                 models of first order. This paper describes the
                 estimation of eigenmodes of AR models of arbitrary
                 order. AR processes of any order can be decomposed into
                 eigenmodes with characteristic oscillation periods,
                 damping times, and excitations. Estimated eigenmodes
                 and confidence intervals for the eigenmodes and their
                 oscillation periods and damping times can be computed
                 from estimated model parameters. As a computationally
                 efficient method of estimating the parameters of AR
                 models from high-dimensional data, a stepwise least
                 squares algorithm is proposed. This algorithm computes
                 model coefficients and evaluates criteria for the
                 selection of the model order stepwise for AR models of
                 successively decreasing order. Numerical simulations
                 indicate that, with the least squares algorithm, the AR
                 model coefficients and the eigenmodes derived from the
                 coefficients are estimated reliably and that the
                 approximate 95\% confidence intervals for the
                 coefficients and eigenmodes are rough approximations of
                 the confidence intervals inferred from the
                 simulations.",
  accepted =     "10 October 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Schneider:2001:AAM,
  author =       "Tapio Schneider and Arnold Neumaier",
  title =        "{Algorithm 808}: {ARfit}---a {Matlab} package for the
                 estimation of parameters and eigenmodes of multivariate
                 autoregressive models",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "58--65",
  month =        mar,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/382043.382316",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "{\sc ARfit} is a collection of Matlab modules for
                 modeling and analyzing multivariate time series with
                 autoregressive (AR) models. {\sc ARfit} contains
                 modules for fitting AR models to given time series
                 data, for analyzing eigenmodes of a fitted model, and
                 for simulating AR processes. {\sc ARfit} estimates the
                 parameters of AR models from given time series data
                 with a stepwise least squares algorithm that is
                 computationally efficient, in particular when the data
                 are high-dimensional. {\sc ARfit} modules construct
                 approximate confidence intervals for the estimated
                 parameters and compute statistics with which the
                 adequacy of a fitted model can be assessed. Dynamical
                 characteristics of the modeled time series can be
                 examined by means of a decomposition of a fitted AR
                 model into eigenmodes and associated oscillation
                 periods, damping times, and excitations. The {\sc
                 ARfit} module that performs the eigendecomposition of a
                 fitted model also constructs approximate confidence
                 intervals for the eigenmodes and their oscillation
                 periods and damping times.",
  accepted =     "10 October 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Leydold:2001:SUG,
  author =       "Josef Leydold",
  title =        "A simple universal generator for continuous and
                 discrete univariate {$T$}-concave distributions",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "66--82",
  month =        mar,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/382043.382322",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We use inequalities to design short universal
                 algorithms that can be used to generate random variates
                 from large classes of univariate continuous or discrete
                 distributions (including all log-concave
                 distributions). The expected time is uniformly bounded
                 over all these distributions. The algorithms can be
                 implemented in a few lines of high-level language code.
                 In opposition to other black-box algorithms hardly any
                 setup step is required, and thus it is superior in the
                 changing-parameter case.",
  accepted =     "27 November 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Morales:2001:APF,
  author =       "Jos{\'e} Luis Morales and Jorge Nocedal",
  title =        "{Algorithm 809}: {PREQN}: {Fortran 77} subroutines for
                 preconditioning the conjugate gradient method",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "83--91",
  month =        mar,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/382043.382343",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "PREQN is a package of Fortran 77 subroutines for
                 automatically generating preconditioners for the
                 conjugate gradient method. It is designed for solving a
                 sequence of linear systems $A_i x=b_i, \,\,
                 i=1,\dots,t$, where the coefficient matrices $A_i$ are
                 symmetric and positive definite and vary slowly. The
                 preconditioners are based on limited memory
                 quasi-Newton updating and are recommended for problems
                 in which: (i) the coefficient matrices are not
                 explicitly known and only matrix-vector products of the
                 form $A_i v$ can be computed; or (ii) the coefficient
                 matrices are not sparse. PREQN is written so that a
                 single call from a conjugate gradient routine performs
                 the preconditioning operation and stores information
                 needed for the generation of a new preconditioner.",
  accepted =     "26 October 2000",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Verdonk:2001:PRIa,
  author =       "Brigitte Verdonk and Annie Cuyt and Dennis
                 Verschaeren",
  title =        "A precision- and range-independent tool for testing
                 floating-point arithmetic {I}: basic operations, square
                 root, and remainder",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "92--118",
  month =        mar,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/382043.382404",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.win.ua.ac.be/~cant/ieeecc754.html",
  abstract =     "This paper introduces a precision- and
                 range-independent tool for testing the compliance of
                 hardware or software implementations of
                 (multiprecision) floating-point arithmetic with the
                 principles of the IEEE standards 754 and 854. The tool
                 consists of a driver program, offering many options to
                 test only specific aspects of the IEEE standards, and a
                 large set of test vectors, encoded in a
                 precision-independent syntax to allow the testing of
                 basic and extended hardware formats as well as
                 multiprecision floating-point implementations. The
                 suite of test vectors stems on one hand from the
                 integration and fully precision- and range-independent
                 generalization of existing hardware test sets, and on
                 the other hand from the systematic testing of exact
                 rounding for all combinations of round and sticky bits
                 that can occur. The former constitutes only 50\% of the
                 resulting test set. In the latter we especially focus
                 on hard-to-round cases. In addition, the test suite
                 implicitly tests properties of floating-point
                 operations, following the idea of Paranoia, and it
                 reports which of the three IEEE-compliant underflow
                 mechanisms is used by the floating-point implementation
                 under consideration. We also check whether that
                 underflow mechanism is used consistently. The tool is
                 backward compatible with the UCBTEST package and with
                 Coonen's test syntax.",
  accepted =     "23 February 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "arithmetic; floating-point testing; IEEE
                 floating-point standard; multiprecision; validation;
                 Verification",
  subject =      "Primary Classification: G. Mathematics of Computing
                 G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer
                 arithmetic\\
                 Additional Classification: D. Software D.3 PROGRAMMING
                 LANGUAGES D.3.0 General Subjects: Standards",
}

@Article{Verdonk:2001:PRIb,
  author =       "Brigitte Verdonk and Annie Cuyt and Dennis
                 Verschaeren",
  title =        "A precision- and range-independent tool for testing
                 floating-point arithmetic {II}: conversions",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "119--140",
  month =        mar,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/382043.382405",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.win.ua.ac.be/~cant/ieeecc754.html",
  abstract =     "The IEEE 754 and 854 standards for floating-point
                 arithmetic are essentially a specification of a
                 programming environment, encompassing aspects from
                 computer hardware, operating systems and compilers to
                 programming languages (see especially section 8). Part
                 I and II of this paper together describe a tool to test
                 floating-point implementations of arbitrary precision
                 and exponent range (hardware as well as software) for
                 compliance with the principles outlined in the IEEE
                 standards. The tool consists of a driver program,
                 together with a very large set of test vectors encoded
                 in a precision independent syntax.\par

                 In Part I we have covered the testing of the basic
                 operations +, -, $ \times $, /, the square root and
                 remainder functions. In Part II we describe the
                 extension of the test tool to deal with conversions
                 between floating-point formats, conversions between
                 floating-point and integer formats, the rounding of
                 floating-point numbers to integral values and last but
                 not least binary-decimal conversions. Conversions can
                 now be tested from a floating-point format of arbitrary
                 precision and exponent range to another arbitrary
                 smaller (larger) floating-point format as well as to
                 and from fixed hardware integer formats. Conversions
                 between the bases 2 and 10 can be tested for a number
                 of precisions ranging from single (24 bits), double (53
                 bits), long double or extended (64 bits) to quadruple
                 (113 bits) precision and a proper multiprecision (240
                 bits) format.\par

                 We conclude Part II with some applications of our test
                 tool and report on the results of testing various
                 floating-point implementations, meaning various
                 language-compiler-hardware combinations as well as
                 multiprecision libraries.",
  accepted =     "23 February 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "decimal floating-point arithmetic; floating-point
                 testing",
}

@Article{Bailey:2001:ASS,
  author =       "P. B. Bailey and W. N. Everitt and A. Zettl",
  title =        "{Algorithm 810}: The {SLEIGN2 Sturm--Liouville} Code",
  journal =      j-TOMS,
  volume =       "27",
  number =       "2",
  pages =        "143--192",
  month =        jun,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/383738.383739",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The SLEIGN2 code is based on the ideas and methods of
                 the original SLEIGN code of 1979. The main purpose of
                 the SLEIGN2 code is to compute eigenvalues and
                 eigenfunctions of regular and singular Sturm--Liouville
                 problems, with both separated and coupled boundary
                 conditions, and to approximate the continuous spectrum
                 in the singular case. The code uses a number of
                 different algorithms, some of which are new, and has a
                 user-friendly interface. In this paper the algorithms
                 and their implementation are discussed, and the class
                 of problems to which each algorithm applies is
                 identified.",
  accepted =     "14 February 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Luksan:2001:ANA,
  author =       "Ladislav Luk{\v{s}}an and Jan Vl{\v{c}}ek",
  title =        "{Algorithm 811}: {NDA}: algorithms for
                 nondifferentiable optimization",
  journal =      j-TOMS,
  volume =       "27",
  number =       "2",
  pages =        "193--213",
  month =        jun,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/383738.383740",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present four basic Fortran subroutines for
                 nondifferentiable optimization with simple bounds and
                 general linear constraints. Subroutine PMIN, intended
                 for minimax optimization, is based on a sequential
                 quadratic programming variable metric algorithm.
                 Subroutine PBUN and PNEW, intended for general
                 non-smooth problems, are based on bundle type methods.
                 Subroutine PVAR is based on special nonsmooth variable
                 metric methods. Besides the description of methods and
                 codes, we propose computational experiments which
                 demonstrate the efficiency of this approach.",
  accepted =     "14 February 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "minimax optimization, discrete Chebychev
                 approximation, sequential quadratic programming
                 methods, variable metric methods, general linear
                 constraints",
}

@Article{Andersen:2001:RFC,
  author =       "Bjarne S. Andersen and Jerzy Wa{\'s}niewski and Fred
                 G. Gustavson",
  title =        "A recursive formulation of {Cholesky} factorization of
                 a matrix in packed storage",
  journal =      j-TOMS,
  volume =       "27",
  number =       "2",
  pages =        "214--244",
  month =        jun,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/383738.383741",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A new compact way to store a symmetric or triangular
                 matrix called RPF for Recursive Packed Format is fully
                 described. Novel ways to transform RPF to and from
                 standard packed format are included. A new algorithm,
                 called RPC for Recursive Packed Cholesky, that operates
                 on the RPG format is presented. Algorithm RPC is basd
                 on level-3 BLAS and requires variants of algorithms
                 TRSM and SYRK that work on RPF. We call these RP\_TRSM
                 and RP\_SYRK and find that they do most of their work
                 by calling GEMM. It follows that most of the execution
                 time of RPC lies in GEMM. The advantage of this storage
                 scheme compared to traditional packed and full storage
                 is demonstrated. First, the RPC storage format uses the
                 minimal amount of storage for the symmetric or
                 triangular matrix. Second, RPC gives a level-3
                 implementation of Cholesky factorization whereas
                 standard packed implementations are only level 2.
                 Hence, the performance of our RPC implementation is
                 decidedly superior. Third, unlike fixed block size
                 algorithms, RPC, requires no block size tuning
                 parameter. We present performance measurements on
                 several current architectures that demonstrate
                 improvements over the traditional packed routines. Also
                 MSP parallel computations on the IBM SMP computer are
                 made. The graphs that are attached in Section 7 show
                 that the RPC algorithms are superior by a factor
                 between 1.6 and 7.4 for order around 1000, and between
                 1.9 and 10.3 for order around 3000 over the traditional
                 packed algorithms. For some architectures, the RPC
                 performance results are almost the same or even better
                 than the traditional full-storage algorithms results.",
  accepted =     "15 March 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cash:2001:ACS,
  author =       "J. R. Cash and G. Moore and R. W. Wright",
  title =        "An automatic continuation strategy for the solution of
                 singularly perturbed nonlinear boundary value
                 problems",
  journal =      j-TOMS,
  volume =       "27",
  number =       "2",
  pages =        "245--266",
  month =        jun,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/383738.383742",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In a recent paper, the present authors derived an
                 automatic continuation algorithm for the solution of
                 linear singular perturbation problems. The algorithm
                 was incorporated into two general-purpose codes for
                 solving boundary value problems, and it was shown to
                 deal effectively with a large test set of linear
                 problems. The present paper describes how the
                 continuation algorithm for linear problems can be
                 extended to deal with the nonlinear case. The results
                 of extensive numerical testing on a set of nonlinear
                 singular perturbation problems are given, and these
                 clearly demonstrate the efficacy of continuation for
                 solving such problems.",
  accepted =     "9 April 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Tsai:2001:ABO,
  author =       "Yi-Feng Tsai and Rida T. Farouki",
  title =        "{Algorithm 812}: {BPOLY}: an object-oriented library
                 of numerical algorithms for polynomials in {Bernstein}
                 form",
  journal =      j-TOMS,
  volume =       "27",
  number =       "2",
  pages =        "267--296",
  month =        jun,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/383738.383743",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The design, implementation, and testing of a C++
                 software library for univariate polynomials in
                 Bernstein form is described. By invoking the class
                 environment and operator overloading, each polynomial
                 in an expression is interpreted as an object compatible
                 with the arithmetic operations and other common
                 functions (subdivision, degree elevation,
                 differentiation and integration, composition, greatest
                 common divisor, real-root solving, etc.) for
                 polynomials in Bernstein form. The library allows
                 compact and intuitive implementation of lengthy
                 manipulations of Bernstein-form polynomials, which
                 often arise in computer graphics and computer-aided
                 design and manufacturing applications. A series of
                 empirical tests indicate that the library functions are
                 typically very accurate and reliable, even for
                 polynomials of surprisingly high degree.",
  accepted =     "4 May 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kierzenka:2001:BSB,
  author =       "Jacek Kierzenka and Lawrence F. Shampine",
  title =        "A {BVP} solver based on residual control and the
                 {Matlab PSE}",
  journal =      j-TOMS,
  volume =       "27",
  number =       "3",
  pages =        "299--316",
  month =        sep,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/502800.502801",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Our goal was to make it as easy as possible to solve a
                 large class of boundary value problems (BVPs) for
                 ordinary differential equations in the Matlab problem
                 solving environment (PSE). We present here theoretical
                 and software developments resulting in bvp4c, a capable
                 BVP solver that is exceptionally easy to use.",
  accepted =     "1 May 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Yang:2001:CPD,
  author =       "Dow-Yung Yang and Ananth Grama and Vivek Sarin and
                 Naren Ramakrishnan",
  title =        "Compression of particle data from hierarchical
                 approximate methods",
  journal =      j-TOMS,
  volume =       "27",
  number =       "3",
  pages =        "317--339",
  month =        sep,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/502800.502802",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article presents an analytical and computational
                 framework for the compression of particle data
                 resulting from hierarchical approximate treecodes such
                 as the {\em Barnes--Hut} and {\em Fast Multipole
                 Methods}. Due to approximations introduced by
                 hierarchical methods, various parameters (such as
                 position, velocity, acceleration, potential) associated
                 with a particle can be bounded by distortion radii.
                 Using this distortion radii, we develop storage schemes
                 that guarantee error bounds while maximizing
                 compression. Our schemes make extensive use of spatial
                 and temporal coherence of particle behavior and yield
                 compression ratios higher than 12:1 over raw data, and
                 6:1 over gzipped (LZ) raw data for selected simulation
                 instances. We demonstrate that for uniform
                 distributions with 2M particles, storage requirements
                 can be reduced from 24 MB to about 1.8 MB (about 7 bits
                 per particle per timestep) for storing particle
                 positions. This is significant because it enables
                 faster storage/retrieval, better temporal resolution,
                 and improved analysis. Our results are shown to scale
                 from small systems (2K particles) to much larger
                 systems (over 2M particles). The associated algorithm
                 is asymptotically optimal in computation time ($O(n)$)
                 with a small constant. Our implementations are
                 demonstrated to run extremely fast---much faster than
                 the time it takes to compute a single time-step
                 advance. In addition, our compression framework relies
                 on a natural hierarchical representation upon which
                 other analysis tasks such as segmented and window
                 retrieval can be built.",
  accepted =     "23 July 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Astrophysics; Barnes--Hut; data compression and
                 analysis; Fast Multipole Method; materials simulation;
                 molecular dynamics; particle dynamics",
}

@Article{Birgin:2001:ASS,
  author =       "Ernesto G. Birgin and Jos{\'e} Mario Mart{\'\i}nez and
                 Marcos Raydan",
  title =        "{Algorithm 813}: {SPG}---Software for
                 {Convex-Constrained Optimization}",
  journal =      j-TOMS,
  volume =       "27",
  number =       "3",
  pages =        "340--349",
  month =        sep,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/502800.502803",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Fortran 77 software implementing the SPG method is
                 introduced. SPG is a nonmonotone projected gradient
                 algorithm for solving large-scale convex-constrained
                 optimization problems. It combines the classical
                 projected gradient method with the spectral gradient
                 choice of steplength and a nonmonotone line-search
                 strategy. The user provides objective function and
                 gradient values, and projections onto the feasible set.
                 Some recent numerical tests are reported on very large
                 location problems, indicating that SPG is substantially
                 more efficient than existing general-purpose software
                 on problems for which projections can be computed
                 efficiently.",
  accepted =     "6 July 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; Bound constrained problems; large-scale
                 problems; nonmonotone line search; projected gradients;
                 spectral gradient method",
  subject =      "Primary Classification: D. Software D.3 PROGRAMMING
                 LANGUAGES D.3.2 Language Classifications

                 Additional Classification: G. Mathematics of Computing
                 G.1 NUMERICAL ANALYSIS G.1.6 Optimization Subjects:
                 Gradient methods G.4 MATHEMATICAL SOFTWARE",
}

@Article{Azulay:2001:RSM,
  author =       "David-Olivier Azulay and Jean-Fran{\c{c}}ois Pique",
  title =        "A revised simplex method with integer {$Q$}-matrices",
  journal =      j-TOMS,
  volume =       "27",
  number =       "3",
  pages =        "350--360",
  month =        sep,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/502800.502804",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe a modification of the simplex formulas in
                 which Q-matrices are used to implement exact
                 computations with an integer multiprecision library.
                 Our motivation comes from the need for efficient and
                 exact incremental solvers in the implementation of
                 constraint solving languages such as Prolog. We explain
                 how to reformulate the problem and the different steps
                 of the simplex algorithm. We compare some measurements
                 obtained with integer and rational computations.",
  accepted =     "26 July 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Benson:2001:CSP,
  author =       "Steven J. Benson and Lois Curfman McInnes and Jorge J.
                 Mor{\'e}",
  title =        "A case study in the performance and scalability of
                 optimization algorithms",
  journal =      j-TOMS,
  volume =       "27",
  number =       "3",
  pages =        "361--376",
  month =        sep,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/502800.502805",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We analyze the performance and scalabilty of
                 algorithms for the solution of large optimization
                 problems on high-performance parallel architectures.
                 Our case study uses the GPCG (gradient projection,
                 conjugate gradient) algorithm for solving
                 bound-constrained convex quadratic problems. Our
                 implementation of the GPCG algorithm within the Toolkit
                 for Advanced Optimization (TAO) is available for a wide
                 range of high-performance architectures and has been
                 tested on problems with over 2.5 million variables. We
                 analyze the performance as a function of the number of
                 variables, the number of free variables, and the
                 preconditioner. In addition, we discuss how the
                 software design facilitates algorithmic comparisons.",
  accepted =     "10 August 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Smith:2001:AFS,
  author =       "David M. Smith",
  title =        "{Algorithm 814}: {Fortran 90} software for
                 floating-point multiple precision arithmetic, gamma and
                 related functions",
  journal =      j-TOMS,
  volume =       "27",
  number =       "4",
  pages =        "377--387",
  month =        dec,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/504210.504211",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 13 08:49:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A collection of Fortran 90 routines for evaluating the
                 Gamma function and related functions using the FM
                 multiple-precision arithmetic package.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Amestoy:2001:ACT,
  author =       "Patrick R. Amestoy and Iain S. Duff and Jean-Yves
                 L'Excellent and Xiaoye S. Li",
  title =        "Analysis and Comparison of Two General Sparse Solvers
                 for Distributed Memory Computers",
  journal =      j-TOMS,
  volume =       "27",
  number =       "4",
  pages =        "388--421",
  month =        dec,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/504210.504212",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 13 08:49:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This paper provides a comprehensive study and
                 comparison of two state-of-the-art direct solvers for
                 large sparse sets of linear equations on large-scale
                 distributed-memory computers. One is a multifrontal
                 solver called MUMPS, the other is a supernodal solver
                 called superLU. We describe the main algorithmic
                 features of the two solvers and compare their
                 performance characteristics with respect to
                 uniprocessor speed, interprocessor communication, and
                 memory requirements. For both solvers, preorderings for
                 numerical stability and sparsity play an important role
                 in achieving high parallel efficiency. We analyse the
                 results with various ordering algorithms. Our
                 performance analysis is based on data obtained from
                 runs on a 512-processor Cray T3E using a set of
                 matrices from real applications. We also use regular 3D
                 grid problems to study the scalability of the two
                 solvers.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gunnels:2001:FFL,
  author =       "John A. Gunnels and Fred G. Gustavson and Greg M.
                 Henry and Robert A. van de Geijn",
  title =        "{FLAME}: {Formal Linear Algebra Methods Environment}",
  journal =      j-TOMS,
  volume =       "27",
  number =       "4",
  pages =        "422--455",
  month =        dec,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/504210.504213",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 13 08:49:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Since the advent of high-performance
                 distributed-memory parallel computing, the need for
                 intelligible code has become ever greater. The
                 development and maintenance of libraries for these
                 architectures is simply too complex to be amenable to
                 conventional approaches to implementation. Attempts to
                 employ traditional methodology have led, in our
                 opinion, to the production of an abundance of
                 anfractuous code that is difficult to maintain and
                 almost impossible to upgrade. Having struggled with
                 these issues for more than a decade, we have concluded
                 that a solution is to apply a technique from
                 theoretical computer science, formal derivation, to the
                 development of high-performance linear algebra
                 libraries. We think the resulting approach results in
                 aesthetically pleasing, coherent code that greatly
                 facilitates intelligent modularity and high performance
                 while enhancing confidence in its correctness. Since
                 the technique is language-independent, it lends itself
                 equally well to a wide spectrum of programming
                 languages (and paradigms) ranging from C and Fortran to
                 C++ and Java. In this paper, we illustrate our
                 observations by looking at the Formal Linear Algebra
                 Methods Environment (FLAME), a framework that
                 facilitates the derivation and implementation of linear
                 algebra algorithms on sequential architectures. This
                 environment demonstrates that lessons learned in the
                 distributed-memory world can guide us toward better
                 approaches even in the sequential world. We present
                 performance experiments on the Intel (R) Pentium (R)
                 III processor that demonstrate that high performance
                 can be attained by coding at a high level of
                 abstraction.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Festa:2001:AFS,
  author =       "Paola Festa and Panos M. Pardalos and Mauricio G. C.
                 Resende",
  title =        "{Algorithm 815}: {FORTRAN} subroutines for computing
                 approximate solutions of feedback set problems using
                 {GRASP}",
  journal =      j-TOMS,
  volume =       "27",
  number =       "4",
  pages =        "456--464",
  month =        dec,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/504210.504214",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 13 08:49:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We propose FORTRAN subroutines for approximately
                 solving the feedback vertex and arc set problems on
                 directed graphs using a Greedy Randomized Adaptive
                 Search Procedure (GRASP). Implementation and usage of
                 the package is outlined and computational experiments
                 are reported illustrating solution quality as a
                 function of running time.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithms; Combinatorial optimization; feedback set
                 problems; FORTRAN subroutines; graph bipartization;
                 GRASP; local search; Performance",
  subject =      "Primary Classification: G. Mathematics of Computing
                 G.1 NUMERICAL ANALYSIS G.1.6 Optimization Subjects:
                 Integer programming

                 Additional Classification: G. Mathematics of Computing
                 G.2 DISCRETE MATHEMATICS G.2.1 Combinatorics Subjects:
                 Combinatorial algorithms G.m MISCELLANEOUS",
}

@Article{Engelborghs:2002:NBA,
  author =       "K. Engelborghs and T. Luzyanina and D. Roose",
  title =        "Numerical bifurcation analysis of delay differential
                 equations using {DDE-BIFTOOL}",
  journal =      j-TOMS,
  volume =       "28",
  number =       "1",
  pages =        "1--21",
  month =        mar,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/513001.513002",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe {DDE-BIFTOOL}, a Matlab package for
                 numerical bifurcation analysis of systems of delay
                 differential equations with several fixed, discrete
                 delays. The package implements continuation of steady
                 state solutions and periodic solutions and their
                 stability analysis. It also computes and continues
                 steady state fold and Hopf bifurcations and, from the
                 latter, it can switch to the emanating branch of
                 periodic solutions. We describe the numerical methods
                 upon which the package is based and illustrate its
                 usage and capabilities through analysing three
                 examples: two models of coupled neurons with delayed
                 feedback and a model of two oscillators coupled with
                 delay.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gockenbach:2002:EAI,
  author =       "Mark S. Gockenbach and Daniel R. Reynolds and Peng
                 Shen and William W. Symes",
  title =        "Efficient and automatic implementation of the adjoint
                 state method",
  journal =      j-TOMS,
  volume =       "28",
  number =       "1",
  pages =        "22--44",
  month =        mar,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/513001.513003",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Combination of object-oriented programming with
                 automatic differentiation techniques facilitates the
                 solution of data fitting, control, and design problems
                 driven by explicit time stepping schemes for
                 initial-boundary value problems. The C++ class {\tt
                 fdtd} takes a complete specification of a single step,
                 along with some associated code, and assembles from it
                 a complete simulator, along with the linearized and
                 adjoint simulations. The result is a (nonlinear)
                 operator in the sense of the Hilbert Class Library
                 (HCL), a C++ software package for optimization. The HCL
                 operator so produced links directly with any of the HCL
                 optimization algorithms. Moreover, the performance of
                 simulators constructed in this way is equivalent to
                 that of optimized Fortran implementations.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gansterer:2002:EDC,
  author =       "Wilfried N. Gansterer and Robert C. Ward and Richard
                 P. Muller",
  title =        "An Extension of the Divide-and-Conquer Method for a
                 Class of Symmetric Block-Tridiagonal Eigenproblems",
  journal =      j-TOMS,
  volume =       "28",
  number =       "1",
  pages =        "45--58",
  month =        mar,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/513001.513004",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A divide-and-conquer method for computing eigenvalues
                 and eigenvectors of a block-tridiagonal matrix with
                 rank-one off-diagonal blocks is presented. The
                 implications of unbalanced merging operations due to
                 unequal block sizes are analyzed and illustrated with
                 numerical examples. It is shown that an unfavorable
                 order for merging blocks in the synthesis phase of the
                 algorithm may lead to a significant increase of the
                 arithmetic complexity. A strategy to determine a good
                 merging order which is at least close to optimal in all
                 cases is given. The method has been implemented and
                 applied to test problems from a Quantum Chemistry
                 application.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hopkins:2002:RCA,
  author =       "Tim Hopkins",
  title =        "Renovating the {Collected Algorithms from ACM}",
  journal =      j-TOMS,
  volume =       "28",
  number =       "1",
  pages =        "59--74",
  month =        mar,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/513001.513005",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Since 1960 the Association for Computing Machinery has
                 published a series of refereed algorithm
                 implementations known as the Collected Algorithms of
                 the ACM (CALGO). Most of those published since 1975 are
                 mathematical algorithms, and many of them remain useful
                 today. In this paper we describe measures that have
                 been taken to bring some 400 of these latter codes to
                 an up-to-date and consistent state.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Robinson:2002:ARA,
  author =       "Ian Robinson and Michael Hill",
  title =        "{Algorithm 816}: {\em r2d2lri\/}: an algorithm for
                 automatic two-dimensional cubature",
  journal =      j-TOMS,
  volume =       "28",
  number =       "1",
  pages =        "75--100",
  month =        mar,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/513001.513006",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "{\em r2d2lri} is a non-adaptive algorithm implemented
                 in C++ for performing automatic cubature over a wide
                 variety of finite and non-finite two-dimensional
                 domains. The core integrator uses a sixth-order Sidi
                 transformation applied to a sequence of embedded
                 lattice rules in such a fashion as to incur virtually
                 no computational overhead. Even for integrals over
                 non-finite domains, for which several non-finite to
                 finite transformations may be attempted, the algorithm
                 remains very fast. Performance data is presented which
                 demonstrates both the effectiveness and efficiency of
                 {\em r2d2lri}, taking into account the number of
                 function evaluations needed and the execution speed.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bertolazzi:2002:APG,
  author =       "Enrico Bertolazzi and Gianmarco Manzini",
  title =        "{Algorithm 817}: {P2MESH}: generic object-oriented
                 interface between {$2$-D} unstructured meshes and
                 {FEM\slash FVM}-based {PDE} solvers",
  journal =      j-TOMS,
  volume =       "28",
  number =       "1",
  pages =        "101--132",
  month =        mar,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/513001.513007",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The software interface P2MESH is a collection of C++
                 class templates suitable for developing prototypes of
                 high-performance PDE solvers on unstructured 2-D
                 meshes. P2MESH supports several discretization methods
                 on triangles and quadrilaterals, such as Finite Volumes
                 or Finite Elements. The design philosophy of P2MESH
                 does not consider neither specific model problems nor
                 built-in approximation algorithms. The software package
                 is of general purpose and it may also be used as a
                 building block in the implementation of numerical both
                 for engineering applications and mathematical
                 problems.",
  accepted =     "21 March 2002",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Boisvert:2002:PSI,
  author =       "Ronald F. Boisvert and Jack J. Dongarra",
  title =        "Preface to the special issue on the {Basic Linear
                 Algebra Subprograms (BLAS)}",
  journal =      j-TOMS,
  volume =       "28",
  number =       "2",
  pages =        "133--134",
  month =        jun,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/567806.567812",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Blackford:2002:USB,
  author =       "L. Susan Blackford and James Demmel and Jack Dongarra
                 and Iain Duff and Sven Hammarling and Greg Henry and
                 Michael Heroux and Linda Kaufman and Andrew Lumsdaine
                 and Antoine Petitet and Roldan Pozo and Karin Remington
                 and R. Clint Whaley",
  title =        "An updated set of {Basic Linear Algebra Subprograms
                 (BLAS)}",
  journal =      j-TOMS,
  volume =       "28",
  number =       "2",
  pages =        "135--151",
  month =        jun,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/567806.567807",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This paper expands the specification of a set of
                 kernel routines for linear algebra, historically called
                 the Basic Linear Algebra Subprograms and commonly known
                 as the BLAS.\par

                 Numerical linear algebra, particularly the solution of
                 linear systems of equations, linear least squares
                 problems, eigenvalue problems and singular value
                 problems, is fundamental to most calculations in
                 scientific computing, and is often the computationally
                 intense part of such calculations. Designers of
                 computer programs involving linear algebraic operations
                 have frequently chosen to implement certain low level
                 operations, such as the dot product or the matrix
                 vector product, as separate subprograms. This may be
                 observed both in many published codes and in codes
                 written for specific applications at many computer
                 installations.\par

                 A major aim of the standards defined in this paper is
                 to enable linear algebra libraries (both public domain
                 and commercial) to interoperate efficiently, reliably
                 and easily.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Li:2002:DIT,
  author =       "Xiaoye S. Li and James W. Demmel and David H. Bailey
                 and Greg Henry and Yozo Hida and Jimmy Iskandar and
                 William Kahan and Suh Y. Kang and Anil Kapur and
                 Michael C. Martin and Brandon J. Thompson and Teresa
                 Tung and Daniel J. Yoo",
  title =        "Design, implementation and testing of extended and
                 mixed precision {BLAS}",
  journal =      j-TOMS,
  volume =       "28",
  number =       "2",
  pages =        "152--205",
  month =        jun,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/567806.567808",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This paper describes the design rationale, a C
                 implementation, and conformance testing of a subset of
                 the new Standard for the BLAS (Basic Linear Algebra
                 Subroutines): Extended and Mixed Precision BLAS.
                 Permitting higher internal precision and mixed
                 input\slash output types and precisions allows us to
                 implement some algorithms that are simpler, more
                 accurate, and sometimes faster than possible without
                 these features. The new BLAS are challenging to
                 implement and test because there are many more
                 subroutines than in the existing Standard, and because
                 we must be able to assess whether a higher precision is
                 used for internal computations than is used for either
                 input or output variables. We have therefore developed
                 an automated process of generating and systematically
                 testing these routines. Our methodology is applicable
                 to languages besides C. In particular, our algorithms
                 used in the testing code will be valuable to all other
                 BLAS implementors. Our extra precision routines achieve
                 excellent performance---close to half of the machine
                 peak Megaflop rate even for the Level 2 BLAS, when the
                 data access is stride one.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accurate floating-point summation",
}

@Article{Bindel:2002:CGR,
  author =       "David Bindel and James Demmel and William Kahan and
                 Osni Marques",
  title =        "On computing {Givens} rotations reliably and
                 efficiently",
  journal =      j-TOMS,
  volume =       "28",
  number =       "2",
  pages =        "206--238",
  month =        jun,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/567806.567809",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We consider the efficient and accurate computation of
                 Givens rotations. When $f$ and $g$ are positive real
                 numbers, this simply amounts to computing the values of
                 $c = f/\sqrt{f^2+g^2}$, $s = g/\sqrt{f^2+g^2}$, and $r
                 = \sqrt{f^2+g^2}$. This apparently trivial computation
                 merits closer consideration for the following three
                 reasons. First, while the definitions of $c$, $s$ and
                 $r$ seem obvious in the case of two nonnegative
                 arguments $f$ and $g$, there is enough freedom of
                 choice when one or more of $f$ and $g$ are negative,
                 zero or complex that LAPACK auxiliary routines SLARTG,
                 CLARTG, SLARGV and CLARGV can compute rather different
                 values of $c$, $s$ and $r$ for mathematically identical
                 values of $f$ and $g$. To eliminate this unnecessary
                 ambiguity, the BLAS Technical Forum chose a single
                 consistent definition of Givens rotations that we will
                 justify here. Second, computing accurate values of $c$,
                 $s$ and $r$ as efficiently as possible and reliably
                 despite over/underflow is surprisingly complicated. For
                 complex Givens rotations, the most efficient formulas
                 require only one real square root and one real divide
                 (as well as several much cheaper additions and
                 multiplications), but a reliable implementation using
                 only working precision has a number of cases. On a Sun
                 Ultra-10, the new implementation is slightly faster
                 than the previous LAPACK implementation in the most
                 common case, and 2.7 to 4.6 times faster than the
                 corresponding vendor, reference or ATLAS routines. It
                 is also more reliable; all previous codes occasionally
                 suffer from large inaccuracies due to over/underflow.
                 For real Givens rotations there are also improvements
                 in speed and accuracy, though not as striking. Third,
                 the design process that led to this reliable
                 implementation is quite systematic, and could be
                 applied to the design of similarly reliable
                 subroutines.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Duff:2002:OSB,
  author =       "Iain S. Duff and Michael A. Heroux and Roldan Pozo",
  title =        "An overview of the {Sparse Basic Linear Algebra
                 Subprograms}: {The} new standard from the {BLAS
                 Technical Forum}",
  journal =      j-TOMS,
  volume =       "28",
  number =       "2",
  pages =        "239--267",
  month =        jun,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/567806.567810",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We discuss the interface design for the Sparse Basic
                 Linear Algebra Subprograms (BLAS), the kernels in the
                 recent standard from the BLAS Technical Forum that are
                 concerned with unstructured sparse matrices. The
                 motivation for such a standard is to encourage portable
                 programming while allowing for library-specific
                 optimizations. In particular, we show how this
                 interface can shield one from concern over the specific
                 storage scheme for the sparse matrix. This design makes
                 it easy to add further functionality to the sparse BLAS
                 in the future. We illustrate the use of the Sparse BLAS
                 with examples in the three supported programming
                 languages, Fortran 95, Fortran 77, and C.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Duff:2002:ARM,
  author =       "Iain S. Duff and Christof V{\"o}mel",
  title =        "{Algorithm 818}: a reference model implementation of
                 the {Sparse BLAS} in {Fortran 95}",
  journal =      j-TOMS,
  volume =       "28",
  number =       "2",
  pages =        "268--283",
  month =        jun,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/567806.567811",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The Basic Linear Algebra Subprograms for sparse
                 matrices (Sparse BLAS) as defined by the BLAS Technical
                 Forum are a set of routines providing basic operations
                 for sparse matrices and vectors. A principal goal for
                 the Sparse BLAS standard is to aid in the development
                 of iterative solvers for large sparse systems by
                 specifying on the one hand interfaces for a high-level
                 description of vector and matrix operations for the
                 algorithm developer and on the other hand leaving
                 enough freedom for vendors to provide the most
                 efficient implementation of the underlying algorithms
                 for their specific architectures.\par

                 The Sparse BLAS standard defines interfaces and
                 bindings for the three target languages: C, Fortran 77
                 and Fortran 95. We describe here our Fortran 95
                 implementation intended as a reference model for the
                 Sparse BLAS. We identify the underlying complex issues
                 of the representation and the handling of sparse
                 matrices and give suggestions to other implementors of
                 how to address them.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hopkins:2002:CPT,
  author =       "Tim Hopkins",
  title =        "A comment on the presentation and testing of {CALGO}
                 codes and a remark on {Algorithm 639}: {To} integrate
                 some infinite oscillating tails",
  journal =      j-TOMS,
  volume =       "28",
  number =       "3",
  pages =        "285--300",
  month =        sep,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/569147.569148",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We report on a number of coding problems that occur
                 frequently in published CALGO software and are still
                 appearing in new algorithm submissions. Using Algorithm
                 639 as an extended example, we describe how these types
                 of faults may be almost entirely eliminated using
                 available commercial compilers and software tools. We
                 consider the levels of testing required to instill
                 confidence that code performs reliably. Finally, we
                 look at how the source code may be re-engineered, and
                 thus made more maintainable, by taking account of
                 advances in hardware and language development.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gupta:2002:RAD,
  author =       "Anshul Gupta",
  title =        "Recent Advances in Direct Methods for Solving
                 Unsymmetric Sparse Systems of Linear Equations",
  journal =      j-TOMS,
  volume =       "28",
  number =       "3",
  pages =        "301--324",
  month =        sep,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/569147.569149",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 11:26:40 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "During the past few years, algorithmic improvements
                 alone have reduced the time required for the direct
                 solution of unsymmetric sparse systems of linear
                 equations by almost an order of magnitude. This paper
                 compares the performance of some well-known software
                 packages for solving general sparse systems. In
                 particular, it demonstrates the consistently high level
                 of performance achieved by WSMP---the most recent of
                 such solvers. It compares the various algorithmic
                 components of these solvers and discusses their impact
                 on solver performance. Our experiments show that the
                 algorithmic choices made in WSMP enable it to run more
                 than twice as fast as the best among similar solvers
                 and that WSMP can factor some of the largest sparse
                 matrices available from real applications in only a few
                 seconds on a 4-CPU workstation. Thus, the combination
                 of advances in hardware and algorithms makes it
                 possible to solve those general sparse linear systems
                 quickly and easily that might have been considered too
                 large until recently.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithms, Performance; Multifrontal Method; Parallel
                 Sparse Solvers; Sparse LU Decomposition; Sparse Matrix
                 Factorization",
  subject =      "Primary Classification: G. Mathematics of Computing
                 G.1 NUMERICAL ANALYSIS G.1.3 Numerical Linear Algebra",
}

@Article{Gil:2002:AAB,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 819}: {AIZ}, {BIZ}: two {Fortran 77}
                 routines for the computation of complex {Airy}
                 functions",
  journal =      j-TOMS,
  volume =       "28",
  number =       "3",
  pages =        "325--336",
  month =        sep,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/569147.569150",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Two Fortran 77 routines for the evaluation of Airy
                 functions of complex arguments $Ai(z)$, $Bi(z)$ and
                 their derivatives are presented. The routines are based
                 on the use of Gaussian quadrature, Maclaurin series and
                 asymptotic expansions. Comparison with a previous code
                 by D. E. Amos (ACM TOMS 12 (1986)) is provided.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ferrando:2002:AFI,
  author =       "Sebastian E. Ferrando and Lawrence A. Kolasa and
                 Natasha Kova{\v{c}}evi{\'c}",
  title =        "{Algorithm 820}: a flexible implementation of matching
                 pursuit for {Gabor} functions on the interval",
  journal =      j-TOMS,
  volume =       "28",
  number =       "3",
  pages =        "337--353",
  month =        sep,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/569147.569151",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The matching pursuit algorithm of Mallat et.~al.~is
                 discussed in the context of discretized Gabor functions
                 on an interval. Results from frame theory are used to
                 introduce corresponding finite dictionaries. We then
                 proceed to describe two software implementations based
                 on these dictionaries. One implementation allows for
                 users to have great flexibility in the Gabor dictionary
                 to be used. This is a useful improvement over other
                 implementations which only allow for a fixed
                 dictionary. The other implementation takes advantage of
                 the FFT algorithm and is faster. These implementations
                 are written in C++, and can be used in many practical
                 situations given its flexibility and generality.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hanson:2002:AFI,
  author =       "Richard J. Hanson and Clay P. Breshears and Henry A.
                 Gabb",
  title =        "{Algorithm 821}: a {Fortran} interface to {POSIX}
                 threads",
  journal =      j-TOMS,
  volume =       "28",
  number =       "3",
  pages =        "354--371",
  month =        sep,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/569147.569152",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Pthreads is the library of POSIX standard functions
                 for concurrent, multithreaded programming. The POSIX
                 standard only defines an application programming
                 interface (API) to the C programming language, not to
                 Fortran. Many scientific and engineering applications
                 are written in Fortran. Also, many of these
                 applications exhibit functional, or task-level,
                 concurrency. They would benefit from multithreading,
                 especially on symmetric multiprocessors (SMP). We
                 present here an interface to that part of the Pthreads
                 library that is compatible with standard Fortran. The
                 contribution consists of two primary source files: a
                 Fortran module and a collection of C wrappers to
                 Pthreads functions. The Fortran module defines the data
                 structures, interface and initialization routines used
                 to manage threads. The stability and portability of the
                 Fortran API to Pthreads is demonstrated using common
                 mathematical computations on three different systems.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hopkins:2002:RAF,
  author =       "Tim Hopkins",
  title =        "Remark on {Algorithm 705}: a {Fortran-77} software
                 package for solving the {Sylvester} matrix equation
                 {$AXB^T + CXD^T = E$}",
  journal =      j-TOMS,
  volume =       "28",
  number =       "3",
  pages =        "372--375",
  month =        sep,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/569147.569153",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Gardiner:1992:AFS}.",
  abstract =     "We present a number of corrections to Algorithm 705
                 [Gardiner et al. 1992].",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Reid:2002:IHE,
  author =       "John K. Reid and Jennifer A. Scott",
  title =        "Implementing {Hager}'s exchange methods for matrix
                 profile reduction",
  journal =      j-TOMS,
  volume =       "28",
  number =       "4",
  pages =        "377--391",
  month =        dec,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/592843.592844",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 08:17:55 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Hager recently introduced down and up exchange methods
                 for reducing the profile of a sparse matrix with a
                 symmetric sparsity pattern. The methods are
                 particularly useful for refining orderings that have
                 been obtained using a standard profile reduction
                 algorithm, such as the Sloan method. The running times
                 for the exchange algorithms reported by Hager suggested
                 their cost could be prohibitive for practical
                 applications. We examine how to implement the exchange
                 algorithms efficiently. For a range of real test
                 problems, it is shown that the cost of running our new
                 implementation does not add a prohibitive overhead to
                 the cost of the original reordering.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Jonsson:2002:RBAa,
  author =       "Isak Jonsson and Bo K{\aa}gstr{\"o}m",
  title =        "Recursive blocked algorithms for solving triangular
                 systems: {Part I}: one-sided and coupled
                 {Sylvester}-type matrix equations",
  journal =      j-TOMS,
  volume =       "28",
  number =       "4",
  pages =        "392--415",
  month =        dec,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/592843.592845",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 08:17:55 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Triangular matrix equations appear naturally in
                 estimating the condition numbers of matrix equations
                 and different eigenspace computations, including
                 block-diagonalization of matrices and matrix pairs and
                 computation of functions of matrices. To solve a
                 triangular matrix equation is also a major step in the
                 classical Bartels--Stewart method for solving the
                 standard continuous-time Sylvester equation ($AX - XB =
                 C$). We present novel recursive blocked algorithms for
                 solving one-sided triangular matrix equations,
                 including the continuous- time Sylvester and Lyapunov
                 equations, and a generalized coupled Sylvester
                 equation. The main parts of the computations are
                 performed as level-3 general matrix multiply and add
                 (GEMM) operations. In contrast to explicit standard
                 blocking techniques, our recursive approach leads to an
                 automatic variable blocking that has the potential of
                 matching the memory hierarchies of today's HPC systems.
                 Different implementation issues are discussed,
                 including when to terminate the recursion, the design
                 of new optimized superscalar kernels for solving
                 leaf-node triangular matrix equations efficiently, and
                 how parallelism is utilized in our implementations.
                 Uniprocessor and SMP parallel performance results of
                 our recursive blocked algorithms and corresponding
                 routines in the state-of-the-art libraries LAPACK and
                 SLICOT are presented. The performance improvements of
                 our recursive algorithms are remarkable, including
                 10-fold speedups compared to standard algorithms.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithms; automatic blocking; GEMM-based;
                 generalized coupled Sylvester; LAPACK; level-3 BLAS;
                 Matrix equations; Performance; recursion; SLICOT; SMP
                 parallelization; standard Sylvester and Lyapunov;
                 superscalar",
  subject =      "Primary Classification: G. Mathematics of Computing
                 G.4 MATHEMATICAL SOFTWARE Subjects: Algorithm design
                 and analysis

                 Additional Classification: F. Theory of Computation F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY F.2.1
                 Numerical Algorithms and Problems Subjects:
                 Computations on matrices

                 G. Mathematics of Computing G.1 NUMERICAL ANALYSIS
                 G.1.3 Numerical Linear Algebra Subjects: Conditioning;
                 Linear systems (direct and iterative methods) G.4
                 MATHEMATICAL SOFTWARE Subjects: Parallel and vector
                 implementations; Efficiency; Reliability and
                 robustness",
}

@Article{Jonsson:2002:RBAb,
  author =       "Isak Jonsson and Bo K{\aa}gstr{\"o}m",
  title =        "Recursive Blocked Algorithms for Solving Triangular
                 Systems: {Part II}: Two-Sided and Generalized
                 {Sylvester} and {Lyapunov} Matrix Equations",
  journal =      j-TOMS,
  volume =       "28",
  number =       "4",
  pages =        "416--435",
  month =        dec,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/592843.592846",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 08:17:55 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We continue our study of high-performance algorithms
                 for solving triangular matrix equations. They appear
                 naturally in different condition estimation problems
                 for matrix equations and various eigenspace
                 computations, and as reduced systems in standard
                 algorithms. Building on our successful recursive
                 approach applied to one-sided matrix equations (Part
                 I), we now present novel recursive blocked algorithms
                 for two-sided matrix equations, which include matrix
                 product terms such as AXBT. Examples are the
                 discrete-time standard and generalized Sylvester and
                 Lyapunov equations. The means for achieving high
                 performance is the recursive variable blocking, which
                 has the potential of matching the memory hierarchies of
                 today's high-performance computing systems, and level-3
                 computations which mainly are performed as GEMM
                 operations. Different implementation issues are
                 discussed, including the design of efficient new
                 algorithms for two-sided matrix products. We present
                 uniprocessor and SMP parallel performance results of
                 recursive blocked algorithms and routines in the
                 state-of-the-art SLICOT library. Although our recursive
                 algorithms with optimized kernels for the two-sided
                 matrix equations perform more operations, the
                 performance improvements are remarkable, including
                 10-fold speedups or more, compared to standard
                 algorithms.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithms; automatic blocking; Design; generalized
                 Sylvester and Lyapunov; LAPACK; level-3 BLAS; Matrix
                 equations; Performance GEMM-based; recursion; SLICOT;
                 SMP parallelization; standard discrete-time Sylvester
                 and Lyapunov; superscalar",
  subject =      "Primary Classification: G. Mathematics of Computing
                 G.4 MATHEMATICAL SOFTWARE Subjects: Algorithm design
                 and analysis

                 Additional Classification: F. Theory of Computation F.2
                 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY F.2.1
                 Numerical Algorithms and Problems Subjects:
                 Computations on matrices

                 G. Mathematics of Computing G.1 NUMERICAL ANALYSIS
                 G.1.3 Numerical Linear Algebra Subjects: Linear systems
                 (direct and iterative methods); Conditioning G.4
                 MATHEMATICAL SOFTWARE Subjects: Parallel and vector
                 implementations; Reliability and robustness;
                 Efficiency",
}

@Article{Gil:2002:AGH,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 822}: {GIZ}, {HIZ}: two {Fortran} 77
                 routines for the computation of complex {Scorer}
                 functions",
  journal =      j-TOMS,
  volume =       "28",
  number =       "4",
  pages =        "436--447",
  month =        dec,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/592843.592847",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 08:17:55 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Two Fortran 77 routines for the evaluation of Scorer
                 functions of complex arguments $Gi(z)$, $Hi(z)$ and
                 their derivatives are presented. The routines are based
                 on the use of quadrature, Maclaurin series and
                 asymptotic expansions. For real $z$ comparison with a
                 previous code by A. J. Macleod (J. Comput. Appl. Math.
                 53 (1994)) is provided.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Edlund:2002:SPS,
  author =       "Ove Edlund",
  title =        "A software package for sparse orthogonal factorization
                 and updating",
  journal =      j-TOMS,
  volume =       "28",
  number =       "4",
  pages =        "448--482",
  month =        dec,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/592843.592848",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 08:17:55 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Though there is good software for sparse QR
                 factorization, there is little support for updating and
                 downdating---something that is absolutely essential in
                 some linear programming algorithms, for example. This
                 paper describes an implementation of sparse LQ
                 factorization, including block triangularization,
                 approximate minimum degree ordering, symbolic
                 factorization, multifrontal factorization, {\em and\/}
                 updating and downdating. The factor $Q$ is not
                 retained. The updating algorithm expands the nonzero
                 pattern of the factor $L$, which is reflected in the
                 dynamic representation of $L$. The block
                 triangularization is used as an ``ordering for
                 sparsity'' rather than as a prerequisite for block
                 backward substitution. In the symbolic factorization,
                 something called ``element counters'' is introduced to
                 reduce the overestimation of the number of nonzeros
                 that the commonly used methods do. Both the approximate
                 minimum degree ordering and the symbolic factorization
                 are done without explicitly forming the nonzero pattern
                 of the symmetric matrix in the corresponding normal
                 equations.\par

                 Tests show that the average time used for a single
                 update or downdate is essentially the same as the time
                 used for a single forward or backward substitution.
                 Other parts of the implementation show the same range
                 of performance as existing code, but cannot be replaced
                 because of the special character of the systems that
                 are solved.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Soderlind:2003:DFA,
  author =       "Gustaf S{\"o}derlind",
  title =        "Digital filters in adaptive time-stepping",
  journal =      j-TOMS,
  volume =       "29",
  number =       "1",
  pages =        "1--26",
  month =        mar,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/641876.641877",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 08:17:55 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Adaptive time-stepping based on linear digital control
                 theory has several advantages: the algorithms can be
                 analyzed in terms of stability and adaptivity, and they
                 can be designed to produce smoother stepsize sequences
                 resulting in significantly improved regularity and
                 computational stability. Here, we extend this approach
                 by viewing the closed-loop transfer map $H\phi: \log
                 \phi \mapsto \log h$ as a digital filter, processing
                 the signal $log \phi$ (the principal error function) in
                 the frequency domain, in order to produce a smooth
                 stepsize sequence $\log h$. The theory covers all
                 previously considered control structures and offers new
                 possibilities to construct stepsize selection
                 algorithms in the asymptotic stepsize-error regime.
                 Without incurring extra computational costs, the
                 controllers can be designed for special purposes such
                 as higher order of adaptivity (for smooth ODE problems)
                 or a stronger ability to suppress high-frequency error
                 components (nonsmooth problems, stochastic ODEs).
                 Simulations verify the controllers' ability to produce
                 stepsize sequences resulting in improved regularity and
                 computational stability.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Adaptivity; algorithm analysis; algorithms; control
                 theory; digital filters; error control; mathematical
                 software; stepsize control; theory",
  subject =      "G. Mathematics of Computing G.1 NUMERICAL ANALYSIS
                 G.1.7 Ordinary Differential Equations Subjects: Initial
                 value problems",
}

@Article{Nievergelt:2003:SFM,
  author =       "Yves Nievergelt",
  title =        "Scalar fused multiply-add instructions produce
                 floating-point matrix arithmetic provably accurate to
                 the penultimate digit",
  journal =      j-TOMS,
  volume =       "29",
  number =       "1",
  pages =        "27--48",
  month =        mar,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/641876.641878",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "68W99 (65Y99 68M99)",
  MRnumber =     "MR2001452",
  bibdate =      "Fri Mar 28 08:17:55 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Combined with doubly compensated summation, scalar
                 fused multiply-add instructions redefine the concept of
                 floating-point arithmetic, because they allow for the
                 computation of sums of real or complex matrix products
                 accurate to the penultimate digit. Particular cases
                 include complex arithmetic, dot products, cross
                 products, residuals of linear systems, determinants of
                 small matrices, discriminants of quadratic, cubic, or
                 quartic equations, and polynomials.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accurate floating-point summation; algorithms; design;
                 doubly compensated summation; floating-point
                 arithmetic; fused multiply-add instruction; languages;
                 matrix arithmetic; provable accuracy; rounding error;
                 standardization; theory",
  subject =      "Primary Classification: B. Hardware, B.2 ARITHMETIC
                 AND LOGIC STRUCTURES, B.2.0 General;

                 Additional Classification: B. Hardware, B.7 INTEGRATED
                 CIRCUITS B.7.1 Types and Design Styles Subjects:
                 Algorithms implemented in hardware B.8 Performance and
                 Reliability B.8.2 Performance Analysis and Design
                 Aids

                 C. Computer Systems Organization C.0 GENERAL Subjects:
                 Instruction set design (e.g., RISC, CISC, VLIW)

                 F. Theory of Computation F.2 ANALYSIS OF ALGORITHMS AND
                 PROBLEM COMPLEXITY F.2.1 Numerical Algorithms and
                 Problems Subjects: Computations on matrices

                 G. Mathematics of Computing G.1 NUMERICAL ANALYSIS
                 G.1.0 General Subjects: Computer arithmetic; Multiple
                 precision arithmetic; Numerical algorithms; Error
                 analysis G.4 MATHEMATICAL SOFTWARE Subjects: Algorithm
                 design and analysis; Certification and testing;
                 Reliability and robustness",
}

@Article{Joe:2003:RAI,
  author =       "Stephen Joe and Frances Y. Kuo",
  title =        "Remark on {Algorithm 659}: {Implementing} {Sobol}'s
                 quasirandom sequence generator",
  journal =      j-TOMS,
  volume =       "29",
  number =       "1",
  pages =        "49--57",
  month =        mar,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/641876.641879",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 08:17:55 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "An algorithm to generate Sobol' sequences to
                 approximate integrals in up to 40 dimensions has been
                 previously given by Bratley and Fox in Algorithm 659.
                 Here, we provide more primitive polynomials and
                 ``direction numbers'' so as to allow the generation of
                 Sobol' sequences to approximate integrals in up to 1111
                 dimensions. The direction numbers given generate Sobol'
                 sequences that satisfy Sobol's so-called Property A.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; Low-discrepancy sequences; primitive
                 polynomials; quasirandom sequences; Sobol' sequences",
  subject =      "G. Mathematics of Computing G.1 NUMERICAL ANALYSIS
                 G.1.4 Quadrature and Numerical Differentiation
                 Subjects: Multidimensional (multiple) quadrature",
}

@Article{Gertz:2003:OOS,
  author =       "E. Michael Gertz and Stephen J. Wright",
  title =        "Object-oriented software for quadratic programming",
  journal =      j-TOMS,
  volume =       "29",
  number =       "1",
  pages =        "58--81",
  month =        mar,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/641876.641880",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 08:17:55 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The object-oriented software package OOQP for solving
                 convex quadratic programming problems (QP) is
                 described. The primal-dual interior point algorithms
                 supplied by OOQP are implemented in a way that is
                 largely independent of the problem structure. Users may
                 exploit problem structure by supplying linear algebra,
                 problem data, and variable classes that are customized
                 to their particular applications. The OOQP distribution
                 contains default implementations that solve several
                 important QP problem types, including general sparse
                 and dense QPs, bound-constrained QPs, and QPs arising
                 from support vector machines and Huber regression. The
                 implementations supplied with the OOQP distribution are
                 based on such well known linear algebra packages as
                 MA27/57, LAPACK, and PETSc. OOQP demonstrates the
                 usefulness of object-oriented design in optimization
                 software development, and establishes standards that
                 can be followed in the design of software packages for
                 other classes of optimization problems. A number of the
                 classes in OOQP may also be reusable directly in other
                 codes.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithms; Design; Interior-Point Methods;
                 Object-Oriented Software; Quadratic Programming",
  subject =      "Primary Classification: D. Software D.2 SOFTWARE
                 ENGINEERING D.2.2 Design Tools and
                 Techniques

                 Additional Classification: G. Mathematics of Computing
                 G.1 NUMERICAL ANALYSIS G.1.6 Optimization Subjects:
                 Quadratic programming methods G.4 MATHEMATICAL SOFTWARE
                 Subjects: Algorithm design and analysis",
}

@Article{Wenzel:2003:IWD,
  author =       "Lothar Wenzel and Ram Rajagopal and Dinesh Nair",
  title =        "Induced well-distributed sets in {Riemannian} spaces",
  journal =      j-TOMS,
  volume =       "29",
  number =       "1",
  pages =        "82--94",
  month =        mar,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/641876.641881",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 08:17:55 MST 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The concept of Riemannian geometries is used to
                 construct induced homogeneous point sets on manifolds
                 that are based on well-distributed point sets in unit
                 cubes of an appropriately chosen Euclidean space. These
                 well-distributed point sets in unit cubes are based on
                 standard low-discrepancy sequences. The approach is
                 algorithmic, that is, the methods developed in this
                 article have been implemented and tested. Applications
                 in image processing, graph theory and measurement-based
                 exploration are presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithms; image processing; low-discrepancy
                 sequences; Measurement; Riemannian geometry; Theory;
                 well-distributed point sets",
  subject =      "J. Computer Applications J.2 PHYSICAL SCIENCES AND
                 ENGINEERING",
}

@Article{Hong:2003:AIS,
  author =       "Hee Sun Hong and Fred J. Hickernell",
  title =        "{Algorithm 823}: {Implementing} scrambled digital
                 sequences",
  journal =      j-TOMS,
  volume =       "29",
  number =       "2",
  pages =        "95--109",
  month =        jun,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/779359.779360",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 7 13:56:17 MDT 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Random scrambling of deterministic $(t, m, s)$-nets
                 and $(t, s)$-sequences eliminates their inherent bias
                 while retaining their low-discrepancy properties. This
                 article describes an implementation of two types of
                 random scrambling, one proposed by Owen and another
                 proposed by Faure and Tezuka. The four different
                 constructions of digital sequences implemented are
                 those proposed by Sobol', Faure, Niederreiter, and
                 Niederreiter and Xing. Because the random scrambling
                 involves manipulating all digits of each point, the
                 code must be written carefully to minimize the
                 execution time. Computed root mean square discrepancies
                 of the scrambled sequences are compared to known
                 theoretical results. Furthermore, the performances of
                 these sequences on various test problems are
                 discussed.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Li:2003:SSD,
  author =       "Xiaoye S. Li and James W. Demmel",
  title =        "{SuperLU\_DIST}: a scalable distributed-memory sparse
                 direct solver for unsymmetric linear systems",
  journal =      j-TOMS,
  volume =       "29",
  number =       "2",
  pages =        "110--140",
  month =        jun,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/779359.779361",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 7 13:56:17 MDT 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present the main algorithmic features in the
                 software package SuperLU\_DIST, a distributed-memory
                 sparse direct solver for large sets of linear
                 equations. We give in detail our parallelization
                 strategies, with a focus on scalability issues, and
                 demonstrate the software's parallel performance and
                 scalability on current machines. The solver is based on
                 sparse Gaussian elimination, with an innovative static
                 pivoting strategy proposed earlier by the authors. The
                 main advantage of static pivoting over classical
                 partial pivoting is that it permits a priori
                 determination of data structures and communication
                 patterns, which lets us exploit techniques used in
                 parallel sparse Cholesky algorithms to better
                 parallelize both LU decomposition and triangular
                 solution on large-scale distributed machines.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Dhooge:2003:MMP,
  author =       "A. Dhooge and W. Govaerts and Yu. A. Kuznetsov",
  title =        "{MATCONT}: {A MATLAB} package for numerical
                 bifurcation analysis of {ODEs}",
  journal =      j-TOMS,
  volume =       "29",
  number =       "2",
  pages =        "141--164",
  month =        jun,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/779359.779362",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 7 13:56:17 MDT 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "MATCONT is a graphical MATLAB software package for the
                 interactive numerical study of dynamical systems. It
                 allows one to compute curves of equilibria, limit
                 points, Hopf points, limit cycles, period doubling
                 bifurcation points of limit cycles, and fold
                 bifurcation points of limit cycles. All curves are
                 computed by the same function that implements a
                 prediction-correction continuation algorithm based on
                 the Moore--Penrose matrix pseudo-inverse. The
                 continuation of bifurcation points of equilibria and
                 limit cycles is based on bordering methods and
                 minimally extended systems. Hence no additional
                 unknowns such as singular vectors and eigenvectors are
                 used and no artificial sparsity in the systems is
                 created. The sparsity of the discretized systems for
                 the computation of limit cycles and their bifurcation
                 points is exploited by using the standard Matlab sparse
                 matrix methods. The MATLAB environment makes the
                 standard MATLAB Ordinary Differential Equations (ODE)
                 Suite interactively available and provides
                 computational and visualization tools; it also
                 eliminates the compilation stage and so makes
                 installation straightforward. Compared to other
                 packages such as AUTO and CONTENT, adding a new type of
                 curves is easy in the MATLAB environment. We illustrate
                 this by a detailed description of the limit point curve
                 type.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Henrion:2003:GGO,
  author =       "Didier Henrion and Jean-Bernard Lasserre",
  title =        "{GloptiPoly}: {Global} optimization over polynomials
                 with {Matlab} and {SeDuMi}",
  journal =      j-TOMS,
  volume =       "29",
  number =       "2",
  pages =        "165--194",
  month =        jun,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/779359.779363",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 7 13:56:17 MDT 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "GloptiPoly is a Matlab\slash SeDuMi add-on to build
                 and solve convex linear matrix inequality relaxations
                 of the (generally nonconvex) global optimization
                 problem of minimizing a multivariable polynomial
                 function subject to polynomial inequality, equality, or
                 integer constraints. It generates a series of lower
                 bounds monotonically converging to the global optimum
                 without any problem splitting. Global optimality is
                 detected and isolated optimal solutions are extracted
                 automatically. Numerical experiments show that for most
                 of the small-scale problems described in the
                 literature, the global optimum is reached at low
                 computational cost.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sarra:2003:SSP,
  author =       "Scott A. Sarra",
  title =        "The spectral signal processing suite",
  journal =      j-TOMS,
  volume =       "29",
  number =       "2",
  pages =        "195--217",
  month =        jun,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/779359.779364",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 7 13:56:17 MDT 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A software suite written in the Java programming
                 language for the postprocessing of Chebyshev
                 approximations to discontinuous functions is presented.
                 It is demonstrated how to use the package to remove the
                 effects of the Gibbs--Wilbraham phenomenon from
                 Chebyshev approximations of discontinuous functions.
                 Additionally, the package is used to postprocess
                 Chebyshev collocation and Chebyshev super spectral
                 viscosity approximations of hyperbolic partial
                 differential equations. The postprocessing method is
                 the Gegenbauer reconstruction procedure. The Spectral
                 Signal Processing Suite is the first publicly available
                 package that implements the procedure. State-of-the-art
                 techniques are used to implement the algorithms with
                 efficiency while reducing round-off error.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Quintana-Orti:2003:FDA,
  author =       "Enrique S. Quintana-Ort{\'\i} and Robert A. van de
                 Geijn",
  title =        "Formal derivation of algorithms: {The} triangular
                 {Sylvester} equation",
  journal =      j-TOMS,
  volume =       "29",
  number =       "2",
  pages =        "218--243",
  month =        jun,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/779359.779365",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 7 13:56:17 MDT 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this paper we apply a formal approach for the
                 derivation of dense linear algebra algorithms to the
                 triangular Sylvester equation. The result is a large
                 family of provably correct algorithms. By using a
                 coding style that reflects the algorithms as they are
                 naturally presented, the correctness of the algorithms
                 carries through to the correctness of the
                 implementations. Analytically motivated heuristics are
                 used to subsequently choose members from the family
                 that can be expected to yield high performance.
                 Finally, we report performance on the Intel (R) Pentium
                 (R) III processor that is competitive with that of
                 recursive algorithms reported previously in the
                 literature for this operation.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Martins:2003:CSD,
  author =       "Joaquim R. R. A. Martins and Peter Sturdza and Juan J.
                 Alonso",
  title =        "The complex-step derivative approximation",
  journal =      j-TOMS,
  volume =       "29",
  number =       "3",
  pages =        "245--262",
  month =        sep,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/838250.838251",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 7 14:01:48 MDT 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The complex-step derivative approximation and its
                 application to numerical algorithms are presented.
                 Improvements to the basic method are suggested that
                 further increase its accuracy and robustness and unveil
                 the connection to algorithmic differentiation theory. A
                 general procedure for the implementation of the
                 complex-step method is described in detail and a script
                 is developed that automates its implementation.
                 Automatic implementations of the complex-step method
                 for Fortran and C/C++ are presented and compared to
                 existing algorithmic differentiation tools. The
                 complex-step method is tested in two large
                 multidisciplinary solvers and the resulting
                 sensitivities are compared to results given by finite
                 differences. The resulting sensitivities are shown to
                 be as accurate as the analyses. Accuracy, robustness,
                 ease of implementation and maintainability make these
                 complex-step derivative approximation tools very
                 attractive options for sensitivity analysis.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Eble:2003:ASP,
  author =       "Ingo Eble and Markus Neher",
  title =        "{ACETAF}: a software package for computing validated
                 bounds for {Taylor} coefficients of analytic
                 functions",
  journal =      j-TOMS,
  volume =       "29",
  number =       "3",
  pages =        "263--286",
  month =        sep,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/838250.838252",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 7 14:01:48 MDT 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article presents methods for practical
                 computation of verified bounds for Taylor coefficients
                 of analytic functions. These bounds are constructed
                 from Cauchy's estimate and from some of its
                 modifications. Interval arithmetic is used to obtain
                 rigorous results.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cools:2003:ACP,
  author =       "Ronald Cools and Ann Haegemans",
  title =        "{Algorithm 824}: {\em {CUBPACK}\/}: a package for
                 automatic cubature; framework description",
  journal =      j-TOMS,
  volume =       "29",
  number =       "3",
  pages =        "287--296",
  month =        sep,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/838250.838253",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 7 14:01:48 MDT 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "CUBPACK aims to offer a collection of re-usable code
                 for automatic $n$-dimensional ($n \geq 1$) numerical
                 integration of functions over a collection of regions,
                 i.e., quadrature and cubature. The current version
                 allows this region to consist of a union of
                 $n$-simplices and $n$-parallelepipeds. The framework of
                 CUBPACK is described as well as its user interface. The
                 functionality of several well known routines is
                 embedded. New features include integration algorithms
                 using the $\epsilon$-algorithm for extrapolation for
                 regions other than triangles and the implementation of
                 a new type of subdivision for 3-cubes.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Genz:2003:ANC,
  author =       "Alan Genz and Ronald Cools",
  title =        "An adaptive numerical cubature algorithm for
                 simplices",
  journal =      j-TOMS,
  volume =       "29",
  number =       "3",
  pages =        "297--308",
  month =        sep,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/838250.838254",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 7 14:01:48 MDT 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A globally adaptive algorithm for numerical cubature
                 of a vector of functions over a collection of
                 $n$-dimensional simplices is described. The algorithm
                 is based on a subdivision strategy that chooses for
                 subdivision at each stage the subregion (of the input
                 simplices) with the largest estimated error. This
                 subregion is divided into two, three or four equal
                 volume subregions by cutting selected edges. These
                 edges are selected using information about the
                 smoothness of the integrands in the edge directions.
                 The algorithm allows a choice from several embedded
                 cubature rule sequences for approximate integration and
                 error estimation. A Fortran 95 implementation as a part
                 of CUBPACK is also discussed. Testing of the algorithm
                 is described.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Shellman:2003:ADC,
  author =       "Spencer Shellman and K. Sikorski",
  title =        "{Algorithm 825}: a deep-cut bisection envelope
                 algorithm for fixed points",
  journal =      j-TOMS,
  volume =       "29",
  number =       "3",
  pages =        "309--325",
  month =        sep,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/838250.838255",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 7 14:01:48 MDT 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present the BEDFix (Bisection Envelope Deep-cut
                 Fixed point) algorithm for the problem of approximating
                 a fixed point of a function of two variables. The
                 function must be Lipschitz continuous with constant 1
                 with respect to the infinity norm; such functions are
                 commonly found in economics and game theory. The
                 computed approximation satisfies a residual criterion
                 given a specified error tolerance. The BEDFix algorithm
                 improves the BEFix algorithm presented in Shellman and
                 Sikorski [2002] by utilizing ``deep cuts,'' that is,
                 eliminating additional segments of the feasible domain
                 which cannot contain a fixed point. The upper bound on
                 the number of required function evaluations is the same
                 for BEDFix and BEFix, but our numerical tests indicate
                 that BEDFix significantly improves the average-case
                 performance. In addition, we show how BEDFix may be
                 used to solve the absolute criterion fixed point
                 problem with significantly better performance than the
                 simple iteration method, when the Lipschitz constant is
                 less than but close to 1. BEDFix is highly efficient
                 when used to compute residual solutions for bivariate
                 functions, having a bound on function evaluations that
                 is twice the logarithm of the reciprocal of the
                 tolerance. In the tests described in this article, the
                 number of evaluations performed by the method averaged
                 31 percent of this worst-case bound. BEDFix works for
                 nonsmooth continuous functions, unlike methods that
                 require gradient information; also, it handles
                 functions with minimum Lipschitz constants equal to 1,
                 whereas the complexity of simple iteration approaches
                 infinity as the minimum Lipschitz constant approaches
                 1. When BEDFix is used to compute absolute criterion
                 solutions, the worst-case complexity depends on the
                 logarithm of the reciprocal of $1-q$, where $q$ is the
                 Lipschitz constant, as well as on the logarithm of the
                 reciprocal of the tolerance.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fahey:2003:APE,
  author =       "Mark R. Fahey",
  title =        "{Algorithm 826}: a parallel eigenvalue routine for
                 complex {Hessenberg} matrices",
  journal =      j-TOMS,
  volume =       "29",
  number =       "3",
  pages =        "326--336",
  month =        sep,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/838250.838256",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 7 14:01:48 MDT 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A code for computing the eigenvalues of a complex
                 Hessenberg matrix is presented. This code computes the
                 Schur decomposition of a complex Hessenberg matrix.
                 Together with existing ScaLAPACK routines, the
                 eigenvalues of dense complex matrices can be directly
                 computed using a parallel QR algorithm. This parallel
                 complex Schur decomposition routine was developed to
                 fill a void in the ScaLAPACK library and was based on
                 the parallel real Schur decomposition routine already
                 in ScaLAPACK. The real-arithmetic version was
                 appropriately modified to make it work with complex
                 arithmetic and implement a complex multiple bulge QR
                 algorithm. This also required the development of new
                 auxiliary routines that perform essential operations
                 for the complex Schur decomposition, and that will
                 provide additional linear algebra computation
                 capability to the parallel numerical library
                 community.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Baglama:2003:AIM,
  author =       "J. Baglama and D. Calvetti and L. Reichel",
  title =        "{Algorithm 827}: {{\tt irbleigs}}: {A MATLAB} program
                 for computing a few eigenpairs of a large sparse
                 {Hermitian} matrix",
  journal =      j-TOMS,
  volume =       "29",
  number =       "3",
  pages =        "337--348",
  month =        sep,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/838250.838257",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 7 14:01:48 MDT 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "{\tt irbleigs} is a MATLAB program for computing a few
                 eigenvalues and associated eigenvectors of a sparse
                 Hermitian matrix of large order $n$. The matrix is
                 accessed only through the evaluation of matrix-vector
                 products. Working space of only a few n-vectors is
                 required. The program implements a restarted
                 block-Lanczos method. Judicious choices of acceleration
                 polynomials make it possible to compute approximations
                 of a few of the largest eigenvalues, a few of the
                 smallest eigenvalues, or a few eigenvalues in the
                 vicinity of a user-specified point on the real axis.
                 {\tt irbleigs} also can be applied to certain large
                 generalized eigenproblems as well as to the computation
                 of a few nearby singular values and associated right
                 and left singular vectors of a large general matrix.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hopkins:2003:RAF,
  author =       "Tim Hopkins",
  title =        "Remark on {Algorithm 769}: {Fortran} subroutines for
                 approximate solution of sparse quadratic assignment
                 problems using {GRASP}",
  journal =      j-TOMS,
  volume =       "29",
  number =       "3",
  pages =        "349--351",
  month =        sep,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/838250.838258",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 7 14:01:48 MDT 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a number of corrections and improvements to
                 Algorithm 769 [Pardalos et al. 1997].",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gould:2003:GLT,
  author =       "Nicholas I. M. Gould and Dominique Orban and Philippe
                 L. Toint",
  title =        "{GALAHAD}, a library of thread-safe {Fortran 90}
                 packages for large-scale nonlinear optimization",
  journal =      j-TOMS,
  volume =       "29",
  number =       "4",
  pages =        "353--372",
  month =        dec,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/962437.962438",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 5 17:18:49 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe the design of version 1.0 of GALAHAD, a
                 library of Fortran 90 packages for large-scale
                 nonlinear optimization. The library particularly
                 addresses quadratic programming problems, containing
                 both interior point and active set algorithms, as well
                 as tools for preprocessing problems prior to solution.
                 It also contains an updated version of the venerable
                 nonlinear programming package, LANCELOT.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gould:2003:CSC,
  author =       "Nicholas I. M. Gould and Dominique Orban and Philippe
                 L. Toint",
  title =        "{CUTEr} and {SifDec}: a constrained and unconstrained
                 testing environment, revisited",
  journal =      j-TOMS,
  volume =       "29",
  number =       "4",
  pages =        "373--394",
  month =        dec,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/962437.962438",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 5 17:18:49 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The initial release of CUTE, a widely used testing
                 environment for optimization software, was described by
                 Bongartz, et al. [1995]. A new version, now known as
                 CUTEr, is presented. Features include reorganisation of
                 the environment to allow simultaneous multi-platform
                 installation, new tools for, and interfaces to,
                 optimization packages, and a considerably simplified
                 and entirely automated installation procedure for Unix
                 systems. The environment is fully backward compatible
                 with its predecessor, and offers support for Fortran
                 90/95 and a general C/C++ Application Programming
                 Interface. The SIF decoder, formerly a part of CUTE,
                 has become a separate tool, easily callable by various
                 packages. It features simple extensions to the SIF test
                 problem format and the generation of files suited to
                 automatic differentiation packages.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Scott:2003:PFS,
  author =       "Jennifer A. Scott",
  title =        "Parallel frontal solvers for large sparse linear
                 systems",
  journal =      j-TOMS,
  volume =       "29",
  number =       "4",
  pages =        "395--417",
  month =        dec,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/962437.962440",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 5 17:18:49 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Many applications in science and engineering give rise
                 to large sparse linear systems of equations that need
                 to be solved as efficiently as possible. As the size of
                 the problems of interest increases, it can become
                 necessary to consider exploiting multiprocessors to
                 solve these systems. We report on the design and
                 development of parallel frontal solvers for the
                 numerical solution of large sparse linear systems.
                 Three codes have been developed for the mathematical
                 software library HSL (www.cse.clrc.ac.uk/Activity/HSL).
                 The first is for unsymmetric finite-element problems;
                 the second is for symmetric positive definite
                 finite-element problems; and the third is for highly
                 unsymmetric linear systems such as those that arise in
                 chemical process engineering. In each case, the problem
                 is subdivided into a small number of loosely connected
                 subproblems and a frontal method is then applied to
                 each of the subproblems in parallel. We discuss how our
                 software is designed to achieve the goals of
                 portability, ease of use, efficiency, and flexibility,
                 and illustrate the performance using problems arising
                 from real applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bradbury:2003:FCS,
  author =       "Emma L. Bradbury and Wayne H. Enright",
  title =        "Fast contouring of solutions to partial differential
                 equations",
  journal =      j-TOMS,
  volume =       "29",
  number =       "4",
  pages =        "418--439",
  month =        dec,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/962437.962441",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 5 17:18:49 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The application of Differential Equation Interpolants
                 (DEIs) to the visualization of the solutions to Partial
                 Differential Equations (PDEs) is investigated. In
                 particular, we describe how a DEI can be used to
                 generate a fine mesh approximation from a coarse mesh
                 approximation; this fine mesh approximation can then be
                 used by a standard contouring function to render an
                 accurate contour plot of the surface. However, the
                 standard approach has a time complexity equivalent to
                 that of rendering a surface plot, $O(fm^2)$ for each
                 element of the coarse mesh, (where $fm$ is the ratio of
                 the width of the coarse mesh to the fine mesh). To
                 address this concern three fast contouring algorithms
                 are proposed that compute accurate contour lines
                 directly from the DEI, and have time complexity at most
                 $O(fm)$ for each coarse mesh element.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bucker:2003:MPI,
  author =       "H. Martin B{\"u}cker and Arno Rasch",
  title =        "Modeling the performance of interface contraction",
  journal =      j-TOMS,
  volume =       "29",
  number =       "4",
  pages =        "440--457",
  month =        dec,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/962437.962442",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 5 17:18:49 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Automatic differentiation is a technique used to
                 transform a computer code implementing some
                 mathematical function into another program capable of
                 evaluating the function and its derivatives. Compared
                 to numerical differentiation, the derivatives obtained
                 from applying automatic differentiation are free from
                 truncation error, and their computation often requires
                 less time. To increase the efficiency of a black box
                 approach of automatic differentiation, a technique
                 called interface contraction may be used. Interface
                 contraction exploits the local structure of a code to
                 temporarily reduce the global number of derivatives
                 propagated through the code. Two performance models are
                 introduced to predict the potential improvement in the
                 execution time of a program making use of interface
                 contraction compared to a program generated by a black
                 box approach of automatic differentiation. The
                 performance models are validated by numerical
                 experiments carried out on different computing
                 platforms. The computer codes used in the experiments
                 stem from the application areas of neutron scattering
                 and biostatistics.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Renka:2003:ADD,
  author =       "Robert J. Renka",
  title =        "{Algorithm 828}: {DNSPLIN1}: discrete nonlinear spline
                 interpolation",
  journal =      j-TOMS,
  volume =       "29",
  number =       "4",
  pages =        "458--468",
  month =        dec,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/962437.962443",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 5 17:18:49 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe a new method and a Fortran-77 code for
                 constructing discrete approximations to nonparametric
                 interpolating nonlinear spline curves. Our approach
                 consists of minimizing the discretized strain energy by
                 a descent method with a Sobolev gradient in place of
                 the standard gradient. It serves as a demonstration of
                 the Sobolev gradient method, which is much more
                 generally applicable. The effectiveness of the method
                 in rapidly producing smooth interpolatory curves is
                 demonstrated by test results for several challenging
                 data sets.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gaviano:2003:ASG,
  author =       "Marco Gaviano and Dmitri E. Kvasov and Daniela Lera
                 and Yaroslav D. Sergeyev",
  title =        "{Algorithm 829}: {Software} for generation of classes
                 of test functions with known local and global minima
                 for global optimization",
  journal =      j-TOMS,
  volume =       "29",
  number =       "4",
  pages =        "469--480",
  month =        dec,
  year =         "2003",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/962437.962444",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 5 17:18:49 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A procedure for generating non-differentiable,
                 continuously differentiable, and twice continuously
                 differentiable classes of test functions for
                 multiextremal multidimensional box-constrained global
                 optimization is presented. Each test class consists of
                 100 functions. Test functions are generated by defining
                 a convex quadratic function systematically distorted by
                 polynomials in order to introduce local minima. To
                 determine a class, the user defines the following
                 parameters: (i) problem dimension, (ii) number of local
                 minima, (iii) value of the global minimum, (iv) radius
                 of the attraction region of the global minimizer, (v)
                 distance from the global minimizer to the vertex of the
                 quadratic function. Then, all other necessary
                 parameters are generated randomly for all 100 functions
                 of the class. Full information about each test function
                 including locations and values of all local minima is
                 supplied to the user. Partial derivatives are also
                 generated where possible.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gonzalez--Pinto:2004:TSE,
  author =       "S. Gonz{\'a}lez--Pinto and J. I. Montijano and S.
                 P{\'e}rez--Rodr{\'\i}guez",
  title =        "Two-step error estimators for implicit {Runge--Kutta}
                 methods applied to stiff systems",
  journal =      j-TOMS,
  volume =       "30",
  number =       "1",
  pages =        "1--18",
  month =        mar,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/974781.974782",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu May 20 13:45:13 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This paper is concerned with local error estimation in
                 the numerical integration of stiff systems of ordinary
                 differential equations by means of Runge--Kutta
                 methods. With implicit Runge--Kutta methods it is often
                 difficult to embed a local error estimate with the
                 appropriate order and stability properties. In this
                 paper local error estimation based on the information
                 from the last two integration steps (that are supposed
                 to have the same steplength) is proposed. It is shown
                 that this technique, applied to Radau IIA methods, lets
                 us get estimators with proper order and stability
                 properties. Numerical examples showing that the
                 proposed estimate improves the efficiency of the
                 integration codes are presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rotkin:2004:DIN,
  author =       "Vladimir Rotkin and Sivan Toledo",
  title =        "The design and implementation of a new out-of-core
                 sparse {Cholesky} factorization method",
  journal =      j-TOMS,
  volume =       "30",
  number =       "1",
  pages =        "19--46",
  month =        mar,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/974781.974783",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu May 20 13:45:13 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe a new out-of-core sparse Cholesky
                 factorization method. The new method uses the
                 elimination tree to partition the matrix, an advanced
                 subtree-scheduling algorithm, and both right-looking
                 and left-looking updates. The implementation of the new
                 method is efficient and robust. On a 2 GHz personal
                 computer with 768 MB of main memory, the code can
                 easily factor matrices with factors of up to 48 GB,
                 usually at rates above 1 Gflop/s. For example, the code
                 can factor audikw, currently the largest matrix in any
                 matrix collection (factor size over 10 GB), in a little
                 over an hour, and can factor a matrix whose graph is a
                 140-by-140-by-140 mesh in about 12 hours (factor size
                 around 27 GB).",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Vaz:2004:SSI,
  author =       "A. Ismael F. Vaz and Edite M. G. P. Fernandes and M.
                 Paula S. F. Gomes",
  title =        "{SIPAMPL}: {Semi-infinite} programming with {AMPL}",
  journal =      j-TOMS,
  volume =       "30",
  number =       "1",
  pages =        "47--61",
  month =        mar,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/974781.974784",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu May 20 13:45:13 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "SIPAMPL is an environment for coding semi-infinite
                 programming (SIP) problems. This environment includes a
                 database containing a set of SIP problems that have
                 been collected from the literature and a set of
                 routines. It allows users to code their own SIP
                 problems in AMPL, to use any problem already in the
                 database, and to develop and test any SIP solver. The
                 SIPAMPL routines support the interface between a
                 potential SIP solver and test problems coded in AMPL.
                 SIPAMPL also provides a tool that allows the selection
                 of problems from the database with specified
                 characteristics. As a concept demonstration, we show
                 how MATLAB can use SIPAMPL to solve the problems in the
                 database. The Linux and Microsoft Windows versions
                 together with the database of coded problems are freely
                 available via the web.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bartlett:2004:VRT,
  author =       "Roscoe A. Bartlett and Bart G. {Van Bloemen Waanders}
                 and Michael A. Heroux",
  title =        "Vector reduction\slash transformation operators",
  journal =      j-TOMS,
  volume =       "30",
  number =       "1",
  pages =        "62--85",
  month =        mar,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/974781.974785",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu May 20 13:45:13 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Development of flexible linear algebra interfaces is
                 an increasingly critical issue. Efficient and
                 expressive interfaces are well established for some
                 linear algebra abstractions, but not for vectors.
                 Vectors differ from other abstractions in the diversity
                 of necessary operations, sometimes requiring dozens for
                 a given algorithm (e.g. interior-point methods for
                 optimization). We discuss a new approach based on
                 operator objects that are transported to the underlying
                 data by the linear algebra library implementation,
                 allowing developers of abstract numerical algorithms to
                 easily extend the functionality regardless of computer
                 architecture, application or data locality\slash
                 organization. Numerical experiments demonstrate
                 efficient implementation.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hanson:2004:AAV,
  author =       "Richard J. Hanson and Tim Hopkins",
  title =        "{Algorithm 830}: {Another} visit with standard and
                 modified {Givens} transformations and a remark on
                 {Algorithm 539}",
  journal =      j-TOMS,
  volume =       "30",
  number =       "1",
  pages =        "86--94",
  month =        mar,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/974781.974786",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu May 20 13:45:13 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Lawson:1979:ABL}.",
  abstract =     "First we report on a correction and improvement to the
                 Level 1 BLAS routine {\tt srotmg} for computing the
                 Modified Givens Transformation (MG). We then, in the
                 light of the performance of the code on modern
                 compiler\slash hardware combinations, reconsider the
                 strategy of supplying separate routines to compute and
                 apply the transformation. Finally, we show that the
                 apparent savings in multiplies obtained by using MG
                 rather than the Standard Givens Transformation (SG) do
                 not always translate into reductions in execution
                 time.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Duff:2004:PDS,
  author =       "Iain S. Duff and Jennifer A. Scott",
  title =        "A parallel direct solver for large sparse highly
                 unsymmetric linear systems",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "95--117",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/992200.992201",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 10 07:24:58 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The need to solve large sparse linear systems of
                 equations efficiently lies at the heart of many
                 applications in computational science and engineering.
                 For very large systems when using direct factorization
                 methods of solution, it can be beneficial and sometimes
                 necessary to use multiple processors, because of
                 increased memory availability as well as reduced
                 factorization time. We report on the development of a
                 new parallel code that is designed to solve linear
                 systems with a highly unsymmetric sparsity structure
                 using a modest number of processors (typically up to
                 about 16). The problem is first subdivided into a
                 number of loosely connected subproblems and a variant
                 of sparse Gaussian elimination is then applied to each
                 of the subproblems in parallel. An interface problem in
                 the variables on the boundaries of the subproblems must
                 also be factorized. We discuss how our software is
                 designed to achieve the goals of portability, ease of
                 use, efficiency, and flexibility, and illustrate its
                 performance on an SGI Origin 2000, a Cray T3E, and a
                 2-processor Compaq DS20, using problems arising from
                 real applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Duff:2004:MCS,
  author =       "Iain S. Duff",
  title =        "{MA57}---a code for the solution of sparse symmetric
                 definite and indefinite systems",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "118--144",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/992200.992202",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 10 07:24:58 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We introduce a new code for the direct solution of
                 sparse symmetric linear equations that solves
                 indefinite systems with $2 \times 2$ pivoting for
                 stability. This code, called MA57, is in HSL 2002 and
                 supersedes the well used HSL code MA27. We describe
                 some of the implementation details and emphasize the
                 novel features of MA57. These include restart
                 facilities, matrix modification, partial solution for
                 matrix factors, solution of multiple right-hand sides,
                 and iterative refinement and error analysis. The code
                 is written in Fortran 77, but there are additional
                 facilities within a Fortran 90 implementation that
                 include the ability to identify and change pivots.
                 Several of these facilities have been developed
                 particularly to support optimization applications, and
                 we illustrate the performance of the code on problems
                 arising therefrom.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gil:2004:CSM,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Computing solutions of the modified {Bessel}
                 differential equation for imaginary orders and positive
                 arguments",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "145--158",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/992200.992203",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 10 07:24:58 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe a variety of methods to compute the
                 functions $K_{ia}(x)$, $L_{ia}(x)$ and their
                 derivatives for real $a$ and positive $x$. These
                 functions are numerically satisfactory independent
                 solutions of the differential equation $x^2 w'' + xw' +
                 (a^2 - x^2)w = 0$. In the accompanying paper [Gil et
                 al. 2004], we describe the implementation of these
                 methods in Fortran 77 codes.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gil:2004:AMB,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 831}: {Modified} {Bessel} functions of
                 imaginary order and positive argument",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "159--164",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/992200.992204",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 10 07:24:58 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Fortran 77 programs for the computation of modified
                 Bessel functions of purely imaginary order are
                 presented. The codes compute the functions $K_{ia}(x)$,
                 $L_{ia}(x)$ and their derivatives for real $a$ and
                 positive $x$; these functions are independent solutions
                 of the differential equation $x^2 w'' + xw' + (a^2 -
                 x^2)w = 0$. The code also computes exponentially scaled
                 functions. The range of computation is $(x, a) \in
                 (0,1500] \times [-1500, 1500]$ when scaled functions
                 are considered and it is larger than $(0,500] \times
                 [-400, 400]$ for standard IEEE double precision
                 arithmetic. The relative accuracy is better than
                 $10^{-13}$ in the range $(0,200] \times [-200, 200]$
                 and close to $10^{-12}$ in $(0, 1500] \times [-1500,
                 1500]$.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Davis:2004:CPO,
  author =       "Timothy A. Davis",
  title =        "A column pre-ordering strategy for the
                 unsymmetric-pattern multifrontal method",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "165--195",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/992200.992205",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 10 07:24:58 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A new method for sparse LU factorization is presented
                 that combines a column pre-ordering strategy with a
                 right-looking unsymmetric-pattern multifrontal
                 numerical factorization. The column ordering is
                 selected to give a good a priori upper bound on fill-in
                 and then refined during numerical factorization (while
                 preserving the bound). Pivot rows are selected to
                 maintain numerical stability and to preserve sparsity.
                 The method analyzes the matrix and automatically
                 selects one of three pre-ordering and pivoting
                 strategies. The number of nonzeros in the LU factors
                 computed by the method is typically less than or equal
                 to those found by a wide range of unsymmetric sparse LU
                 factorization methods, including left-looking methods
                 and prior multifrontal methods.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Davis:2004:AUV,
  author =       "Timothy A. Davis",
  title =        "{Algorithm 832}: {UMFPACK V4.3}---an
                 unsymmetric-pattern multifrontal method",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "196--199",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/992200.992206",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 10 07:24:58 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "An ANSI C code for sparse LU factorization is
                 presented that combines a column pre-ordering strategy
                 with a right-looking unsymmetric-pattern multifrontal
                 numerical factorization. The pre-ordering and symbolic
                 analysis phase computes an upper bound on fill-in,
                 work, and memory usage during the subsequent numerical
                 factorization. User-callable routines are provided for
                 ordering and analyzing a sparse matrix, computing the
                 numerical factorization, solving a system with the LU
                 factors, transposing and permuting a sparse matrix, and
                 converting between sparse matrix representations. The
                 simple user interface shields the user from the details
                 of the complex sparse factorization data structures by
                 returning simple handles to opaque objects. Additional
                 user-callable routines are provided for printing and
                 extracting the contents of these opaque objects. An
                 even simpler way to use the package is through its
                 MATLAB interface. UMFPACK is incorporated as a built-in
                 operator in MATLAB 6.5 as $x = A \backslash b$ when $A$
                 is sparse and unsymmetric.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Renka:2004:ACI,
  author =       "Robert J. Renka",
  title =        "{Algorithm 833}: {CSRFPACK}---interpolation of
                 scattered data with a {$C^1$} convexity-preserving
                 surface",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "200--211",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/992200.992207",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 10 07:24:58 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe a Fortran-77 software package for
                 constructing a $C^1$ convex surface that interpolates a
                 convex data set consisting of data values at
                 arbitrarily distributed points in the plane (nodes)
                 such that there exists a triangulation of the nodes for
                 which the triangle-based piecewise linear interpolant
                 is convex. The method consists of constructing this
                 data-dependent triangulation, computing a set of nodal
                 gradients for which there exists a convex piecewise
                 linear Hermite interpolant $H$ of the nodal values and
                 gradients, and applying convolution smoothing to $H$.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Renka:2004:AGI,
  author =       "Robert J. Renka",
  title =        "{Algorithm 834}: {{\tt glsurf}} --- an interactive
                 surface plotting program using {OpenGL}",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "212--217",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/992200.992208",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 10 07:24:58 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe an interactive surface visualization tool
                 implemented in C, OpenGL, and GLUT. The surface is
                 represented by a set of triangles in Euclidean 3-space,
                 thus allowing for unrestricted topology. Capabilities
                 include color-filled contour plots (for the graph of a
                 bivariate function) and surface perspective plots with
                 lighting and smooth shading. Interactive zooms and axis
                 rotations are executed with a single keypress or mouse
                 motion. The advantage of this code over the many
                 alternatives is that it is small, simple, portable,
                 easy to install and use, and the source code is
                 available if the user wishes to change defaults, add
                 light sources, or whatever.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Zeng:2004:AMM,
  author =       "Zhonggang Zeng",
  title =        "{Algorithm 835}: {MultRoot}---a {Matlab} package for
                 computing polynomial roots and multiplicities",
  journal =      j-TOMS,
  volume =       "30",
  number =       "2",
  pages =        "218--236",
  month =        jun,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/992200.992209",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 10 07:24:58 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "MultRoot is a collection of Matlab modules for
                 accurate computation of polynomial roots, especially
                 roots with non-trivial multiplicities. As a
                 blackbox-type software, MultRoot requires the
                 polynomial coefficients as the only input, and outputs
                 the computed roots, multiplicities, backward error,
                 estimated forward error, and the structure-preserving
                 condition number. The most significant features of
                 MultRoot are the multiplicity identification capability
                 and high accuracy on multiple roots without using
                 multiprecision arithmetic, even if the polynomial
                 coefficients are inexact. A comprehensive test suite of
                 polynomials that are collected from the literature is
                 included for numerical experiments and performance
                 comparison.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Matthey:2004:POO,
  author =       "Thierry Matthey and Trevor Cickovski and Scott Hampton
                 and Alice Ko and Qun Ma and Matthew Nyerges and Troy
                 Raeder and Thomas Slabach and Jes{\'u}s A. Izaguirre",
  title =        "{ProtoMol}, an object-oriented framework for
                 prototyping novel algorithms for molecular dynamics",
  journal =      j-TOMS,
  volume =       "30",
  number =       "3",
  pages =        "237--265",
  month =        sep,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1024074.1024075",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 29 06:31:52 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "ProtoMol is a high-performance framework in C++ for
                 rapid prototyping of novel algorithms for molecular
                 dynamics and related applications. Its flexibility is
                 achieved primarily through the use of inheritance and
                 design patterns (object-oriented programming).
                 Performance is obtained by using templates that enable
                 generation of efficient code for sections critical to
                 performance (generic programming). The framework
                 encapsulates important optimizations that can be used
                 by developers, such as parallelism in the force
                 computation. Its design is based on domain analysis of
                 numerical integrators for molecular dynamics (MD) and
                 of fast solvers for the force computation, particularly
                 due to electrostatic interactions. Several new and
                 efficient algorithms are implemented in ProtoMol.
                 Finally, it is shown that ProtoMol's sequential
                 performance is excellent when compared to a leading MD
                 program, and that it scales well for moderate number of
                 processors. Binaries and source codes for Windows,
                 Linux, Solaris, IRIX, HP-UX, and AIX platforms are
                 available under open source license at
                 http://protomol.sourceforge.net.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Forth:2004:JCG,
  author =       "Shaun A. Forth and Mohamed Tadjouddine and John D.
                 Pryce and John K. Reid",
  title =        "{Jacobian} code generated by source transformation and
                 vertex elimination can be as efficient as hand-coding",
  journal =      j-TOMS,
  volume =       "30",
  number =       "3",
  pages =        "266--299",
  month =        sep,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1024074.1024076",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 29 06:31:52 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article presents the first extended set of
                 results from EliAD, a source-transformation
                 implementation of the vertex-elimination Automatic
                 Differentiation approach to calculating the Jacobians
                 of functions defined by Fortran code (Griewank and
                 Reese, Automatic Differentiation of Algorithms: Theory,
                 Implementation, and Application, 1991, pp. 126--135).
                 We introduce the necessary theory in terms of well
                 known algorithms of numerical linear algebra applied to
                 the linear, extended Jacobian system that prescribes
                 the relationship between the derivatives of all
                 variables in the function code. Using an example, we
                 highlight the potential for numerical instability in
                 vertex-elimination. We describe the source
                 transformation implementation of our tool EliAD and
                 present results from five test cases, four of which are
                 taken from the MINPACK-2 collection (Averick et al,
                 Report ANL/MCS-TM-150, 1992) and for which hand-coded
                 Jacobian codes are available. On five computer/compiler
                 platforms, we show that the Jacobian code obtained by
                 EliAD is as efficient as hand-coded Jacobian code. It
                 is also between 2 to 20 times more efficient than that
                 produced by current, state of the art, Automatic
                 Differentiation tools even when such tools make use of
                 sophisticated techniques such as sparse Jacobian
                 compression. We demonstrate the effectiveness of
                 reverse-ordered pre-elimination from the (successively
                 updated) extended Jacobian system of all intermediate
                 variables used once. Thereafter, the monotonic
                 forward/reverse ordered eliminations of all other
                 intermediates is shown to be very efficient. On only
                 one test case were orderings determined by the
                 Markowitz or related VLR heuristics found superior. A
                 re-ordering of the statements of the Jacobian code,
                 with the aim of reducing reads and writes of data from
                 cache to registers, was found to have mixed effects but
                 could be very beneficial.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gould:2004:NEH,
  author =       "Nicholas I. M. Gould and Jennifer A. Scott",
  title =        "A numerical evaluation of {HSL} packages for the
                 direct solution of large sparse, symmetric linear
                 systems of equations",
  journal =      j-TOMS,
  volume =       "30",
  number =       "3",
  pages =        "300--325",
  month =        sep,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1024074.1024077",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 29 06:31:52 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In recent years, a number of new direct solvers for
                 the solution of large sparse, symmetric linear systems
                 of equations have been added to the mathematical
                 software library HSL. These include solvers that are
                 designed for the solution of positive-definite systems
                 as well as solvers that are principally intended for
                 solving indefinite problems. The available choice can
                 make it difficult for users to know which solver is the
                 most appropriate for their use. In this study, we use
                 performance profiles as a tool for evaluating and
                 comparing the performance of the HSL solvers on an
                 extensive set of test problems taken from a range of
                 practical applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bai:2004:BTE,
  author =       "Yihua Bai and Wilfried N. Gansterer and Robert C.
                 Ward",
  title =        "Block tridiagonalization of ``effectively'' sparse
                 symmetric matrices",
  journal =      j-TOMS,
  volume =       "30",
  number =       "3",
  pages =        "326--352",
  month =        sep,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1024074.1024078",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 29 06:31:52 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A block tridiagonalization algorithm is proposed for
                 transforming a sparse (or ``effectively'' sparse)
                 symmetric matrix into a related block tridiagonal
                 matrix, such that the eigenvalue error remains bounded
                 by some prescribed accuracy tolerance. It is based on a
                 heuristic for imposing a block tridiagonal structure on
                 matrices with a large percentage of zero or
                 ``effectively zero'' (with respect to the given
                 accuracy tolerance) elements. In the light of a
                 recently developed block tridiagonal divide-and-conquer
                 eigensolver [Gansterer, Ward, Muller, and Goddard, III,
                 SIAM J. Sci. Comput. 25 (2003), pp. 65--85], for which
                 block tridiagonalization may be needed as a
                 preprocessing step, the algorithm also provides an
                 option for attempting to produce at least a few very
                 small diagonal blocks in the block tridiagonal matrix.
                 This leads to low time complexity of the last merging
                 operation in the block divide-and-conquer method.
                 Numerical experiments are presented and various block
                 tridiagonalization strategies are compared.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Davis:2004:CAM,
  author =       "Timothy A. Davis and John R. Gilbert and Stefan I.
                 Larimore and Esmond G. Ng",
  title =        "A column approximate minimum degree ordering
                 algorithm",
  journal =      j-TOMS,
  volume =       "30",
  number =       "3",
  pages =        "353--376",
  month =        sep,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1024074.1024079",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 29 06:31:52 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Sparse Gaussian elimination with partial pivoting
                 computes the factorization $PAQ = LU$ of a sparse
                 matrix $A$, where the row ordering $P$ is selected
                 during factorization using standard partial pivoting
                 with row interchanges. The goal is to select a column
                 preordering, $Q$, based solely on the nonzero pattern
                 of $A$, that limits the worst-case number of nonzeros
                 in the factorization. The fill-in also depends on $P$,
                 but $Q$ is selected to reduce an upper bound on the
                 fill-in for any subsequent choice of $P$. The choice of
                 $Q$ can have a dramatic impact on the number of
                 nonzeros in $L$ and $U$. One scheme for determining a
                 good column ordering for $A$ is to compute a symmetric
                 ordering that reduces fill-in in the Cholesky
                 factorization of $A^T A$. A conventional minimum degree
                 ordering algorithm would require the sparsity structure
                 of $A^T A$ to be computed, which can be expensive both
                 in terms of space and time since $A^T A$ may be much
                 denser than $A$. An alternative is to compute $Q$
                 directly from the sparsity structure of $A$; this
                 strategy is used by MATLAB's COLMMD preordering
                 algorithm. A new ordering algorithm, COLAMD, is
                 presented. It is based on the same strategy but uses a
                 better ordering heuristic. COLAMD is faster and
                 computes better orderings, with fewer nonzeros in the
                 factors of the matrix.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Davis:2004:ACC,
  author =       "Timothy A. Davis and John R. Gilbert and Stefan I.
                 Larimore and Esmond G. Ng",
  title =        "{Algorithm 836}: {COLAMD}, a column approximate
                 minimum degree ordering algorithm",
  journal =      j-TOMS,
  volume =       "30",
  number =       "3",
  pages =        "377--380",
  month =        sep,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1024074.1024080",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 29 06:31:52 MDT 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Two codes are discussed, COLAMD and SYMAMD, that
                 compute approximate minimum degree orderings for sparse
                 matrices in two contexts: (1) sparse partial pivoting,
                 which requires a sparsity preserving column
                 pre-ordering prior to numerical factorization, and (2)
                 sparse Cholesky factorization, which requires a
                 symmetric permutation of both the rows and columns of
                 the matrix being factorized. These orderings are
                 computed by COLAMD and SYMAMD, respectively. The
                 ordering from COLAMD is also suitable for sparse QR
                 factorization, and the factorization of matrices of the
                 form $A^T A$ and $A A^T$, such as those that arise in
                 least-squares problems and interior point methods for
                 linear programming problems. The two routines are
                 available both in MATLAB and C-callable forms. They
                 appear as built-in routines in MATLAB Version 6.0.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Amestoy:2004:AAA,
  author =       "Patrick R. Amestoy and Timothy A. Davis and Iain S.
                 Duff",
  title =        "{Algorithm 837}: {AMD}, an approximate minimum degree
                 ordering algorithm",
  journal =      j-TOMS,
  volume =       "30",
  number =       "3",
  pages =        "381--388",
  month =        sep,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1024074.1024081",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F50 (05C85)",
  MRnumber =     "MR2124398",
  bibdate =      "Mon Jan 2 09:11:24 2006",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "AMD is a set of routines that implements the
                 approximate minimum degree ordering algorithm to
                 permute sparse matrices prior to numerical
                 factorization. There are versions written in both C and
                 Fortran 77. A MATLAB interface is included.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algorithms; Experimentation; Linear equations; minimum
                 degree; ordering methods; Performance; sparse",
}

@Article{Priest:2004:ESC,
  author =       "Douglas M. Priest",
  title =        "Efficient scaling for complex division",
  journal =      j-TOMS,
  volume =       "30",
  number =       "4",
  pages =        "389--401",
  month =        dec,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1039813.109814",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We develop a simple method for scaling to avoid
                 overflow and harmful underflow in complex division. The
                 method guarantees that no overflow will occur unless at
                 least one component of the quotient must overflow,
                 otherwise the normwise error in the computed result is
                 at most a few units in the last place. Moreover, the
                 scaling requires only four floating point
                 multiplications and a small amount of integer
                 arithmetic to compute the scale factor. Thus, on many
                 modern CPUs, our method is both safer and faster than
                 Smith's widely used algorithm.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "complex division",
}

@Article{Nievergelt:2004:AAP,
  author =       "Yves Nievergelt",
  title =        "Analysis and applications of {Priest}'s distillation",
  journal =      j-TOMS,
  volume =       "30",
  number =       "4",
  pages =        "402--433",
  month =        dec,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1039813.1039815",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Correcting an infinite loop in Douglas M. Priest's
                 renormalization algorithm, the theory proved here
                 supports streamlined algorithms to resolve the
                 tablemaker's dilemma for the floating-point computation
                 of real and complex sums and dot-products, properly
                 rounded to the ultimate digit. Applications include
                 computations of areas, volumes, and intersections.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Whittle:2004:AIK,
  author =       "Jon Whittle and Johann Schumann",
  title =        "Automating the implementation of {Kalman} filter
                 algorithms",
  journal =      j-TOMS,
  volume =       "30",
  number =       "4",
  pages =        "434--453",
  month =        dec,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1039813.1039816",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "{\tt autofilter} is a tool that generates
                 implementations that solve state estimation problems
                 using Kalman filters. From a high-level,
                 mathematics-based description of a state estimation
                 problem, {\tt autofilter} automatically generates code
                 that computes a statistically optimal estimate using
                 one or more of a number of well-known variants of the
                 Kalman filter algorithm. The problem description may be
                 given in terms of continuous or discrete, linear or
                 nonlinear process and measurement dynamics. From this
                 description, {\tt autofilter} automates many common
                 solution methods (e.g., linearization, discretization)
                 and generates C or Matlab code fully automatically.
                 {\tt autofilter} surpasses toolkit-based programming
                 approaches for Kalman filters because it requires no
                 low-level programming skills (e.g., to ``glue''
                 together library function calls). {\tt autofilter}
                 raises the level of discourse to the mathematics of the
                 problem at hand rather than the details of what
                 algorithms, data structures, optimizations and so on
                 are required to implement it. An overview of {\tt
                 autofilter} is given along with an example of its
                 practical application to deep space attitude
                 estimation.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Wang:2004:BBS,
  author =       "R. Wang and P. Keast and P. Muir",
  title =        "{BACOL}: {B}-spline adaptive collocation software for
                 {$1$-D} parabolic {PDEs}",
  journal =      j-TOMS,
  volume =       "30",
  number =       "4",
  pages =        "454--470",
  month =        dec,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1039813.1039817",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "BACOL is a new, high quality, robust software package
                 in Fortran 77 for solving one-dimensional parabolic
                 PDEs, which has been shown to be significantly more
                 efficient than any other widely available software
                 package of the same class (to our knowledge),
                 especially for problems with solutions exhibiting rapid
                 spatial variation. A novel feature of this package is
                 that it employs high order, adaptive methods in both
                 time and space, controlling and balancing both spatial
                 and temporal error estimates. The software implements a
                 spline collocation method at Gaussian points, with a
                 B-spline basis, for the spatial discretization. The
                 time integration is performed using a modification of
                 the popular DAE solver, DASSL. Based on the computation
                 of a second, higher order, global solution, a high
                 quality a posteriori spatial error estimate is obtained
                 after each successful time step. The spatial error is
                 controlled by a sophisticated new mesh selection
                 algorithm based on an equidistribution principle. In
                 this article we describe the overall structure of the
                 BACOL package, and in particular the modifications to
                 the DASSL package that improve its performance within
                 BACOL. An example is provided in the online Appendix to
                 illustrate the use of the package.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fabijonas:2004:CCA,
  author =       "B. R. Fabijonas and D. W. Lozier and F. W. J. Olver",
  title =        "Computation of complex {Airy} functions and their
                 zeros using asymptotics and the differential equation",
  journal =      j-TOMS,
  volume =       "30",
  number =       "4",
  pages =        "471--490",
  month =        dec,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1039813.1039818",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe a method by which one can compute the
                 solutions of Airy's differential equation, and their
                 derivatives, both on the real line and in the complex
                 plane. The computational methods are numerical
                 integration of the differential equation and summation
                 of asymptotic expansions for large argument. We give
                 details involved in obtaining all of the parameter
                 values, and we control the truncation errors
                 rigorously. Using the same computational methods, we
                 describe an algorithm that computes the zeros and
                 associated values of the Airy functions and their
                 derivatives, and the modulus and phase functions on the
                 negative real axis.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fabijonas:2004:AAF,
  author =       "B. R. Fabijonas",
  title =        "{Algorithm 838}: {Airy} Functions",
  journal =      j-TOMS,
  volume =       "30",
  number =       "4",
  pages =        "491--501",
  month =        dec,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1039813.1039819",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a Fortran 90 module, which computes the
                 solutions and their derivatives of Airy's differential
                 equation, both on the real line and in the complex
                 plane. The module also computes the zeros and
                 associated values of the solutions and their
                 derivatives, and the modulus and phase functions on the
                 negative real axis. The computational methods are
                 numerical integration of the differential equation and
                 summation of asymptotic expansions for large argument.
                 These methods were chosen because they are simple,
                 adaptable to any precision, and amenable to rigorous
                 error analysis. The module can be used to validate
                 other codes or as a component in programs that require
                 Airy functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kirby:2004:AFN,
  author =       "Robert C. Kirby",
  title =        "{Algorithm 839}: {FIAT}, a new paradigm for computing
                 finite element basis functions",
  journal =      j-TOMS,
  volume =       "30",
  number =       "4",
  pages =        "502--516",
  month =        dec,
  year =         "2004",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1039813.1039820",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Much of finite element computation is constrained by
                 the difficulty of evaluating high-order nodal basis
                 functions. While most codes rely on explicit formulae
                 for these basis functions, we present a new approach
                 that allows us to construct a general class of finite
                 element basis functions from orthonormal polynomials
                 and evaluate and differentiate them at any points. This
                 approach relies on fundamental ideas from linear
                 algebra and is implemented in Python using several
                 object-oriented and functional programming
                 techniques.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bientinesi:2005:SDD,
  author =       "Paolo Bientinesi and John A. Gunnels and Margaret E.
                 Myers and Enrique S. Quintana-Ort{\'\i} and Robert A.
                 van de Geijn",
  title =        "The science of deriving dense linear algebra
                 algorithms",
  journal =      j-TOMS,
  volume =       "31",
  number =       "1",
  pages =        "1--26",
  month =        mar,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1055531.1055532",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this article we present a systematic approach to
                 the derivation of families of high-performance
                 algorithms for a large set of frequently encountered
                 dense linear algebra operations. As part of the
                 derivation a constructive proof of the correctness of
                 the algorithm is generated. The article is structured
                 so that it can be used as a tutorial for novices.
                 However, the method has been shown to yield new
                 high-performance algorithms for well-studied linear
                 algebra operations and should also be of interest to
                 those who wish to produce best-in-class
                 high-performance codes.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bientinesi:2005:RLA,
  author =       "Paolo Bientinesi and Enrique S. Quintana-Ort{\'\i} and
                 Robert A. van de Geijn",
  title =        "Representing linear algebra algorithms in code: the
                 {FLAME} application program interfaces",
  journal =      j-TOMS,
  volume =       "31",
  number =       "1",
  pages =        "27--59",
  month =        mar,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1055531.1055533",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this article, we present a number of Application
                 Program Interfaces (APIs) for coding linear algebra
                 algorithms. On the surface, these APIs for the MATLAB
                 M-script and C programming languages appear to be
                 simple, almost trivial, extensions of those languages.
                 Yet with them, the task of programming and maintaining
                 families of algorithms for a broad spectrum of linear
                 algebra operations is greatly simplified. In
                 combination with our Formal Linear Algebra Methods
                 Environment (FLAME) approach to deriving such families
                 of algorithms, dozens of algorithms for a single linear
                 algebra operation can be derived, verified to be
                 correct, implemented, and tested, often in a matter of
                 minutes per algorithm. Since the algorithms are
                 expressed in code much like they are explained in a
                 classroom setting, these APIs become not just a tool
                 for implementing libraries, but also a valuable tool
                 for teaching the algorithms that are incorporated in
                 the libraries. In combination with an extension of the
                 Parallel Linear Algebra Package (PLAPACK) API, the
                 approach presents a migratory path from algorithm to
                 MATLAB implementation to high-performance sequential
                 implementation to parallel implementation. Finally, the
                 APIs are being used to create a repository of
                 algorithms and implementations for linear algebra
                 operations, the FLAME Interface REpository (FIRE),
                 which already features hundreds of algorithms for
                 dozens of commonly encountered linear algebra
                 operations.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gunter:2005:PCC,
  author =       "Brian C. Gunter and Robert A. {Van De Geijn}",
  title =        "Parallel out-of-core computation and updating of the
                 {QR} factorization",
  journal =      j-TOMS,
  volume =       "31",
  number =       "1",
  pages =        "60--78",
  month =        mar,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1055531.1055534",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article discusses the high-performance parallel
                 implementation of the computation and updating of QR
                 factorizations of dense matrices, including problems
                 large enough to require out-of-core computation, where
                 the matrix is stored on disk. The algorithms presented
                 here are scalable both in problem size and as the
                 number of processors increases. Implementation using
                 the Parallel Linear Algebra Package (PLAPACK) and the
                 Parallel Out-of-Core Linear Algebra Package
                 (POOCLAPACK) is discussed. The methods are shown to
                 attain excellent performance, in some cases attaining
                 roughly 80\% of the ``realizable'' peak of the
                 architectures on which the experiments were
                 performed.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Shampine:2005:UAS,
  author =       "L. F. Shampine and Robert Ketzscher and Shaun A.
                 Forth",
  title =        "Using {AD} to solve {BVPs} in {MATLAB}",
  journal =      j-TOMS,
  volume =       "31",
  number =       "1",
  pages =        "79--94",
  month =        mar,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1055531.1055535",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The MATLAB program {\tt bvp4c} solves two--point
                 boundary value problems (BVPs) of considerable
                 generality. The numerical method requires partial
                 derivatives of several kinds. To make solving BVPs as
                 easy as possible, the default in {\tt bvp4c} is to
                 approximate these derivatives with finite differences.
                 The solver is more robust and efficient if analytical
                 derivatives are supplied. In this article we
                 investigate how to use automatic differentiation (AD)
                 to obtain the advantages of analytical derivatives
                 without giving up the convenience of finite
                 differences. In {\tt bvp4cAD} we have approached this
                 ideal by a careful use of the MAD AD tool and some
                 modification of {\tt bvp4c}.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Dercole:2005:SAD,
  author =       "Fabio Dercole and Yuri A. Kuznetsov",
  title =        "{SlideCont}: an {AUTO97} driver for bifurcation
                 analysis of {Filippov} systems",
  journal =      j-TOMS,
  volume =       "31",
  number =       "1",
  pages =        "95--119",
  month =        mar,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1055531.1055536",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "SLIDECONT, an AUTO97 driver for sliding bifurcation
                 analysis of discontinuous piecewise-smooth autonomous
                 systems, known as Filippov systems, is described in
                 detail. Sliding bifurcations are those in which some
                 sliding on the discontinuity boundary is critically
                 involved. The software allows for detection and
                 continuation of codimension-1 sliding bifurcations as
                 well as detection of some codimension-2 singularities,
                 with special attention to planar systems ($n = 2$).
                 Some bifurcations are also supported for
                 $n$-dimensional systems. This article gives a brief
                 introduction to Filippov systems, describes the
                 structure of SLIDECONT and all computations supported
                 by SLIDECONT 2.0. Several examples, which are
                 distributed together with the source code of SLIDECONT,
                 are presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Jin:2005:SFE,
  author =       "Guohua Jin and John Mellor-Crummey",
  title =        "{SFCGen}: a framework for efficient generation of
                 multi-dimensional space-filling curves by recursion",
  journal =      j-TOMS,
  volume =       "31",
  number =       "1",
  pages =        "120--148",
  month =        mar,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1055531.1055537",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Because they are continuous and self-similar,
                 space-filling curves have been widely used in
                 mathematics to transform multi-dimensional problems
                 into one-dimensional forms. For scientific
                 applications, reordering computation by certain
                 space-filling curves can significantly improve data
                 reuse because of the locality properties of these
                 curves. However, when space-filling curves are used in
                 programs for reordering data, traversal or indexing of
                 the curves must be efficient. To address this problem,
                 we present the table-driven framework SFCGen to
                 efficiently generate multi-dimensional space-filling
                 curves on the fly. The framework is general and easy
                 enough to be used in any application that can be
                 partitioned recursively in multiple dimensions. We
                 describe a movement specification table, a universal
                 turtle algorithm to enumerate points along a
                 space-filling curve, a table-based indexing algorithm
                 to transform coordinates of a point into its position
                 along the curve and an algorithm to pregenerate the
                 table automatically. As examples, we show how
                 high-dimensional Hilbert, Morton, and Peano curves and
                 a two-dimensional Sierpi{\'n}ski curve can be generated
                 with our algorithms. We present performance results for
                 Hilbert, Morton, and Peano curves and compare the
                 efficiency of our curve generation algorithm with the
                 most recent work on generating Hilbert curves. Our
                 experimental results on three modern
                 microprocessor-based platforms show that SFCGen
                 performs up to 63\% faster than the most recent
                 recursive algorithm on 2D curve generation and up to a
                 factor of 132 faster than two previous byte-oriented
                 non-recursive implementations. On curve indexing,
                 SFCGen performs as much as a factor of three faster
                 than the byte-oriented implementation. Our results on
                 4D space-filling curves also show that SFCGen scales
                 very well with curve level for higher dimensional
                 spaces.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Boyd:2005:ACG,
  author =       "John P. Boyd",
  title =        "{Algorithm 840}: Computation of grid points,
                 quadrature weights and derivatives for spectral element
                 methods using prolate spheroidal wave
                 functions---prolate elements",
  journal =      j-TOMS,
  volume =       "31",
  number =       "1",
  pages =        "149--165",
  month =        mar,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1055531.1055538",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "High order domain decomposition methods using a basis
                 of Legendre polynomials, known variously as ``spectral
                 elements'' or ``$p$-type finite elements,'' have become
                 very popular. Recent studies suggest that accuracy and
                 efficiency can be improved by replacing Legendre
                 polynomials by prolate spheroidal wave functions of
                 zeroth order. In this article, we explain the
                 practicalities of computing all the numbers needed to
                 switch bases: the grid points $x_j$, the quadrature
                 weights $w_j$, and the values of the prolate functions
                 and their derivatives at the grid points. The prolate
                 functions themselves are computed by a
                 Legendre--Galerkin discretization of the prolate
                 differential equation; this yields a symmetric
                 tridiagonal matrix. The prolate functions are then
                 defined by Legendre series whose coefficients are the
                 eigenfunctions of the matrix eigenproblem. The grid
                 points and weights are found simultaneously through a
                 Newton iteration. For large $N$ and $c$, the iteration
                 diverges from a first guess of the Legendre--Lobatto
                 points and weights. Fortunately, the variations of the
                 $x_j$ and $w_j$ with $c$ are well-approximated by a
                 symmetric parabola over the whole range of interest.
                 This makes it possible to bypass the continuation
                 procedures of earlier authors.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Howell:2005:ABG,
  author =       "Gary W. Howell and Nadia Diaa",
  title =        "{Algorithm 841}: {BHESS}: {Gaussian} reduction to a
                 similar banded {Hessenberg} form",
  journal =      j-TOMS,
  volume =       "31",
  number =       "1",
  pages =        "166--185",
  month =        mar,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1055531.1055539",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 12 06:34:31 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "BHESS uses Gaussian similarity transformations to
                 reduce a general real square matrix to similar upper
                 Hessenberg form. Multipliers are bounded in root mean
                 square by a user-supplied parameter. If the input
                 matrix is not highly nonnormal and the user-supplied
                 tolerance on multipliers is of a size greater than ten,
                 the returned matrix usually has small upper bandwidth.
                 In such a case, eigenvalues of the returned matrix can
                 be determined by the bulge-chasing BR iteration or by
                 Rayleigh quotient iteration. BHESS followed by BR
                 iteration determines a complete spectrum in about
                 one-fifth the time required for orthogonal reduction to
                 Hessenberg form followed by QR iterations. The FORTRAN
                 77 code provided for BHESS runs efficiently on a
                 cache-based architecture.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Xin:2005:IHB,
  author =       "Jianguo Xin and Katia Pinchedez and Joseph E.
                 Flaherty",
  title =        "Implementation of hierarchical bases in {FEMLAB} for
                 simplicial elements",
  journal =      j-TOMS,
  volume =       "31",
  number =       "2",
  pages =        "187--200",
  month =        jun,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1067967.1067968",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Jun 21 16:55:57 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present the implementation of well-conditioned
                 hierarchical bases for one-dimensional, triangular and
                 tetrahedral elements in finite element FEMLAB software.
                 Using the domain mesh information provided by FEMLAB,
                 we found an easy way to maintain the continuity of
                 solution across the interelement boundaries. The
                 conditionings of the global stiffness matrices of
                 several standard problems are compared with the
                 Lagrange bases and are smaller for all cases.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Andersen:2005:FPH,
  author =       "Bjarne S. Andersen and John A. Gunnels and Fred G.
                 Gustavson and John K. Reid and Jerzy Wa{\'s}niewski",
  title =        "A fully portable high performance minimal storage
                 hybrid format {Cholesky} algorithm",
  journal =      j-TOMS,
  volume =       "31",
  number =       "2",
  pages =        "201--227",
  month =        jun,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1067967.1067969",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Jun 21 16:55:57 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We consider the efficient implementation of the
                 Cholesky solution of symmetric positive-definite dense
                 linear systems of equations using packed storage. We
                 take the same starting point as that of LINPACK and
                 LAPACK, with the upper (or lower) triangular part of
                 the matrix stored by columns. Following LINPACK and
                 LAPACK, we overwrite the given matrix by its Cholesky
                 factor. We consider the use of a hybrid format in which
                 blocks of the matrices are held contiguously and
                 compare this to the present LAPACK code. Code based on
                 this format has the storage advantages of the present
                 code but substantially outperforms it. Furthermore, it
                 compares favorably to using conventional full format
                 (LAPACK) and using the recursive format of Andersen et
                 al. [2001].",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fraysse:2005:ASG,
  author =       "Val\'rie Frayss{\'e} and Luc Giraud and Serge Gratton
                 and Julien Langou",
  title =        "{Algorithm 842}: a set of {GMRES} routines for real
                 and complex arithmetics on high performance computers",
  journal =      j-TOMS,
  volume =       "31",
  number =       "2",
  pages =        "228--238",
  month =        jun,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1067967.1067970",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Jun 21 16:55:57 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this article we describe our implementations of the
                 GMRES algorithm for both real and complex, single and
                 double precision arithmetics suitable for serial,
                 shared memory and distributed memory computers. For the
                 sake of portability, simplicity, flexibility and
                 efficiency the GMRES solvers have been implemented in
                 Fortran 77 using the reverse communication mechanism
                 for the matrix-vector product, the preconditioning and
                 the dot product computations. For distributed memory
                 computation, several orthogonalization procedures have
                 been implemented to reduce the cost of the dot product
                 calculation, which is a well-known bottleneck of
                 efficiency for the Krylov methods. Either implicit or
                 explicit calculation of the residual at restart are
                 possible depending on the actual cost of the
                 matrix-vector product. Finally the implemented stopping
                 criterion is based on a normwise backward error.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Driscoll:2005:AIS,
  author =       "Tobin A. Driscoll",
  title =        "{Algorithm 843}: {Improvements} to the
                 {Schwarz--Christoffel} toolbox for {MATLAB}",
  journal =      j-TOMS,
  volume =       "31",
  number =       "2",
  pages =        "239--251",
  month =        jun,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1067967.1067971",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Jun 21 16:55:57 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The Schwarz--Christoffel Toolbox (SC Toolbox) for
                 MATLAB, first released in 1994, made possible the
                 interactive creation and visualization of conformal
                 maps to regions bounded by polygons. The most recent
                 release supports new features, including an
                 object-oriented command-line interface model, new
                 algorithms for multiply elongated and multiple-sheeted
                 regions, and a module for solving Laplace's equation on
                 a polygon with Dirichlet and homogeneous Neumann
                 conditions. Brief examples are given to demonstrate the
                 new capabilities.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Berry:2005:ACS,
  author =       "Michael W. Berry and Shakhina A. Pulatova and G. W.
                 Stewart",
  title =        "{Algorithm 844}: {Computing} sparse reduced-rank
                 approximations to sparse matrices",
  journal =      j-TOMS,
  volume =       "31",
  number =       "2",
  pages =        "252--269",
  month =        jun,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1067967.1067972",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Jun 21 16:55:57 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In many applications---latent semantic indexing, for
                 example---it is required to obtain a reduced rank
                 approximation to a sparse matrix $A$. Unfortunately,
                 the approximations based on traditional decompositions,
                 like the singular value and QR decompositions, are not
                 in general sparse. Stewart [(1999), 313--323] has shown
                 how to use a variant of the classical Gram--Schmidt
                 algorithm, called the quasi-Gram--Schmidt-algorithm, to
                 obtain two kinds of low-rank approximations. The first,
                 the SPQR, approximation, is a pivoted, Q-less QR
                 approximation of the form $(XR11^{-1})(R11 R12)$, where
                 $X$ consists of columns of $A$. The second, the SCR
                 approximation, is of the form the form $A \approx
                 XTYT$, where $X$ and $Y$ consist of columns and rows
                 $A$, and $T$ is small. In this article we treat the
                 computational details of these algorithms and describe
                 a MATLAB implementation.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Money:2005:AEM,
  author =       "James H. Money and Qiang Ye",
  title =        "{Algorithm 845}: {EIGIFP}: a {MATLAB} program for
                 solving large symmetric generalized eigenvalue
                 problems",
  journal =      j-TOMS,
  volume =       "31",
  number =       "2",
  pages =        "270--279",
  month =        jun,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1067967.1067973",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Jun 21 16:55:57 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "{\tt eigifp} is a MATLAB program for computing a few
                 extreme eigenvalues and eigenvectors of the large
                 symmetric generalized eigenvalue problem $Ax = \lambda
                 Bx$. It is a black-box implementation of an inverse
                 free preconditioned Krylov subspace projection method
                 developed by Golub and Ye [2002]. It has important
                 features that allow it to solve some difficult problems
                 without any input from users. It is particularly
                 suitable for problems where preconditioning by the
                 standard shift-and-invert transformation is not
                 feasible.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Boisvert:2005:ISI,
  author =       "Ronald F. Boisvert and L. A. Drummond and Osni A.
                 Marques",
  title =        "Introduction to the special issue on the {Advanced
                 CompuTational Software (ACTS)} collection",
  journal =      j-TOMS,
  volume =       "31",
  number =       "3",
  pages =        "281--281",
  month =        sep,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1089014.1089015",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 5 07:43:35 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Drummond:2005:OAC,
  author =       "L. A. Drummond and O. A. Marques",
  title =        "An overview of the {Advanced CompuTational Software
                 (ACTS)} collection",
  journal =      j-TOMS,
  volume =       "31",
  number =       "3",
  pages =        "282--301",
  month =        sep,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1089014.1089016",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 5 07:43:35 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The ACTS Collection brings together a number of
                 general-purpose computational tools that were developed
                 by independent research projects mostly funded and
                 supported by the U.S. Department of Energy. These tools
                 tackle a number of common computational issues found in
                 many applications, mainly implementation of numerical
                 algorithms, and support for code development,
                 execution, and optimization. In this article, we
                 introduce the numerical tools in the collection and
                 their functionalities, present a model for developing
                 more complex computational applications on top of ACTS
                 tools, and summarize applications that use these tools.
                 Last, we present a vision of the ACTS project for
                 deployment of the ACTS Collection by the computational
                 sciences community.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Li:2005:OSA,
  author =       "Xiaoye S. Li",
  title =        "An overview of {SuperLU}: {Algorithms},
                 implementation, and user interface",
  journal =      j-TOMS,
  volume =       "31",
  number =       "3",
  pages =        "302--325",
  month =        sep,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1089014.1089017",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 5 07:43:35 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We give an overview of the algorithms, design
                 philosophy, and implementation techniques in the
                 software SuperLU, for solving sparse unsymmetric linear
                 systems. In particular, we highlight the differences
                 between the sequential SuperLU (including its
                 multithreaded extension) and parallel SuperLU\_DIST.
                 These include the numerical pivoting strategy, the
                 ordering strategy for preserving sparsity, the ordering
                 in which the updating tasks are performed, the
                 numerical kernel, and the parallelization strategy.
                 Because of the scalability concern, the parallel code
                 is drastically different from the sequential one. We
                 describe the user interfaces of the libraries, and
                 illustrate how to use the libraries most efficiently
                 depending on some matrix characteristics. Finally, we
                 give some examples of how the solver has been used in
                 large-scale scientific applications, and the
                 performance.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Falgout:2005:PSH,
  author =       "Robert D. Falgout and Jim E. Jones and Ulrike Meier
                 Yang",
  title =        "Pursuing scalability for {\em hypre\/}'s conceptual
                 interfaces",
  journal =      j-TOMS,
  volume =       "31",
  number =       "3",
  pages =        "326--350",
  month =        sep,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1089014.1089018",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 5 07:43:35 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The software library {\em hypre\/} provides
                 high-performance preconditioners and solvers for the
                 solution of large, sparse linear systems on massively
                 parallel computers as well as conceptual interfaces
                 that allow users to access the library in the way they
                 naturally think about their problems. These interfaces
                 include a stencil-based structured interface (Struct);
                 a semistructured interface (semiStruct), which is
                 appropriate for applications that are mostly
                 structured, for example, block structured grids,
                 composite grids in structured adaptive mesh refinement
                 applications, and overset grids; and a finite element
                 interface (FEI) for unstructured problems, as well as a
                 conventional linear-algebraic interface (IJ). It is
                 extremely important to provide an efficient, scalable
                 implementation of these interfaces in order to support
                 the scalable solvers of the library, especially when
                 using tens of thousands of processors. This article
                 describes the data structures, parallel implementation,
                 and resulting performance of the IJ, Struct and
                 semiStruct interfaces. It investigates their
                 scalability, presents successes as well as pitfalls of
                 some of the approaches and suggests ways of dealing
                 with them.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hernandez:2005:SSF,
  author =       "Vicente Hernandez and Jose E. Roman and Vicente
                 Vidal",
  title =        "{SLEPc}: a scalable and flexible toolkit for the
                 solution of eigenvalue problems",
  journal =      j-TOMS,
  volume =       "31",
  number =       "3",
  pages =        "351--362",
  month =        sep,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1089014.1089019",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 5 07:43:35 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The Scalable Library for Eigenvalue Problem
                 Computations (SLEPc) is a software library for
                 computing a few eigenvalues and associated eigenvectors
                 of a large sparse matrix or matrix pencil. It has been
                 developed on top of PETSc and enforces the same
                 programming paradigm. The emphasis of the software is
                 on methods and techniques appropriate for problems in
                 which the associated matrices are sparse, for example,
                 those arising after the discretization of partial
                 differential equations. Therefore, most of the methods
                 offered by the library are projection methods such as
                 Arnoldi or Lanczos, or other methods with similar
                 properties. SLEPc provides basic methods as well as
                 more sophisticated algorithms. It also provides
                 built-in support for spectral transformations such as
                 the shift-and-invert technique. SLEPc is a general
                 library in the sense that it covers standard and
                 generalized eigenvalue problems, both Hermitian and
                 non-Hermitian, with either real or complex
                 arithmetic.SLEPc can be easily applied to real world
                 problems. To illustrate this, several case studies
                 arising from real applications are presented and solved
                 with SLEPc with little programming effort. The
                 addressed problems include a matrix-free standard
                 problem, a complex generalized problem, and a singular
                 value decomposition. The implemented codes exhibit good
                 properties regarding flexibility as well as parallel
                 performance.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hindmarsh:2005:SSN,
  author =       "Alan C. Hindmarsh and Peter N. Brown and Keith E.
                 Grant and Steven L. Lee and Radu Serban and Dan E.
                 Shumaker and Carol S. Woodward",
  title =        "{SUNDIALS}: {Suite} of nonlinear and
                 differential\slash algebraic equation solvers",
  journal =      j-TOMS,
  volume =       "31",
  number =       "3",
  pages =        "363--396",
  month =        sep,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1089014.1089020",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 5 07:43:35 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "SUNDIALS is a suite of advanced computational codes
                 for solving large-scale problems that can be modeled as
                 a system of nonlinear algebraic equations, or as
                 initial-value problems in ordinary differential or
                 differential-algebraic equations. The basic versions of
                 these codes are called KINSOL, CVODE, and IDA,
                 respectively. The codes are written in ANSI standard C
                 and are suitable for either serial or parallel machine
                 environments. Common and notable features of these
                 codes include inexact Newton--Krylov methods for
                 solving large-scale nonlinear systems; linear multistep
                 methods for time-dependent problems; a highly modular
                 structure to allow incorporation of different
                 preconditioning and/or linear solver methods; and clear
                 interfaces allowing for users to provide their own data
                 structures underneath the solvers. We describe the
                 current capabilities of the codes, along with some of
                 the algorithms and heuristics used to achieve
                 efficiency and robustness. We also describe how the
                 codes stem from previous and widely used Fortran 77
                 solvers, and how the codes have been augmented with
                 forward and adjoint methods for carrying out
                 first-order sensitivity analysis with respect to model
                 parameters or initial conditions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Heroux:2005:OTP,
  author =       "Michael A. Heroux and Roscoe A. Bartlett and Vicki E.
                 Howle and Robert J. Hoekstra and Jonathan J. Hu and
                 Tamara G. Kolda and Richard B. Lehoucq and Kevin R.
                 Long and Roger P. Pawlowski and Eric T. Phipps and
                 Andrew G. Salinger and Heidi K. Thornquist and Ray S.
                 Tuminaro and James M. Willenbring and Alan Williams and
                 Kendall S. Stanley",
  title =        "An overview of the {Trilinos} project",
  journal =      j-TOMS,
  volume =       "31",
  number =       "3",
  pages =        "397--423",
  month =        sep,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1089014.1089021",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 5 07:43:35 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The Trilinos Project is an effort to facilitate the
                 design, development, integration, and ongoing support
                 of mathematical software libraries within an
                 object-oriented framework for the solution of
                 large-scale, complex multiphysics engineering and
                 scientific problems. Trilinos addresses two fundamental
                 issues of developing software for these problems: (i)
                 providing a streamlined process and set of tools for
                 development of new algorithmic implementations and (ii)
                 promoting interoperability of independently developed
                 software. Trilinos uses a two-level software structure
                 designed around collections of packages. A Trilinos
                 package is an integral unit usually developed by a
                 small team of experts in a particular algorithms area
                 such as algebraic preconditioners, nonlinear solvers,
                 etc. Packages exist underneath the Trilinos top level,
                 which provides a common look-and-feel, including
                 configuration, documentation, licensing, and
                 bug-tracking. Here we present the overall Trilinos
                 design, describing our use of abstract interfaces and
                 default concrete implementations. We discuss the
                 services that Trilinos provides to a prospective
                 package and how these services are used by various
                 packages. We also illustrate how packages can be
                 combined to rapidly develop new algorithms. Finally, we
                 discuss how Trilinos facilitates high-quality software
                 engineering practices that are increasingly required
                 from simulation software.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Castillo:2005:FOO,
  author =       "Paul Castillo and Robert Rieben and Daniel White",
  title =        "{FEMSTER}: an object-oriented class library of
                 high-order discrete differential forms",
  journal =      j-TOMS,
  volume =       "31",
  number =       "4",
  pages =        "425--457",
  month =        dec,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1114268.1114269",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 16 11:39:20 MST 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "FEMSTER is a modular finite element class library for
                 solving three-dimensional problems arising in
                 electromagnetism. The library was designed using a
                 modern geometrical approach based on differential forms
                 (or p-forms) and can be used for high-order spatial
                 discretizations of well-known H(div)- and
                 H(curl)-conforming finite element methods. The software
                 consists of a set of abstract interfaces and concrete
                 classes, providing a framework in which the user is
                 able to add new schemes by reusing the existing classes
                 or by incorporating new user-defined data types.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Naumann:2005:DEF,
  author =       "Uwe Naumann and Jan Riehme",
  title =        "A differentiation-enabled {Fortran 95} compiler",
  journal =      j-TOMS,
  volume =       "31",
  number =       "4",
  pages =        "458--474",
  month =        dec,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1114268.1114270",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 16 11:39:20 MST 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The availability of first derivatives of vector
                 functions is crucial for the robustness and efficiency
                 of a large number of numerical algorithms. An upcoming
                 new version of the differentiation-enabled NAGWare
                 Fortran 95 compiler is described that uses programming
                 language extensions and a semantic code transformation
                 known as automatic differentiation to provide Jacobians
                 of numerical programs with machine accuracy. We
                 describe a new user interface as well as the relevant
                 algorithmic details. In particular, we focus on the
                 source transformation approach that generates locally
                 optimal gradient code for single assignments by vertex
                 elimination in the linearized computational graph.
                 Extensive tests show the superiority of this method
                 over the current overloading-based approach. The
                 robustness and convenience of the new compiler-feature
                 is illustrated by various case studies.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Tang:2005:DNI,
  author =       "Ping Tak Peter Tang",
  title =        "{DFTI} --- a new interface for {Fast Fourier
                 Transform} libraries",
  journal =      j-TOMS,
  volume =       "31",
  number =       "4",
  pages =        "475--507",
  month =        dec,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1114268.1114271",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 16 11:39:20 MST 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The Fast Fourier Transform (FFT) algorithm that
                 calculates the Discrete Fourier Transform (DFT) is one
                 of the major breakthroughs in scientific computing and
                 is now an indispensable tool in a vast number of
                 fields. Unfortunately, software applications that
                 provide fast computation of DFT via FFT differ vastly
                 in functionality and lack uniformity. A widely accepted
                 Applications Programmer Interface (API) for DFT would
                 advance the field of scientific computing
                 significantly. In this article, we present the
                 specification of DFTI, a new interface that combines
                 functionality with ease of use. This API is our
                 strawman proposal toward a common interface for DFT
                 calculations.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Mu:2005:PMN,
  author =       "Mo Mu",
  title =        "{PDE.Mart}: a network-based problem-solving
                 environment for {PDEs}",
  journal =      j-TOMS,
  volume =       "31",
  number =       "4",
  pages =        "508--531",
  month =        dec,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1114268.1114272",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 16 11:39:20 MST 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "PDE.Mart is a network-based problem-solving
                 environment (PSE) for solving partial differential
                 equations (PDEs) in numerical simulations and academic
                 research, as well as in educational settings. The
                 client-server protocol consists of a
                 Web-browser-enabled graphical user interface, PDE-GUI,
                 that runs on client machines to manage the server
                 connection, geometric and model specifications,
                 computational method selection, and postprocessing; a
                 server system, PDE-Server, to build computational
                 engines and provide PDE solution services on the host
                 machine; and a library, PDE-LIB, that contains building
                 blocks for developing network-based and PDE-oriented
                 PSEs.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ledoux:2005:MMP,
  author =       "V. Ledoux and M. {Van Daele} and G. {Vanden Berghe}",
  title =        "{MATSLISE}: {A MATLAB} package for the numerical
                 solution of {Sturm--Liouville} and {Schr{\"o}dinger}
                 equations",
  journal =      j-TOMS,
  volume =       "31",
  number =       "4",
  pages =        "532--554",
  month =        dec,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1114268.1114273",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 16 11:39:20 MST 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "MATSLISE is a graphical MATLAB software package for
                 the interactive numerical study of regular
                 Sturm--Liouville problems, one-dimensional
                 Schr{\"o}dinger equations, and radial Schr{\"o}dinger
                 equations with a distorted Coulomb potential. It allows
                 the fast and accurate computation of the eigenvalues
                 and the visualization of the corresponding
                 eigenfunctions. This is realized by making use of the
                 power of high-order piecewise constant perturbation
                 methods, a technique described by Ixaru. For a
                 well-outlined class of problems, the implemented
                 algorithms are more efficient than the well-established
                 SL-solvers SL02f, SLEDGE, SLEIGN, and SLEIGN2, which
                 are included by Pryce in the SLDRIVER code that has
                 been built on top of SLTSTPAK.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gao:2005:AMS,
  author =       "Tangan Gao and T. Y. Li and Mengnien Wu",
  title =        "{Algorithm 846}: {MixedVol}: a software package for
                 mixed-volume computation",
  journal =      j-TOMS,
  volume =       "31",
  number =       "4",
  pages =        "555--560",
  month =        dec,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1114268.1114274",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 16 11:39:20 MST 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "MixedVol is a C++ software package that computes the
                 mixed volume of n finite subsets of $\mathbb{Z}^n$ or
                 the support of a system of n polynomials in $n$
                 variables. The software produces the mixed volume as
                 well as the mixed cells. The mixed cells are crucial
                 for solving polynomial systems by the polyhedral
                 homotopy continuation method. The software leads
                 existing codes for mixed-volume computation in speed by
                 a substantial margin and its memory requirement is very
                 low.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Klimke:2005:ASP,
  author =       "Andreas Klimke and Barbara Wohlmuth",
  title =        "{Algorithm 847}: {Spinterp}: piecewise multilinear
                 hierarchical sparse grid interpolation in {MATLAB}",
  journal =      j-TOMS,
  volume =       "31",
  number =       "4",
  pages =        "561--579",
  month =        dec,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1114268.1114275",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 16 11:39:20 MST 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "To recover or approximate smooth multivariate
                 functions, sparse grids are superior to full grids due
                 to a significant reduction of the required support
                 nodes. The order of the convergence rate in the maximum
                 norm is preserved up to a logarithmic factor. We
                 describe three possible piecewise multilinear
                 hierarchical interpolation schemes in detail and
                 conduct a numerical comparison. Furthermore, we
                 document the features of our sparse grid interpolation
                 software package {\tt spinterp} for MATLAB.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Shellman:2005:ARF,
  author =       "Spencer Shellman and K. Sikorski",
  title =        "{Algorithm 848}: a recursive fixed-point algorithm for
                 the infinity-norm case",
  journal =      j-TOMS,
  volume =       "31",
  number =       "4",
  pages =        "580--586",
  month =        dec,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1114268.1114276",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 16 11:39:20 MST 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present the PFix algorithm for approximating a
                 fixed point of a function f that has arbitrary
                 dimensionality, is defined on a rectangular domain, and
                 is Lipschitz continuous with respect to the infinity
                 norm with constant 1. PFix has applications in
                 economics, game theory, and the solution of partial
                 differential equations. PFix computes an approximation
                 that satisfies the residual error criterion, and can
                 also compute an approximation satisfying the absolute
                 error criterion when the Lipschitz constant is less
                 than 1. For functions defined on all rectangular
                 domains, the worst-case complexity of PFix has order
                 equal to the logarithm of the reciprocal of the
                 tolerance, raised to the power of the dimension.
                 Dividing this order expression by the factorial of the
                 dimension yields the order of the worst-case bound for
                 the case of the unit hypercube. PFix is a recursive
                 algorithm, in that it uses solutions to a d-dimensional
                 problem to compute a solution to a $(d +
                 1)$-dimensional problem. A full analysis of PFix may be
                 found in Shellman and Sikorski [2003b], and a C
                 implementation is available through ACM ToMS.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Davis:2005:ACS,
  author =       "Timothy A. Davis",
  title =        "{Algorithm 849}: a concise sparse {Cholesky}
                 factorization package",
  journal =      j-TOMS,
  volume =       "31",
  number =       "4",
  pages =        "587--591",
  month =        dec,
  year =         "2005",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1114268.1114277",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 16 11:39:20 MST 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The LDL software package is a set of short, concise
                 routines for factorizing symmetric positive-definite
                 sparse matrices, with some applicability to symmetric
                 indefinite matrices. Its primary purpose is to
                 illustrate much of the basic theory of sparse matrix
                 algorithms in as concise a code as possible, including
                 an elegant method of sparse symmetric factorization
                 that computes the factorization row-by-row but stores
                 it column-by-column. The entire symbolic and numeric
                 factorization consists of less than 50 executable lines
                 of code. The package is written in C, and includes a
                 MATLAB interface.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Panneton:2006:ILP,
  author =       "Fran{\c{c}}ois Panneton and Pierre L'Ecuyer and Makoto
                 Matsumoto",
  title =        "Improved long-period generators based on linear
                 recurrences modulo $2$",
  journal =      j-TOMS,
  volume =       "32",
  number =       "1",
  pages =        "1--16",
  month =        mar,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1132973.1132974",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri May 26 06:32:19 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Fast uniform random number generators with extremely
                 long periods have been defined and implemented based on
                 linear recurrences modulo $2$. The twisted GFSR and the
                 Mersenne twister are famous recent examples. Besides
                 the period length, the statistical quality of these
                 generators is usually assessed via their
                 equidistribution properties. The huge-period generators
                 proposed so far are not quite optimal in this respect.
                 In this article, we propose new generators of that form
                 with better equidistribution and ``bit-mixing''
                 properties for equivalent period length and speed. The
                 state of our new generators evolves in a more chaotic
                 way than for the Mersenne twister. We illustrate how
                 this can reduce the impact of persistent dependencies
                 among successive output values, which can be observed
                 in certain parts of the period of gigantic generators
                 such as the Mersenne twister.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Guermouche:2006:CMM,
  author =       "Abdou Guermouche and Jean-Yves L'Excellent",
  title =        "Constructing memory-minimizing schedules for
                 multifrontal methods",
  journal =      j-TOMS,
  volume =       "32",
  number =       "1",
  pages =        "17--32",
  month =        mar,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1132973.1132975",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri May 26 06:32:19 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We are interested in the memory usage of multifrontal
                 methods. Starting from the algorithms introduced by
                 Liu, we propose new schedules to allocate and process
                 tasks that improve memory usage. This generalizes two
                 existing factorization and memory-allocation schedules
                 by allowing a more flexible task allocation together
                 with a specific tree traversal. We present optimal
                 algorithms for this new class of schedules, and
                 demonstrate experimentally their benefit for some
                 real-world matrices from sparse matrix collections
                 where either the active memory or the total memory is
                 minimized.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Koyuturk:2006:NDB,
  author =       "Mehmet Koyut{\"u}rk and Ananth Grama and Naren
                 Ramakrishnan",
  title =        "Nonorthogonal decomposition of binary matrices for
                 bounded-error data compression and analysis",
  journal =      j-TOMS,
  volume =       "32",
  number =       "1",
  pages =        "33--69",
  month =        mar,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1132973.1132976",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri May 26 06:32:19 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article presents the design and implementation of
                 a software tool, PROXIMUS, for error-bounded
                 approximation of high-dimensional binary attributed
                 datasets based on nonorthogonal decomposition of binary
                 matrices. This tool can be used for analyzing data
                 arising in a variety of domains ranging from commercial
                 to scientific applications. Using a combination of
                 innovative algorithms, novel data structures, and
                 efficient implementation, PROXIMUS demonstrates
                 excellent accuracy, performance, and scalability to
                 large datasets. We experimentally demonstrate these on
                 diverse applications in association rule mining and DNA
                 microarray analysis. In limited beta release, PROXIMUS
                 currently has over 300 installations in over 10
                 countries.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gil:2006:CRP,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Computing the real parabolic cylinder functions
                 {$U(a,x)$, $V(a,x)$}",
  journal =      j-TOMS,
  volume =       "32",
  number =       "1",
  pages =        "70--101",
  month =        mar,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1132973.1132977",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri May 26 06:32:19 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Methods for the computation of real parabolic cylinder
                 functions $U(a, x)$, and $V(a, x)$ and their
                 derivatives are described. We give details on power
                 series, asymptotic series, recursion and quadrature. A
                 combination of these methods can be used for computing
                 parabolic cylinder functions for unrestricted values of
                 the order $a$ and the variable $x$ except for the
                 overflow\slash underflow limitations. By factoring the
                 dominant exponential factor, scaled functions can be
                 computed without practical overflow\slash underflow
                 limitations. In an accompanying article we describe the
                 precise domains for these methods and we present the
                 Fortran 90 codes for the computation of these
                 functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gil:2006:ARP,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 850}: {Real} parabolic cylinder functions
                 {$U(a,x)$, $V(a,x)$}",
  journal =      j-TOMS,
  volume =       "32",
  number =       "1",
  pages =        "102--112",
  month =        mar,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1132973.1132978",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri May 26 06:32:19 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Fortran 90 programs for the computation of real
                 parabolic cylinder functions are presented. The code
                 computes the functions $U(a, x)$, $V(a, x)$ and their
                 derivatives for real $a$ and $x (x \geq 0)$. The code
                 also computes scaled functions. The range of
                 computation for scaled PCFs is practically
                 unrestricted. The aimed relative accuracy for scaled
                 functions is better than $5 \times 10^{14}$. Exceptions
                 to this accuracy are the evaluation of the functions
                 near their zeros and the error caused by the evaluation
                 of trigonometric functions of large arguments when $|a|
                 > x$. The routines always give values for which the
                 Wronskian relation for scaled functions is verified
                 with a relative accuracy better than $5 \times
                 10^{14}$. The accuracy of the unscaled functions is
                 also better than $5 \times 10^{14}$ for moderate values
                 of $x$ and $a$ (except close to the zeros), while for
                 large $x$ and $a$ the error is dominated by exponential
                 and trigonometric function evaluations. For IEEE
                 standard double precision arithmetic, the accuracy is
                 better than $5 \times 10^{13}$ in the computable range
                 of unscaled PCFs (except close to the zeros).",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hager:2006:ACD,
  author =       "William W. Hager and Hongchao Zhang",
  title =        "{Algorithm 851}: {CG\_DESCENT}, a conjugate gradient
                 method with guaranteed descent",
  journal =      j-TOMS,
  volume =       "32",
  number =       "1",
  pages =        "113--137",
  month =        mar,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1132973.1132979",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri May 26 06:32:19 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Recently, a new nonlinear conjugate gradient scheme
                 was developed which satisfies the descent condition
                 $g^T_k d_k \leq -7/8 ||g_k||^2$ and which is globally
                 convergent whenever the line search fulfills the Wolfe
                 conditions. This article studies the convergence
                 behavior of the algorithm; extensive numerical tests
                 and comparisons with other methods for large-scale
                 unconstrained optimization are given.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Granvilliers:2006:ARI,
  author =       "Laurent Granvilliers and Fr{\'e}d{\'e}ric Benhamou",
  title =        "{Algorithm 852}: {RealPaver}: an interval solver using
                 constraint satisfaction techniques",
  journal =      j-TOMS,
  volume =       "32",
  number =       "1",
  pages =        "138--156",
  month =        mar,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1132973.1132980",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri May 26 06:32:19 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.sciences.univ-nantes.fr/info/perso/permanents/granvil/papers/gbtoms05.pdf",
  abstract =     "RealPaver is an interval software for modeling and
                 solving nonlinear systems. Reliable approximations of
                 continuous or discrete solution sets are computed using
                 Cartesian products of intervals. Systems are given by
                 sets of equations or inequality constraints over
                 integer and real variables. Moreover, they may have
                 different natures, being square or nonsquare, sparse or
                 dense, linear, polynomial, or involving transcendental
                 functions. The modeling language permits stating
                 constraint models and tuning parameters of solving
                 algorithms which efficiently combine interval methods
                 and constraint satisfaction techniques. Several
                 consistency techniques (box, hull, and 3B) are
                 implemented. The distribution includes C sources,
                 executables for different machine architectures,
                 documentation, and benchmarks. The portability is
                 ensured by the GNU C compiler.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Foster:2006:AEA,
  author =       "Leslie Foster and Rajesh Kommu",
  title =        "{Algorithm 853}: an efficient algorithm for solving
                 rank-deficient least squares problems",
  journal =      j-TOMS,
  volume =       "32",
  number =       "1",
  pages =        "157--165",
  month =        mar,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1132973.1132981",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri May 26 06:32:19 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Existing routines, such as xGELSY or xGELSD in LAPACK,
                 for solving rank-deficient least squares problems
                 require {$O(m n^2)$} operations to solve $\min ||b -
                 Ax||$ where $A$ is an $m$ by $n$ matrix. We present a
                 modification of the LAPACK routine xGELSY that requires
                 $O(m n k)$ operations where $k$ is the effective
                 numerical rank of the matrix $A$. For low rank matrices
                 the modification is an order of magnitude faster than
                 the LAPACK code.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hasselman:2006:RAF,
  author =       "Berend Hasselman",
  title =        "Remark on {Algorithm 815}: {FORTRAN} subroutines for
                 computing approximate solutions of feedback set
                 problems using {GRASP}",
  journal =      j-TOMS,
  volume =       "32",
  number =       "1",
  pages =        "166--168",
  month =        mar,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1132973.1132982",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri May 26 06:32:19 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We show that the Fortran source code for Algorithm 815
                 contains an error and we propose a correction. The
                 error may cause the algorithm to generate incorrect
                 results. We also show that the performance of the
                 corrected algorithm can be improved by a minor
                 adjustment in the code.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Joffrain:2006:AHT,
  author =       "Thierry Joffrain and Tze Meng Low and Enrique S.
                 Quintana-Ort{\'\i} and Robert van de Geijn and Field G.
                 {Van Zee}",
  title =        "Accumulating {Householder} transformations,
                 revisited",
  journal =      j-TOMS,
  volume =       "32",
  number =       "2",
  pages =        "169--179",
  month =        jun,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1141885.1141886",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Aug 23 10:29:48 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A theorem related to the accumulation of Householder
                 transformations into a single orthogonal transformation
                 known as the compact WY transform is presented. It
                 provides a simple characterization of the computation
                 of this transformation and suggests an alternative
                 algorithm for computing it. It also suggests an
                 alternative transformation, the UT transform, with the
                 same utility as the compact WY Transform which requires
                 less computation and has similar stability properties.
                 That alternative transformation was first published
                 over a decade ago but has gone unnoticed by the
                 community.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Quintana-Orti:2006:IPR,
  author =       "Gregorio Quintana-Ort{\'\i} and Robert van de Geijn",
  title =        "Improving the performance of reduction to {Hessenberg}
                 form",
  journal =      j-TOMS,
  volume =       "32",
  number =       "2",
  pages =        "180--194",
  month =        jun,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1141885.1141887",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Aug 23 10:29:48 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this article, a modification of the blocked
                 algorithm for reduction to Hessenberg form is presented
                 that improves performance by shifting more computation
                 from less efficient matrix-vector operations to highly
                 efficient matrix-matrix operations. Significant
                 performance improvements are reported relative to the
                 performance achieved by the current LAPACK
                 implementation.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Forth:2006:EOI,
  author =       "Shaun A. Forth",
  title =        "An efficient overloaded implementation of forward mode
                 automatic differentiation in {MATLAB}",
  journal =      j-TOMS,
  volume =       "32",
  number =       "2",
  pages =        "195--222",
  month =        jun,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1141885.1141888",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Aug 23 10:29:48 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The Mad package described here facilitates the
                 evaluation of first derivatives of multidimensional
                 functions that are defined by computer codes written in
                 MATLAB. The underlying algorithm is the well-known
                 forward mode of automatic differentiation implemented
                 via operator overloading on variables of the class
                 fmad. The main distinguishing feature of this MATLAB
                 implementation is the separation of the linear
                 combination of derivative vectors into a separate
                 derivative vector class derivvec. This allows for the
                 straightforward performance optimization of the overall
                 package. Additionally, by internally using a matrix
                 (two-dimensional) representation of arbitrary dimension
                 directional derivatives, we may utilize MATLAB's sparse
                 matrix class to propagate sparse directional
                 derivatives for MATLAB code which uses arbitrary
                 dimension arrays. On several examples, the package is
                 shown to be more efficient than Verma's ADMAT package
                 [Verma 1998a].",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kirby:2006:OFL,
  author =       "Robert C. Kirby",
  title =        "Optimizing {FIAT} with {Level 3 BLAS}",
  journal =      j-TOMS,
  volume =       "32",
  number =       "2",
  pages =        "223--235",
  month =        jun,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1141885.1141889",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Aug 23 10:29:48 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Our previous work on FIAT (Finite Element Automatic
                 Tabulator) developed a ``computational representation
                 theory'' that allowed us to construct arbitrary order
                 instances of a wide range of finite elements, many of
                 which are infrequently used owing to their associated
                 code complexity. In our present work, we further hone
                 this theory by rephrasing most of the internal
                 operations as linear transformations over
                 finite-dimensional Banach spaces. This additional
                 insight has led to increased code granularity and
                 allowed the use of level 3 BLAS operations. This is
                 both a conceptual and a practical development; as the
                 run-time performance of FIAT has been improved multiple
                 orders of magnitude.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Brisebarre:2006:CME,
  author =       "Nicolas Brisebarre and Jean-Michel Muller and Arnaud
                 Tisserand",
  title =        "Computing machine-efficient polynomial
                 approximations",
  journal =      j-TOMS,
  volume =       "32",
  number =       "2",
  pages =        "236--256",
  month =        jun,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1141885.1141890",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Aug 23 10:29:48 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Polynomial approximations are almost always used when
                 implementing functions on a computing system. In most
                 cases, the polynomial that best approximates (for a
                 given distance and in a given interval) a function has
                 coefficients that are not exactly representable with a
                 finite number of bits. And yet, the polynomial
                 approximations that are actually implemented do have
                 coefficients that are represented with a finite---and
                 sometimes small---number of bits. This is due to the
                 finiteness of the floating-point representations (for
                 software implementations), and to the need to have
                 small, hence fast and/or inexpensive, multipliers (for
                 hardware implementations). We then have to consider
                 polynomial approximations for which the degree-$i$
                 coefficient has at most $m_i$ fractional bits; in other
                 words, it is a rational number with denominator
                 $2^{m_i}$. We provide a general and efficient method
                 for finding the best polynomial approximation under
                 this constraint. Moreover, our method also applies if
                 some other constraints (such as requiring some
                 coefficients to be equal to some predefined constants
                 or minimizing relative error instead of absolute error)
                 are required.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kolonko:2006:SRS,
  author =       "M. Kolonko and D. W{\"a}sch",
  title =        "Sequential reservoir sampling with a nonuniform
                 distribution",
  journal =      j-TOMS,
  volume =       "32",
  number =       "2",
  pages =        "257--273",
  month =        jun,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1141885.1141891",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Aug 23 10:29:48 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a simple algorithm that allows sampling
                 from a stream of data items without knowing the number
                 of items in advance and without having to store all
                 items in main memory. The sampling distribution may be
                 general, that is, the probability of selecting a data
                 item i may depend on the individual item. The main
                 advantage of the algorithms is that they have to pass
                 through the data items only once to produce a sample of
                 arbitrary size $n$. We give different variants of the
                 algorithm for sampling with and without replacement and
                 analyze their complexity. We generalize earlier results
                 of Knuth on reservoir sampling with a uniform sampling
                 distribution. The general distribution considered here
                 allows us to sample an item with a probability equal to
                 the relative weight (or fitness) of the data item
                 within the whole set of items. Applications include
                 heuristic optimization procedures such as genetic
                 algorithms where solutions are sampled from a
                 population with probability proportional to their
                 fitness.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cameron:2006:MPA,
  author =       "Frank Cameron",
  title =        "A {Matlab} package for automatically generating
                 {Runge--Kutta} trees, order conditions, and truncation
                 error coefficients",
  journal =      j-TOMS,
  volume =       "32",
  number =       "2",
  pages =        "274--298",
  month =        jun,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1141885.1141892",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Aug 23 10:29:48 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In designing parts of Runge--Kutta methods, order
                 conditions and truncation error coefficients (TECs) are
                 needed. Order conditions and TECs are typically
                 presented as a set of trees combined with rules for
                 producing algebraic expressions from the trees. The
                 tree sets are defined recursively and can be generated
                 by hand only for low orders. This article describes a
                 package of Matlab routines for automatically generating
                 Runge--Kutta trees, order conditions, and TECs. The
                 routines are capable of generating Maple code, Matlab
                 code, or \LaTeX{} expressions for ODEs or DAEs of index
                 1 and 2. In producing the package, two theoretical
                 problems are tackled: (a) avoiding the repeated
                 generation of the same tree and (b) the efficient
                 storage of TECs.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lerch:2006:FFI,
  author =       "Michael Lerch and German Tischler and J{\"u}rgen Wolff
                 Von Gudenberg and Werner Hofschuster and Walter
                 Kr{\"a}mer",
  title =        "{FILIB++}, a fast interval library supporting
                 containment computations",
  journal =      j-TOMS,
  volume =       "32",
  number =       "2",
  pages =        "299--324",
  month =        jun,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1141885.1141893",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Aug 23 10:29:48 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "filib++ is an extension of the interval library filib
                 originally developed at the University of Karlsruhe.
                 The most important aim of filib is the fast computation
                 of guaranteed bounds for interval versions of a
                 comprehensive set of elementary functions. filib++
                 extends this library in two aspects. First, it adds a
                 second mode, the extended mode, that extends the
                 exception-free computation mode (using special values
                 to represent infinities and NaNs known from the IEEE
                 floating-point standard 754) to intervals. In this
                 mode, the so-called containment sets are computed to
                 enclose the topological closure of a range of a
                 function over an interval. Second, our new design uses
                 templates and traits classes to obtain an efficient,
                 easily extendable, and portable C++ library.",
  acknowledgement = ack-nhfb,
  author-dates = "1952--2014 (WK)",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Demmel:2006:EBE,
  author =       "James Demmel and Yozo Hida and William Kahan and
                 Xiaoye S. Li and Sonil Mukherjee and E. Jason Riedy",
  title =        "Error bounds from extra-precise iterative refinement",
  journal =      j-TOMS,
  volume =       "32",
  number =       "2",
  pages =        "325--351",
  month =        jun,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1141885.1141894",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Aug 23 10:29:48 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present the design and testing of an algorithm for
                 iterative refinement of the solution of linear
                 equations where the residual is computed with extra
                 precision. This algorithm was originally proposed in
                 1948 and analyzed in the 1960s as a means to compute
                 very accurate solutions to all but the most
                 ill-conditioned linear systems. However, two obstacles
                 have until now prevented its adoption in standard
                 subroutine libraries like LAPACK: (1) There was no
                 standard way to access the higher precision arithmetic
                 needed to compute residuals, and (2) it was unclear how
                 to compute a reliable error bound for the computed
                 solution. The completion of the new BLAS Technical
                 Forum Standard has essentially removed the first
                 obstacle. To overcome the second obstacle, we show how
                 the application of iterative refinement can be used to
                 compute an error bound in any norm at small cost and
                 use this to compute both an error bound in the usual
                 infinity norm, and a componentwise relative error
                 bound. We report extensive test results on over $6.2$
                 million matrices of dimensions $5$, $10$, $100$, and
                 $1000$. As long as a normwise (componentwise) condition
                 number computed by the algorithm is less than
                 $1/max\{10,\sqrt{n}\}\varepsilon_w$, the computed
                 normwise (componentwise) error bound is at most $2
                 max\{10, \sqrt{n}\} \cdot \varepsilon_w$, and indeed
                 bounds the true error. Here, $n$ is the matrix
                 dimension and $\varepsilon_w = 2^{-24}$ is the working
                 precision. Residuals were computed in double precision
                 (53 bits of precision). In other words, the algorithm
                 always computed a tiny error at negligible extra cost
                 for most linear systems. For worse conditioned problems
                 (which we can detect using condition estimation), we
                 obtained small correct error bounds in over 90\% of
                 cases.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Benner:2006:AFS,
  author =       "Peter Benner and Daniel Kressner",
  title =        "{Algorithm 854}: {Fortran 77} subroutines for
                 computing the eigenvalues of {Hamiltonian} matrices
                 {II}",
  journal =      j-TOMS,
  volume =       "32",
  number =       "2",
  pages =        "352--373",
  month =        jun,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1141885.1141895",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Aug 23 10:29:48 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article describes Fortran 77 subroutines for
                 computing eigenvalues and invariant subspaces of
                 Hamiltonian and skew-Hamiltonian matrices. The
                 implemented algorithms are based on orthogonal
                 symplectic decompositions, implying numerical backward
                 stability as well as symmetry preservation for the
                 computed eigenvalues. These algorithms are supplemented
                 with balancing and block algorithms which can lead to
                 considerable accuracy and performance improvements. As
                 a by-product, an efficient implementation for computing
                 symplectic QR decompositions is provided. We
                 demonstrate the usefulness of the subroutines for
                 several, practically relevant examples.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sharp:2006:BSP,
  author =       "Philip W. Sharp",
  title =        "{$N$}-body simulations: {The} performance of some
                 integrators",
  journal =      j-TOMS,
  volume =       "32",
  number =       "3",
  pages =        "375--395",
  month =        sep,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1163641.1163642",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 27 05:51:43 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe four challenging $N$-body test problems
                 involving the Sun and planets and use them to compare
                 the performance of nine nonsymplectic and two
                 symplectic integrators. Each problem has a long
                 interval of integration and two have non-Newtonian
                 gravitational interactions. The emphasis in our
                 comparison is on the accuracy of the solution,
                 including the phase information produced by
                 nonsympletic methods; the symplectic methods have been
                 included to provide a contrast. Long intervals of
                 integration necessitate small local error tolerances
                 for the nonsymplectic integrators. Among
                 variable-stepsize integrators, RKNINT requires the
                 least CPU time on the two problems with Newtonian
                 interactions and DIVA the least CPU time on the other
                 two problems for the intervals of integration we used.
                 We find that the error growth on some integrations is
                 noticeably slower than predicted by asymptotic analysis
                 of the truncation and round-off error. Our comparisons
                 suggest that the numerical solutions near the end of a
                 billion year simulation in double precision with
                 variable-stepsize nonsymplectic methods would have poor
                 accuracy.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sala:2006:OOF,
  author =       "Marzio Sala",
  title =        "An object-oriented framework for the development of
                 scalable parallel multilevel preconditioners",
  journal =      j-TOMS,
  volume =       "32",
  number =       "3",
  pages =        "396--416",
  month =        sep,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1163641.1163643",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 27 05:51:43 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present the design of a high-performance
                 object-oriented framework that enables the rapid
                 development and usage of efficient, scalable, and
                 portable implementations of multilevel preconditioners
                 for distributed sparse real matrices, in both serial
                 and (massively) parallel environments. The main feature
                 of the proposed framework is the use of several
                 programming paradigms for the different implementation
                 layers, with a strong emphasis on object-oriented
                 classes and operator overloading for the top layer, and
                 optimized FORTRAN and C code for the layers underneath.
                 We describe an implementation of the proposed framework
                 that is based on the ML library, the algebraic
                 multilevel preconditioning package of Trilinos, which
                 supports state-of-the-art parallel smoothed aggregation
                 methods, and can be used to define general algebraic
                 and geometric multilevel and multigrid preconditioners
                 and solvers. The article demonstrates that we can take
                 advantage of object-oriented programming and operator
                 overloading to obtain intuitive, easy-to-read, and
                 easy-to-develop codes that are at the same time
                 efficient and scalable. Several numerical experiments
                 obtained on serial and parallel computers show that the
                 overhead required by the object-oriented layer is very
                 modest, therefore allowing developers to focus on the
                 new algorithms they are developing and testing, rather
                 than on implementation details.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kirby:2006:CVF,
  author =       "Robert C. Kirby and Anders Logg",
  title =        "A compiler for variational forms",
  journal =      j-TOMS,
  volume =       "32",
  number =       "3",
  pages =        "417--444",
  month =        sep,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1163641.1163644",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 27 05:51:43 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "As a key step towards a complete automation of the
                 finite element method, we present a new algorithm for
                 automatic and efficient evaluation of multilinear
                 variational forms. The algorithm has been implemented
                 in the form of a compiler, the FEniCS Form Compiler
                 (FFC). We present benchmark results for a series of
                 standard variational forms, including the
                 incompressible Navier--Stokes equations and linear
                 elasticity. The speedup compared to the standard
                 quadrature-based approach is impressive; in some cases
                 the speedup is as large as a factor of 1000.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Meshar:2006:CSS,
  author =       "Omer Meshar and Dror Irony and Sivan Toledo",
  title =        "An out-of-core sparse symmetric-indefinite
                 factorization method",
  journal =      j-TOMS,
  volume =       "32",
  number =       "3",
  pages =        "445--471",
  month =        sep,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1163641.1163645",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 27 05:51:43 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a new out-of-core sparse
                 symmetric-indefinite factorization algorithm. The most
                 significant innovation of the new algorithm is a
                 dynamic partitioning method for the sparse factor. This
                 partitioning method results in very low I/O traffic and
                 allows the algorithm to run at high computational
                 rates, even though the factor is stored on a slow disk.
                 Our implementation of the new code compares well with
                 both high-performance in-core sparse
                 symmetric-indefinite codes and a high-performance
                 out-of-core sparse Cholesky code.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Alhargan:2006:ASC,
  author =       "Fayez A. Alhargan",
  title =        "{Algorithm 855}: {Subroutines} for the computation of
                 {Mathieu} characteristic numbers and their general
                 orders",
  journal =      j-TOMS,
  volume =       "32",
  number =       "3",
  pages =        "472--484",
  month =        sep,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1163641.1163646",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 27 05:51:43 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A continued fraction function algorithm is developed
                 to evaluate general-order Mathieu characteristic
                 numbers, and a new technique is presented for
                 evaluating the Mathieu determinant which can be used to
                 compute the order directly. Approximate expressions are
                 developed to estimate the orders and Mathieu
                 characteristic numbers for the root, finding
                 algorithms. The algorithms, with minor modifications,
                 were used for computing Mathieu coefficients of general
                 order. The algorithms can deal with a large range of
                 Mathieu characteristic number $c$, real and complex
                 order $\nu$, and parameter $h$.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gray:2006:AAA,
  author =       "Genetha A. Gray and Tamara G. Kolda",
  title =        "{Algorithm 856}: {APPSPACK 4.0}: asynchronous parallel
                 pattern search for derivative-free optimization",
  journal =      j-TOMS,
  volume =       "32",
  number =       "3",
  pages =        "485--507",
  month =        sep,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1163641.1163647",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 27 05:51:43 MDT 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "APPSPACK is software for solving unconstrained and
                 bound-constrained optimization problems. It implements
                 an asynchronous parallel pattern search method that has
                 been specifically designed for problems characterized
                 by expensive function evaluations. Using APPSPACK to
                 solve optimization problems has several advantages: No
                 derivative information is needed; the procedure for
                 evaluating the objective function can be executed via a
                 separate program or script; the code can be run
                 serially or in parallel, regardless of whether the
                 function evaluation itself is parallel; and the
                 software is freely available. We describe the
                 underlying algorithm, data structures, and features of
                 APPSPACK version 4.0, as well as how to use and
                 customize the software.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{LEcuyer:2006:ISB,
  author =       "Pierre L'Ecuyer and Richard Simard",
  title =        "Inverting the symmetrical beta distribution",
  journal =      j-TOMS,
  volume =       "32",
  number =       "4",
  pages =        "509--520",
  month =        dec,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1186785.1186786",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:57 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We propose a fast algorithm for computing the inverse
                 symmetrical beta distribution. Four series (two around
                 $x = 0$ and two around $x = 1/2$) are used to
                 approximate the distribution function, and its inverse
                 is found via Newton's method. This algorithm can be
                 used to generate beta random variates by inversion and
                 is much faster than currently available general
                 inversion methods for the beta distribution. It turns
                 out to be very useful for generating gamma processes
                 efficiently via bridge sampling.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kressner:2006:BAR,
  author =       "Daniel Kressner",
  title =        "Block algorithms for reordering standard and
                 generalized {Schur} forms",
  journal =      j-TOMS,
  volume =       "32",
  number =       "4",
  pages =        "521--532",
  month =        dec,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1186785.1186787",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:57 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Block algorithms for reordering a selected set of
                 eigenvalues in a standard or generalized Schur form are
                 proposed. Efficiency is achieved by delaying orthogonal
                 transformations and (optionally) making use of level 3
                 BLAS operations. Numerical experiments demonstrate that
                 existing algorithms, as currently implemented in
                 LAPACK, are outperformed by up to a factor of four.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Dhillon:2006:DIM,
  author =       "Inderjit S. Dhillon and Beresford N. Parlett and
                 Christof V{\"o}mel",
  title =        "The design and implementation of the {MRRR}
                 algorithm",
  journal =      j-TOMS,
  volume =       "32",
  number =       "4",
  pages =        "533--560",
  month =        dec,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1186785.1186788",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:57 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In the 1990's, Dhillon and Parlett devised the
                 algorithm of multiple relatively robust representations
                 (MRRR) for computing numerically orthogonal
                 eigenvectors of a symmetric tridiagonal matrix $T$ with
                 $O(n^2)$ cost. While previous publications related to
                 MRRR focused on theoretical aspects of the algorithm, a
                 documentation of software issues has been missing. In
                 this article, we discuss the design and implementation
                 of the new MRRR version STEGR that will be included in
                 the next LAPACK release. By giving an algorithmic
                 description of MRRR and identifying governing
                 parameters, we hope to make STEGR more easily
                 accessible and suitable for future performance tuning.
                 Furthermore, this should help users understand design
                 choices and tradeoffs when using the code.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Su:2006:APP,
  author =       "Hai-Jun Su and J. Michael McCarthy and Masha Sosonkina
                 and Layne T. Watson",
  title =        "{Algorithm 857}: {POLSYS\_GLP}---a parallel general
                 linear product homotopy code for solving polynomial
                 systems of equations",
  journal =      j-TOMS,
  volume =       "32",
  number =       "4",
  pages =        "561--579",
  month =        dec,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1186785.1186789",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:57 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Globally convergent, probability-one homotopy methods
                 have proven to be very effective for finding all the
                 isolated solutions to polynomial systems of equations.
                 After many years of development, homotopy path trackers
                 based on probability-one homotopy methods are reliable
                 and fast. Now, theoretical advances reducing the number
                 of homotopy paths that must be tracked and handling
                 singular solutions have made probability-one homotopy
                 methods even more practical. POLSYS\_GLP consists of
                 Fortran 95 modules for finding all isolated solutions
                 of a complex coefficient polynomial system of
                 equations. The package is intended to be used on a
                 distributed memory multiprocessor in conjunction with
                 HOMPACK90 (Algorithm 777), and makes extensive use of
                 Fortran 95-derived data types and MPI to support a
                 general linear product (GLP) polynomial system
                 structure. GLP structure is intermediate between the
                 partitioned linear product structure used by
                 POLSYS\_PLP (Algorithm 801) and the BKK-based structure
                 used by PHCPACK. The code requires a GLP structure as
                 input, and although finding the optimal GLP structure
                 is a difficult combinatorial problem, generally
                 physical or engineering intuition about a problem
                 yields a very good GLP structure. POLSYS\_GLP employs a
                 sophisticated power series end game for handling
                 singular solutions, and provides support for problem
                 definition both at a high level and via hand-crafted
                 code. Different GLP structures and their corresponding
                 B{\'e}zout numbers can be systematically explored
                 before committing to root finding.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{VanDeun:2006:ACI,
  author =       "Joris {Van Deun} and Ronald Cools",
  title =        "{Algorithm 858}: {Computing} infinite range integrals
                 of an arbitrary product of {Bessel} functions",
  journal =      j-TOMS,
  volume =       "32",
  number =       "4",
  pages =        "580--596",
  month =        dec,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1186785.1186790",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:57 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present an algorithm to compute integrals of the
                 form $\int_0^\infty x^m \prod^k_i = 1J_{\nu_i}(a_ix)dx$
                 with $J_{\nu_i}(x)$ the Bessel function of the first
                 kind and (real) order $\nu_i$. The parameter $m$ is a
                 real number such that $\sum_i \nu_i + m > -1$ and the
                 coefficients $a_i$ are strictly positive real numbers.
                 The main ingredients in this algorithm are the
                 well-known asymptotic expansion for $J_{\nu_i}(x)$ and
                 the observation that the infinite part of the integral
                 can be approximated using the incomplete Gamma function
                 $\Gamma(a,z)$. Accurate error estimates are included in
                 the algorithm, which is implemented as a MATLAB
                 program.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Amodio:2006:ABF,
  author =       "Pierluigi Amodio and Giuseppe Romanazzi",
  title =        "{Algorithm 859}: {BABDCR}---a {Fortran 90} package for
                 the solution of bordered {ABD} linear systems",
  journal =      j-TOMS,
  volume =       "32",
  number =       "4",
  pages =        "597--608",
  month =        dec,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1186785.1186791",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:57 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "BABDCR is a package of Fortran 90 subroutines for the
                 solution of linear systems with bordered almost block
                 diagonal coefficient matrices. It is designed to handle
                 matrices with blocks of the same size, that is, having
                 a block upper bidiagonal structure with an additional
                 block in the right upper corner. The algorithm
                 implemented in the package performs cyclic reduction of
                 the coefficient matrix in order to reduce the fill-in
                 due to the corner block.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Goncalves:2006:ASE,
  author =       "Eduardo N. Gon{\c{c}}alves and Reinaldo M. Palhares
                 and Ricardo H. C. Takahashi and Renato C. Mesquita",
  title =        "{Algorithm 860}: {SimpleS}---an extension of
                 {Freudenthal}'s simplex subdivision",
  journal =      j-TOMS,
  volume =       "32",
  number =       "4",
  pages =        "609--621",
  month =        dec,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1186785.1186792",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:57 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article presents a simple efficient algorithm for
                 the subdivision of a $d$-dimensional simplex in $k^d$
                 simplices, where $k$ is any positive integer number.
                 The algorithm is an extension of Freudenthal's
                 subdivision method. The proposed algorithm deals with
                 the more general case of $k^d$ subdivision, and is
                 considerably simpler than the RedRefinementND algorithm
                 for implementation of Freudenthal's strategy. The
                 proposed simplex subdivision algorithm is motivated by
                 a problem in the field of robust control theory: the
                 computation of a tight upper bound of a dynamical
                 system performance index by means of a branch-and-bound
                 algorithm.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Erricolo:2006:AFS,
  author =       "Danilo Erricolo",
  title =        "{Algorithm 861}: {Fortran 90} subroutines for
                 computing the expansion coefficients of {Mathieu}
                 functions using {Blanch}'s algorithm",
  journal =      j-TOMS,
  volume =       "32",
  number =       "4",
  pages =        "622--634",
  month =        dec,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1186785.1186793",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:57 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A translation to Fortran 90 of Gertrude Blanch's
                 algorithm for computing the expansion coefficients of
                 the series that represent Mathieu functions is
                 presented. Its advantages are portability, higher
                 precision, practicality of use, and extended
                 documentation. In addition, numerical validations and
                 comparisons with other existing methods are
                 presented.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bader:2006:AMT,
  author =       "Brett W. Bader and Tamara G. Kolda",
  title =        "{Algorithm 862}: {MATLAB} tensor classes for fast
                 algorithm prototyping",
  journal =      j-TOMS,
  volume =       "32",
  number =       "4",
  pages =        "635--653",
  month =        dec,
  year =         "2006",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1186785.1186794",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:57 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Tensors (also known as multidimensional arrays or
                 $N$-way arrays) are used in a variety of applications
                 ranging from chemometrics to psychometrics. We describe
                 four MATLAB classes for tensor manipulations that can
                 be used for fast algorithm prototyping. The tensor
                 class extends the functionality of MATLAB's
                 multidimensional arrays by supporting additional
                 operations such as tensor multiplication. The
                 tensor\_as\_matrix class supports the ``matricization''
                 of a tensor, that is, the conversion of a tensor to a
                 matrix (and vice versa), a commonly used operation in
                 many algorithms. Two additional classes represent
                 tensors stored in decomposed formats: cp\_tensor and
                 tucker\_tensor. We describe all of these classes and
                 then demonstrate their use by showing how to implement
                 several tensor algorithms that have appeared in the
                 literature.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Enright:2007:RRD,
  author =       "W. H. Enright and Wayne B. Hayes",
  title =        "Robust and reliable defect control for {Runge--Kutta}
                 methods",
  journal =      j-TOMS,
  volume =       "33",
  number =       "1",
  pages =        "1:1--1:19",
  month =        mar,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1206040.1206041",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:58 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The quest for reliable integration of initial value
                 problems (IVPs) for ordinary differential equations
                 (ODEs) is a long-standing problem in numerical
                 analysis. At one end of the reliability spectrum are
                 fixed stepsize methods implemented using standard
                 floating point, where the onus lies entirely with the
                 user to ensure the stepsize chosen is adequate for the
                 desired accuracy. At the other end of the reliability
                 spectrum are rigorous interval-based methods, that can
                 provide provably correct bounds on the error of a
                 numerical solution. This rigour comes at a price,
                 however: interval methods are generally two to three
                 orders of magnitude more expensive than fixed stepsize
                 floating-point methods. Along the spectrum between
                 these two extremes lie various methods of different
                 expense that estimate and control some measure of the
                 local errors and adjust the stepsize accordingly.

                 In this article, we continue previous investigations
                 into a class of interpolants for use in Runge--Kutta
                 methods that have a defect function whose qualitative
                 behavior is asymptotically independent of the problem
                 being integrated. In particular the point, in a step,
                 where the maximum defect occurs as $ h \rightarrow 0 $
                 is known a priori. This property allows the defect to
                 be monitored and controlled in an efficient and robust
                 manner even for modestly large stepsizes. Our
                 interpolants also have a defect with the highest
                 possible order given the constraints imposed by the
                 order of the underlying discrete formula. We
                 demonstrate the approach on three Runge--Kutta methods
                 of orders 5, 6, and 8, and provide Fortran and
                 preliminary Matlab interfaces to these three new
                 integrators. We also consider how sensitive such
                 methods are to roundoff errors. Numerical results for
                 four problems on a range of accuracy requests are
                 presented.",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Neher:2007:CSF,
  author =       "Markus Neher",
  title =        "Complex standard functions and their implementation in
                 the {CoStLy} library",
  journal =      j-TOMS,
  volume =       "33",
  number =       "1",
  pages =        "2:1--2:27",
  month =        mar,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1206040.1206042",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:58 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The practical calculation of range bounds for some
                 complex standard functions is addressed in this
                 article. The functions under consideration are root and
                 power functions, the exponential, trigonometric and
                 hyperbolic functions, and their inverse functions. For
                 such a function $f$ and a given rectangular complex
                 interval $z$, some interval $w$ is computed that
                 contains all function values of $f$ in $z$. This is
                 done by expressing the real and the imaginary part of
                 $f$ as compositions of real standard functions and then
                 estimating the ranges of these compositions. In many
                 cases, the inclusions are optimal, such that $w$ is the
                 smallest rectangular interval containing the range of
                 $f$.

                 The algorithms presented in this article have been
                 implemented in a C++ class library called CoStLy
                 (Complex Standard Functions License), which is
                 distributed under the conditions of the GNU General
                 Public License.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gould:2007:FFF,
  author =       "Nicholas I. M. Gould and Philippe L. Toint",
  title =        "{FILTRANE}, a {Fortran 95} filter-trust-region package
                 for solving nonlinear least-squares and nonlinear
                 feasibility problems",
  journal =      j-TOMS,
  volume =       "33",
  number =       "1",
  pages =        "3:1--3:23",
  month =        mar,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1206040.1206043",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:58 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/gould-nicholas-ian.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "FILTRANE, a new Fortran 95 package for finding vectors
                 satisfying general sets of nonlinear equations and/or
                 inequalities, is presented. Several algorithmic
                 variants are discussed and extensively compared on a
                 set of CUTEr test problems, indicating that the default
                 variant is both reliable and efficient. This discussion
                 provides a first experimental study of the parameters
                 inherent in filter algorithms.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Berland:2007:EMP,
  author =       "H{\aa}vard Berland and B{\aa}rd Skaflestad and Will M.
                 Wright",
  title =        "{EXPINT} --- a {MATLAB} package for exponential
                 integrators",
  journal =      j-TOMS,
  volume =       "33",
  number =       "1",
  pages =        "4:1--4:17",
  month =        mar,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1206040.1206044",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:58 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Recently, a great deal of attention has been focused
                 on the construction of exponential integrators for
                 semilinear problems. In this article we describe a
                 MATLAB1 package which aims to facilitate the quick
                 deployment and testing of exponential integrators, of
                 Runge--Kutta, multistep, and general linear type. A
                 large number of integrators are included in this
                 package along with several well-known examples. The
                 so-called $ \varphi $ functions and their evaluation is
                 crucial for accuracy, stability, and efficiency of
                 exponential integrators, and the approach taken here is
                 through a modification of the scaling and squaring
                 technique, the most common approach used for computing
                 the matrix exponential.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Morandini:2007:UDS,
  author =       "Marco Morandini and Paolo Mantegazza",
  title =        "Using dense storage to solve small sparse linear
                 systems",
  journal =      j-TOMS,
  volume =       "33",
  number =       "1",
  pages =        "5:1--5:12",
  month =        mar,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1206040.1206045",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:58 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/multithreading.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A data structure is used to build a linear solver
                 specialized for relatively small sparse systems. The
                 proposed solver, optimized for run-time performance at
                 the expense of memory footprint, outperforms widely
                 used direct and sparse solvers for systems with between
                 100 and 3000 equations. A multithreaded version of the
                 solver is shown to give some speedups for problems with
                 medium fill-in, while it does not give any benefit for
                 very sparse problems.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Demetriou:2007:ALF,
  author =       "Ioannis C. Demetriou",
  title =        "{Algorithm 863}: {L2WPMA}, a {Fortran 77} package for
                 weighted least-squares piecewise monotonic data
                 approximation",
  journal =      j-TOMS,
  volume =       "33",
  number =       "1",
  pages =        "6:1--6:19",
  month =        mar,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1206040.1206046",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:58 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Fortran software is developed that calculates a best
                 piecewise monotonic approximation to $n$ univariate
                 data contaminated by random errors. The underlying
                 method minimizes the weighted sum of the squares of the
                 errors by requiring $ k - 1 $ sign changes in the first
                 divided differences of the approximation, where $k$ is
                 a given positive integer. Hence, the piecewise linear
                 interpolant to the fit consists of $k$ monotonic
                 sections, alternately increasing and decreasing. This
                 calculation can have about $ O(n^k) $ local minima,
                 because the positions of the turning points of the fit
                 are integer variables of the problem. The method,
                 however, by employing a dynamic programming technique
                 divides the data into at most $k$ disjoint sets of
                 adjacent data and solves a $ k = 1 $ problem (monotonic
                 fit or isotonic regression) for each set. So it
                 calculates efficiently a global solution in only $ O(n
                 \sigma + k \sigma^2) $ computer operations when $ k
                 \geq 3 $, where $ \sigma $ is the number of local
                 minima of the data, always bounded by $ n / 2 $. This
                 complexity reduces to only $ O(n) $ when $ k = 1 $ or $
                 k = 2 $ (unimodal case). At the end of the calculation
                 a spline representation of the solution and the
                 corresponding Lagrange multipliers are provided. The
                 software package has been tested on a variety of data
                 sets showing a performance that does provide in
                 practice shorter computation times than the complexity
                 indicates in theory. An application of the method on
                 identifying turning points and monotonic trends of data
                 from 1947--1996 on the U.K. pound over the U.S. dollar
                 exchange rate is presented. Generally, the method may
                 have useful applications as, for example, in estimating
                 the turning points of a function from some noisy
                 measurements of its values, or in image and signal
                 processing, or in providing a preliminary or
                 complementary smoothing phase to further analyses of
                 the data.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Martello:2007:AGR,
  author =       "Silvano Martello and David Pisinger and Daniele Vigo
                 and Edgar Den Boef and Jan Korst",
  title =        "{Algorithm 864}: {General} and robot-packable variants
                 of the three-dimensional bin packing problem",
  journal =      j-TOMS,
  volume =       "33",
  number =       "1",
  pages =        "7:1--7:12",
  month =        mar,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1206040.1206047",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:58 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We consider the problem of orthogonally packing a
                 given set of rectangular-shaped boxes into the minimum
                 number of three-dimensional rectangular bins. The
                 problem is NP-hard in the strong sense and extremely
                 difficult to solve in practice. We characterize
                 relevant subclasses of packing and present an algorithm
                 which is able to solve moderately large instances to
                 optimality. Extensive computational experiments compare
                 the algorithm for the three-dimensional bin packing
                 when solving general orthogonal packings and when
                 restricted to robot packings.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gustavson:2007:AFS,
  author =       "Fred G. Gustavson and John K. Reid and Jerzy
                 Wa{\'s}niewski",
  title =        "{Algorithm 865}: {Fortran 95} subroutines for
                 {Cholesky} factorization in block hybrid format",
  journal =      j-TOMS,
  volume =       "33",
  number =       "1",
  pages =        "8:1--8:5",
  month =        mar,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1206040.1206048",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Apr 14 09:48:58 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present subroutines for the Cholesky factorization
                 of a positive-definite symmetric matrix and for solving
                 corresponding sets of linear equations. They exploit
                 cache memory by using the block hybrid format proposed
                 by the authors in a companion article. The matrix is
                 packed into $ n(n + 1) / 2 $ real variables, and the
                 speed is usually better than that of the LAPACK
                 algorithm that uses full storage ($ n^2 $ variables).
                 Included are subroutines for rearranging a matrix whose
                 upper or lower-triangular part is packed by columns to
                 this format and for the inverse rearrangement. Also
                 included is a kernel subroutine that is used for the
                 Cholesky factorization of the diagonal blocks since it
                 is suitable for any positive-definite symmetric matrix
                 that is small enough to be held in cache. We provide a
                 comprehensive test program and simple example
                 programs.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Zhang:2007:SSI,
  author =       "Hong Zhang and Barry Smith and Michael Sternberg and
                 Peter Zapol",
  title =        "{SIPs}: Shift-and-invert parallel spectral
                 transformations",
  journal =      j-TOMS,
  volume =       "33",
  number =       "2",
  pages =        "1--19",
  month =        jun,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1236463.1236464",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 26 17:36:59 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "SIPs is a new efficient and robust software package
                 implementing multiple shift-and-invert spectral
                 transformations on parallel computers. Built on top of
                 SLEPc and PETSc, it can compute very large numbers of
                 eigenpairs for sparse symmetric generalized eigenvalue
                 problems. The development of SIPs is motivated by
                 applications in nanoscale materials modeling, in which
                 the growing size of the matrices and the pathological
                 eigenvalue distribution challenge the efficiency and
                 robustness of the solver. In this article, we present a
                 parallel eigenvalue algorithm based on distributed
                 spectrum slicing. We describe the object-oriented
                 design and implementation techniques in SIPs, and
                 demonstrate its numerical performance on an advanced
                 distributed computer.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gould:2007:NES,
  author =       "Nicholas I. M. Gould and Jennifer A. Scott and Yifan
                 Hu",
  title =        "A numerical evaluation of sparse direct solvers for
                 the solution of large sparse symmetric linear systems
                 of equations",
  journal =      j-TOMS,
  volume =       "33",
  number =       "2",
  pages =        "1--32",
  month =        jun,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1236463.1236465",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 26 17:36:59 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In recent years a number of solvers for the direct
                 solution of large sparse symmetric linear systems of
                 equations have been developed. These include solvers
                 that are designed for the solution of positive definite
                 systems as well as those that are principally intended
                 for solving indefinite problems. In this study, we use
                 performance profiles as a tool for evaluating and
                 comparing the performance of serial sparse direct
                 solvers on an extensive set of symmetric test problems
                 taken from a range of practical applications.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Benson:2007:UGT,
  author =       "Steven Benson and Manojkumar Krishnan and Lois Mcinnes
                 and Jarek Nieplocha and Jason Sarich",
  title =        "Using the {GA} and {TAO} toolkits for solving
                 large-scale optimization problems on parallel
                 computers",
  journal =      j-TOMS,
  volume =       "33",
  number =       "2",
  pages =        "1--21",
  month =        jun,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1236463.1236466",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 26 17:36:59 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Challenges in the scalable solution of large-scale
                 optimization problems include the development of
                 innovative algorithms and efficient tools for parallel
                 data manipulation. This article discusses two
                 complementary toolkits from the collection of Advanced
                 CompuTational Software (ACTS), namely, Global Arrays
                 (GA) for parallel data management and the Toolkit for
                 Advanced Optimization (TAO), which have been integrated
                 to support large-scale scientific applications of
                 unconstrained and bound constrained minimization
                 problems. Most likely to benefit are minimization
                 problems arising in classical molecular dynamics, free
                 energy simulations, and other applications where the
                 coupling among variables requires dense data
                 structures. TAO uses abstractions for vectors and
                 matrices so that its optimization algorithms can easily
                 interface to distributed data management and linear
                 algebra capabilities implemented in the GA library. The
                 GA/TAO interfaces are available both in the traditional
                 library mode and as components compliant with the
                 Common Component Architecture (CCA). We highlight the
                 design of each toolkit, describe the interfaces between
                 them, and demonstrate their use.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Meza:2007:OPO,
  author =       "J. C. Meza and R. A. Oliva and P. D. Hough and P. J.
                 Williams",
  title =        "{OPT++}: an object-oriented toolkit for nonlinear
                 optimization",
  journal =      j-TOMS,
  volume =       "33",
  number =       "2",
  pages =        "1--27",
  month =        jun,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1236463.1236467",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 26 17:36:59 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Object-oriented programming is a relatively new tool
                 in the development of optimization software. The code
                 extensibility and the rapid algorithm prototyping
                 capability enabled by this programming paradigm promise
                 to enhance the reliability, utility, and ease of use of
                 optimization software. While the use of object-oriented
                 programming is growing, there are still few examples of
                 general purpose codes written in this manner, and a
                 common approach is far from obvious. This paper
                 describes OPT++, a C++ class library for nonlinear
                 optimization. The design is predicated on the concept
                 of distinguishing between an algorithm-independent
                 class hierarchy for nonlinear optimization problems and
                 a class hierarchy for nonlinear optimization methods
                 that is based on common algorithmic traits. The
                 interface is designed for ease of use while being
                 general enough so that new optimization algorithms can
                 be added easily to the existing framework. A number of
                 nonlinear optimization algorithms have been implemented
                 in OPT++ and are accessible through this interface.
                 Furthermore, example applications demonstrate the
                 simplicity of the interface as well as the advantages
                 of a common interface in comparing multiple
                 algorithms.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fousse:2007:MMP,
  author =       "Laurent Fousse and Guillaume Hanrot and Vincent
                 Lef{\`e}vre and Patrick P{\'e}lissier and Paul
                 Zimmermann",
  title =        "{MPFR}: a multiple-precision binary floating-point
                 library with correct rounding",
  journal =      j-TOMS,
  volume =       "33",
  number =       "2",
  pages =        "1--15",
  month =        jun,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1236463.1236468",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65G99",
  MRnumber =     "MR2326955",
  bibdate =      "Thu Jul 26 17:36:59 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article presents a multiple-precision binary
                 floating-point library, written in the ISO C language,
                 and based on the GNU MP library. Its particularity is
                 to extend to arbitrary-precision, ideas from the IEEE
                 754 standard, by providing correct rounding and
                 exceptions. We demonstrate how these strong semantics
                 are achieved---with no significant slowdown with
                 respect to other arbitrary-precision tools---and
                 discuss a few applications where such a library can be
                 useful.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Elman:2007:AIM,
  author =       "Howard C. Elman and Alison Ramage and David J.
                 Silvester",
  title =        "{Algorithm 866}: {IFISS}, a {Matlab} toolbox for
                 modelling incompressible flow",
  journal =      j-TOMS,
  volume =       "33",
  number =       "2",
  pages =        "1--18",
  month =        jun,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1236463.1236469",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 26 17:36:59 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "IFISS is a graphical Matlab package for the
                 interactive numerical study of incompressible flow
                 problems. It includes algorithms for discretization by
                 mixed finite element methods and a posteriori error
                 estimation of the computed solutions. The package can
                 also be used as a computational laboratory for
                 experimenting with state-of-the-art preconditioned
                 iterative solvers for the discrete linear equation
                 systems that arise in incompressible flow modelling. A
                 unique feature of the package is its comprehensive
                 nature; for each problem addressed, it enables the
                 study of both discretization and iterative solution
                 algorithms as well as the interaction between the two
                 and the resulting effect on overall efficiency.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Crouse:2007:RAG,
  author =       "David F. Crouse",
  title =        "Remark on {Algorithm 515}: {Generation} of a vector
                 from the lexicographical index combinations",
  journal =      j-TOMS,
  volume =       "33",
  number =       "2",
  pages =        "1--2",
  month =        jun,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1236463.1236470",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jul 26 17:36:59 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a correction to Algorithm 515 [Buckles and
                 Lybanon 1977].",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rioux:2007:ANF,
  author =       "J. Rioux and M. Halse and E. Aubanel and B. J. Balcom
                 and J. Kaffanke and S. Romanzetti and T. Dierkes and N.
                 J. Shah",
  title =        "An accurate nonuniform {Fourier} transform for
                 {SPRITE} magnetic resonance imaging data",
  journal =      j-TOMS,
  volume =       "33",
  number =       "3",
  pages =        "16:1--16:21",
  month =        aug,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1268769.1268770",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 5 14:34:54 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A new algorithm is proposed for computing the discrete
                 Fourier Transform (DFT) of purely phase encoded data
                 acquired during Magnetic Resonance Imaging (MRI)
                 experiments. These experiments use the SPRITE (Single
                 Point Ramped Imaging with $T_1$ Enhancement) method and
                 multiple-point acquisition, sampling data in a
                 nonuniform manner that prohibits reconstruction by fast
                 Fourier transform. The chirp $z$-transform algorithm of
                 Rabiner, Schafer, and Rader can be combined with phase
                 corrections to compute the DFT of this data to
                 extremely high accuracy. This algorithm outperforms the
                 interpolation methods that are traditionally used to
                 process nonuniform data, both in terms of execution
                 time and in terms of accuracy as compared to the DFT.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kirby:2007:ECC,
  author =       "Robert C. Kirby and Anders Logg",
  title =        "Efficient compilation of a class of variational
                 forms",
  journal =      j-TOMS,
  volume =       "33",
  number =       "3",
  pages =        "17:1--17:20",
  month =        aug,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1268769.1268771",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 5 14:34:54 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We investigate the compilation of general multilinear
                 variational forms over affines simplices and prove a
                 representation theorem for the representation of the
                 element tensor (element stiffness matrix) as the
                 contraction of a constant reference tensor and a
                 geometry tensor that accounts for geometry and variable
                 coefficients. Based on this representation theorem, we
                 design an algorithm for efficient pretabulation of the
                 reference tensor. The new algorithm has been
                 implemented in the FEniCS Form Compiler (FFC) and
                 improves on a previous loop-based implementation by
                 several orders of magnitude, thus shortening
                 compile-times and development cycles for users of
                 FFC.",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Scott:2007:ESD,
  author =       "Jennifer A. Scott and Yifan Hu",
  title =        "Experiences of sparse direct symmetric solvers",
  journal =      j-TOMS,
  volume =       "33",
  number =       "3",
  pages =        "18:1--18:28",
  month =        aug,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1268769.1268772",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 5 14:34:54 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We recently carried out an extensive comparison of the
                 performance of state-of-the-art sparse direct solvers
                 for the numerical solution of symmetric linear systems
                 of equations. Some of these solvers were written
                 primarily as research codes while others have been
                 developed for commercial use. Our experiences of using
                 the different packages to solve a wide range of
                 problems arising from real applications were mixed. In
                 this paper, we highlight some of these experiences with
                 the aim of providing advice to both software developers
                 and users of sparse direct solvers. We discuss key
                 features that a direct solver should offer and conclude
                 that while performance is an essential factor to
                 consider when choosing a code, there are other features
                 that a user should also consider looking for that vary
                 significantly between packages.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ball:2007:EGR,
  author =       "James S. Ball and Nelson H. F. Beebe",
  title =        "Efficient {Gauss}-related quadrature for two classes
                 of logarithmic weight functions",
  journal =      j-TOMS,
  volume =       "33",
  number =       "3",
  pages =        "19:1--19:21",
  month =        aug,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1268769.1268773",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 5 14:34:54 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Integrals with logarithmic singularities are often
                 difficult to evaluate by numerical methods. In this
                 work, a quadrature method is developed that allows the
                 exact evaluation (up to machine accuracy) of integrals
                 of polynomials with two general types of logarithmic
                 weights.\par

                 The total work for the determination of $N$ nodes and
                 points of the quadrature method is $O(N^2)$.
                 Subsequently, integrals can be evaluated with $O(N)$
                 operations and function evaluations, so the quadrature
                 is efficient.\par

                 This quadrature method can then be used to generate the
                 nonclassical orthogonal polynomials for weight
                 functions containing logarithms and obtain Gauss and
                 Gauss-related quadratures for these weights. Two
                 algorithms for each of the two types of logarithmic
                 weights that incorporate these methods are given in
                 this paper.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Beebe:2007:AQP,
  author =       "Nelson H. F. Beebe and James S. Ball",
  title =        "{Algorithm 867}: {QUADLOG}---a package of routines for
                 generating {Gauss}-related quadrature for two classes
                 of logarithmic weight functions",
  journal =      j-TOMS,
  volume =       "33",
  number =       "3",
  pages =        "20:1--20:30",
  month =        aug,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1268769.1268774",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 5 14:34:54 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A collection of subroutines and examples of their uses
                 are described for the quadrature method developed in
                 the companion article. These allow the exact evaluation
                 (up to computer truncation and rounding errors) of
                 integrals of polynomials with two general types of
                 logarithmic weights, and also with the corresponding
                 nonlogarithmic weights. The recurrence coefficients for
                 the related nonclassical orthogonal polynomials with
                 logarithmic weight functions can also be obtained.
                 Tests of accuracy on various platforms are
                 presented.\par

                 The routines are usable from Fortran, C, and C++
                 programs conforming to any of at least six
                 international programming-language standards.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Espelid:2007:AGD,
  author =       "Terje O. Espelid",
  title =        "{Algorithm 868}: {Globally} doubly adaptive
                 quadrature---reliable {Matlab} codes",
  journal =      j-TOMS,
  volume =       "33",
  number =       "3",
  pages =        "21:1--21:21",
  month =        aug,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1268769.1268775",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 5 14:34:54 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We discuss how to modify a recently published Matlab
                 code, {\tt coteglob}, so that the excellent performance
                 this code demonstrates for low and intermediate
                 accuracy requests is retained while the performance is
                 improved for high accuracy requests. {\tt coteglob} is
                 a globally adaptive code using a 5 and 9 point pair of
                 Newton--Cotes rules. Combining an extended sequence of
                 rules using 5, 9, 17 and 33 points with a doubly
                 adaptive bisection strategy is the main focus of the
                 paper. We also discuss local versus global adaptivity
                 and conclude that globally adaptive codes are to be
                 preferred. Based on this we develop several new
                 globally adaptive codes that all compare favorably both
                 with {\tt coteglob}, with Matlab's best currently
                 available quadrature software {\tt quadl} and the
                 general purpose QUADPACK codes {\tt dqk15} and {\tt
                 dqk21}. We include the results from extensive testing
                 using both a Lyness--Kaganove testing technique and a
                 battery test.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{LEcuyer:2007:TCL,
  author =       "Pierre L'Ecuyer and Richard Simard",
  title =        "{TestU01}: {A C} library for empirical testing of
                 random number generators",
  journal =      j-TOMS,
  volume =       "33",
  number =       "4",
  pages =        "22:1--22:40",
  month =        aug,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1268776.1268777",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Dec 17 18:09:13 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We introduce TestU01, a software library implemented
                 in the ANSI C language, and offering a collection of
                 utilities for the empirical statistical testing of
                 uniform random number generators (RNGs). It provides
                 general implementations of the classical statistical
                 tests for RNGs, as well as several others tests
                 proposed in the literature, and some original ones.
                 Predefined tests suites for sequences of uniform random
                 numbers over the interval (0, 1) and for bit sequences
                 are available. Tools are also offered to perform
                 systematic studies of the interaction between a
                 specific test and the structure of the point sets
                 produced by a given family of RNGs. That is, for a
                 given kind of test and a given class of RNGs, to
                 determine how large should be the sample size of the
                 test, as a function of the generator's period length,
                 before the generator starts to fail the test
                 systematically. Finally, the library provides various
                 types of generators implemented in generic form, as
                 well as many specific generators proposed in the
                 literature or found in widely used software. The tests
                 can be applied to instances of the generators
                 predefined in the library, or to user-defined
                 generators, or to streams of random numbers produced by
                 any kind of device or stored in files. Besides
                 introducing TestU01, the article provides a survey and
                 a classification of statistical tests for RNGs. It also
                 applies batteries of tests to a long list of widely
                 used RNGs.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pesch:2007:HSF,
  author =       "Lars Pesch and Alexander Bell and Henk Sollie and
                 Vijaya R. Ambati and Onno Bokhove and Jaap J. W. {Van
                 Der Vegt}",
  title =        "{hpGEM} --- a software framework for discontinuous
                 {Galerkin} finite element methods",
  journal =      j-TOMS,
  volume =       "33",
  number =       "4",
  pages =        "23:1--23:25",
  month =        aug,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1268776.1268778",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Dec 17 18:09:13 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "hpGEM, a novel framework for the implementation of
                 discontinuous Galerkin finite element methods (FEMs),
                 is described. We present data structures and methods
                 that are common for many (discontinuous) FEMs and show
                 how we have implemented the components as an
                 object-oriented framework. This framework facilitates
                 and accelerates the implementation of finite element
                 programs, the assessment of algorithms, and their
                 application to real-world problems. The article
                 documents the status of the framework, exemplifies
                 aspects of its philosophy and design, and demonstrates
                 the feasibility of the approach with several
                 application examples.",
  acknowledgement = ack-nhfb,
  articleno =    "23",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bangerth:2007:DIG,
  author =       "W. Bangerth and R. Hartmann and G. Kanschat",
  title =        "{deal.II} --- a general-purpose object-oriented
                 finite element library",
  journal =      j-TOMS,
  volume =       "33",
  number =       "4",
  pages =        "24:1--24:27",
  month =        aug,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1268776.1268779",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Dec 17 18:09:13 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "An overview of the software design and data
                 abstraction decisions chosen for deal.II, a general
                 purpose finite element library written in C++, is
                 given. The library uses advanced object-oriented and
                 data encapsulation techniques to break finite element
                 implementations into smaller blocks that can be
                 arranged to fit users requirements. Through this
                 approach, deal.II supports a large number of different
                 applications covering a wide range of scientific areas,
                 programming methodologies, and application-specific
                 algorithms, without imposing a rigid framework into
                 which they have to fit. A judicious use of programming
                 techniques allows us to avoid the computational costs
                 frequently associated with abstract object-oriented
                 class libraries.\par

                 The paper presents a detailed description of the
                 abstractions chosen for defining geometric information
                 of meshes and the handling of degrees of freedom
                 associated with finite element spaces, as well as of
                 linear algebra, input/output capabilities and of
                 interfaces to other software, such as visualization
                 tools. Finally, some results obtained with applications
                 built atop deal.II are shown to demonstrate the
                 powerful capabilities of this toolbox.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bai:2007:PSB,
  author =       "Yihua Bai and Robert C. Ward",
  title =        "A parallel symmetric block-tridiagonal
                 divide-and-conquer algorithm",
  journal =      j-TOMS,
  volume =       "33",
  number =       "4",
  pages =        "25:1--25:23",
  month =        aug,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1268776.1268780",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Dec 17 18:09:13 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a parallel implementation of the
                 block-tridiagonal divide-and-conquer algorithm that
                 computes eigensolutions of symmetric block-tridiagonal
                 matrices to reduced accuracy. In our implementation, we
                 use mixed data/task parallelism to achieve data
                 distribution and workload balance. Numerical tests show
                 that our implementation is efficient, scalable and
                 computes eigenpairs to prescribed accuracy. We compare
                 the performance of our parallel eigensolver with that
                 of the ScaLAPACK divide-and-conquer eigensolver on
                 block-tridiagonal matrices.",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Shampine:2007:AND,
  author =       "L. F. Shampine",
  title =        "Accurate numerical derivatives in {MATLAB}",
  journal =      j-TOMS,
  volume =       "33",
  number =       "4",
  pages =        "26:1--26:17",
  month =        aug,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1268776.1268781",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Dec 17 18:09:13 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Complex step differentiation (CSD) is a technique for
                 computing very accurate numerical derivatives in
                 languages that support complex arithmetic. We describe
                 here the development of a CSD package in MATLAB called
                 PMAD. We have extended work done in other languages for
                 scalars to the arrays that are fundamental to MATLAB.
                 This extension raises questions that we have been able
                 to resolve in a satisfactory way. Our goal has been to
                 make it as easy as possible to compute approximate
                 Jacobians in MATLAB that are all but exact. Although
                 PMAD has a fast option for the expert that implements
                 CSD as in previous work, the default is an
                 object-oriented implementation that asks very little of
                 the user.",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Zwolak:2007:AOW,
  author =       "Jason W. Zwolak and Paul T. Boggs and Layne T.
                 Watson",
  title =        "{Algorithm 869}: {ODRPACK95}: a weighted orthogonal
                 distance regression code with bound constraints",
  journal =      j-TOMS,
  volume =       "33",
  number =       "4",
  pages =        "27:1--27:12",
  month =        aug,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1268776.1268782",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Dec 17 18:09:13 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "ODRPACK (TOMS Algorithm 676) has provided a complete
                 package for weighted orthogonal distance regression for
                 many years. The code is complete with user selectable
                 reporting facilities, numerical and analytic
                 derivatives, derivative checking, and many more
                 features. The foundation for the algorithm is a stable
                 and efficient trust region Levenberg--Marquardt
                 minimizer that exploits the structure of the orthogonal
                 distance regression problem. ODRPACK95 was created to
                 extend the functionality and usability of ODRPACK.
                 ODRPACK95 adds bound constraints, uses the newer
                 Fortran 95 language, and simplifies the interface to
                 the user called subroutine.",
  acknowledgement = ack-nhfb,
  articleno =    "27",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kodama:2007:RA,
  author =       "Masao Kodama",
  title =        "Remark on {Algorithm 644}",
  journal =      j-TOMS,
  volume =       "33",
  number =       "4",
  pages =        "28:1--28:3",
  month =        aug,
  year =         "2007",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1268776.1268783",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Dec 17 18:09:13 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See
                 \cite{Amos:1986:APP,Amos:1990:RPP,Amos:1995:RAP}.",
  abstract =     "This remark details correction for errors in the
                 functions which compute the modified Bessel function of
                 the second kind and the log of the gamma function. In
                 both cases these errors cause a loss of precision for a
                 small range of values of the $\nu$ argument. These
                 routines are used in the calculation of a number of
                 other functions within the package whose accuracy is
                 thus similarly affected.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kressner:2008:BVH,
  author =       "Daniel Kressner",
  title =        "Block variants of {Hammarling}'s method for solving
                 {Lyapunov} equations",
  journal =      j-TOMS,
  volume =       "34",
  number =       "1",
  pages =        "1:1--1:15",
  month =        jan,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1322436.1322437",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 12 17:39:58 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article is concerned with the efficient numerical
                 solution of the Lyapunov equation $A^T X + XA = -C$
                 with a stable matrix $A$ and a symmetric positive
                 semidefinite matrix $C$ of possibly small rank. We
                 discuss the efficient implementation of Hammarling's
                 method and propose among other algorithmic improvements
                 a block variant, which is demonstrated to perform
                 significantly better than existing implementations. An
                 extension to the discrete-time Lyapunov equation $A^T X
                 A - X = -C$ is also described.",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rouson:2008:GFA,
  author =       "Damian W. I. Rouson and Robert Rosenberg and Xiaofeng
                 Xu and Irene Moulitsas and Stavros C. Kassinos",
  title =        "A grid-free abstraction of the {Navier--Stokes}
                 equations in {Fortran 95\slash 2003}",
  journal =      j-TOMS,
  volume =       "34",
  number =       "1",
  pages =        "2:1--2:33",
  month =        jan,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1322436.1322438",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 12 17:39:58 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Computational complexity theory inspires a grid-free
                 abstraction of the Navier--Stokes equations in Fortran
                 95/2003. A novel complexity analysis estimates that
                 structured programming time grows at least
                 quadratically with the number of program lines. Further
                 analysis demonstrates how an object-oriented strategy
                 focused on mathematical objects renders the quadratic
                 estimate scale-invariant, so the time required for the
                 limiting factor in program development (debugging) no
                 longer grows as the code grows. Compared to the
                 coordinate-free C++ programming of Grant et al. [2000],
                 grid-free Fortran programming eliminates a layer of
                 procedure calls, eliminates a related need for the C++
                 template construct, and offers a shorter migration path
                 for Fortran programmers. The grid-free strategy is
                 demonstrated by constructing a physical-space driver
                 for a Fourier-space Navier--Stokes solver. Separating
                 the expression of the continuous mathematical model
                 from the discrete numerics clarifies issues that are
                 otherwise easily conflated. A run-time profile suggests
                 that grid-free design substantially reduces the
                 fraction of the procedures that significantly impact
                 runtime, freeing more code to be structured in ways
                 that reduce development time. Applying Amdahl's law to
                 the total solution time (development time plus run
                 time) leads to a strategy that negligibly impacts
                 development time but achieves 58\% of the maximum
                 possible speedup.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Walther:2008:CSH,
  author =       "Andrea Walther",
  title =        "Computing sparse {Hessians} with automatic
                 differentiation",
  journal =      j-TOMS,
  volume =       "34",
  number =       "1",
  pages =        "3:1--3:15",
  month =        jan,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1322436.1322439",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 12 17:39:58 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A new approach for computing a sparsity pattern for a
                 Hessian is presented: nonlinearity information is
                 propagated through the function evaluation yielding the
                 nonzero structure. A complexity analysis of the
                 proposed algorithm is given. Once the sparsity pattern
                 is available, coloring algorithms can be applied to
                 compute a seed matrix. To evaluate the product of the
                 Hessian and the seed matrix, a vector version for
                 evaluating second order adjoints is analysed. New
                 drivers of ADOL-C are provided implementing the
                 presented algorithms. Runtime analyses are given for
                 some problems of the CUTE collection.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Linardakis:2008:ASG,
  author =       "Leonidas Linardakis and Nikos Chrisochoides",
  title =        "{Algorithm 870}: a static geometric {Medial Axis}
                 domain decomposition in {$2$D} {Euclidean} space",
  journal =      j-TOMS,
  volume =       "34",
  number =       "1",
  pages =        "4:1--4:28",
  month =        jan,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1322436.1322440",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 12 17:39:58 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a geometric domain decomposition method and
                 its implementation, which produces good domain
                 decompositions in terms of three basic criteria: (1)
                 The boundary of the subdomains create good angles, that
                 is, angles no smaller than a given tolerance $\Phi_0$,
                 where the value of $\Phi_0$ is determined by the
                 application which will use the domain decomposition.
                 (2) The size of the separator should be relatively
                 small compared to the area of the subdomains. (3) The
                 maximum area of the subdomains should be close to the
                 average subdomain area. The domain decomposition method
                 uses an approximation of a Medial Axis as an auxiliary
                 structure for constructing the boundary of the
                 subdomains (separators). The N-way decomposition is
                 based on the ``divide and conquer'' algorithmic
                 paradigm and on a smoothing procedure that eliminates
                 the creation of any new artifacts in the subdomains.
                 This approach produces well shaped uniform and graded
                 domain decompositions, which are suitable for parallel
                 mesh generation.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Schreppers:2008:ACC,
  author =       "Walter Schreppers and Annie Cuyt",
  title =        "{Algorithm 871}: a {C\slash C++} precompiler for
                 autogeneration of multiprecision programs",
  journal =      j-TOMS,
  volume =       "34",
  number =       "1",
  pages =        "5:1--5:20",
  month =        jan,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1322436.1322441",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 12 17:39:58 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In the past decade a number of libraries for
                 multiprecision floating-point arithmetic have been
                 developed. We describe an easy to use, generic C/C++
                 transcription program or precompiler for the conversion
                 of C or C++ source code into new code that uses a C++
                 multiprecision library of choice. The precompiler can
                 convert any type in the input source code to another
                 type in the output source code. The input source can be
                 either C or C++ , while the output code generated by
                 the precompiler and using the new types, is C++. The
                 type conversion is based on a simple XML configuration
                 file which is provided by either the developer of the
                 multiprecision library or by the user of the
                 precompiler. The precompiler can also convert to data
                 types with additional features, which are not supported
                 in the types of the source code. Applicability of the
                 precompiler is shown with the successful conversion of
                 large subsets of the GNU Scientific Library and
                 Numerical Recipes.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Chernikov:2008:APC,
  author =       "Andrey N. Chernikov and Nikos P. Chrisochoides",
  title =        "{Algorithm 872}: {Parallel} {$2$D} constrained
                 {Delaunay} mesh generation",
  journal =      j-TOMS,
  volume =       "34",
  number =       "1",
  pages =        "6:1--6:20",
  month =        jan,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1322436.1322442",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 12 17:39:58 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Delaunay refinement is a widely used method for the
                 construction of guaranteed quality triangular and
                 tetrahedral meshes. We present an algorithm and a
                 software for the parallel constrained Delaunay mesh
                 generation in two dimensions. Our approach is based on
                 the decomposition of the original mesh generation
                 problem into $N$ smaller subproblems which are meshed
                 in parallel. The parallel algorithm is asynchronous
                 with small messages which can be aggregated and
                 exhibits low communication costs. On a heterogeneous
                 cluster of more than 100 processors our implementation
                 can generate over one billion triangles in less than 3
                 minutes, while the single-node performance is
                 comparable to that of the fastest to our knowledge
                 sequential guaranteed quality Delaunay meshing library
                 (the Triangle).",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sala:2008:PHP,
  author =       "Marzio Sala and W. F. Spotz and M. A. Heroux",
  title =        "{PyTrilinos}: {High-performance} distributed-memory
                 solvers for {Python}",
  journal =      j-TOMS,
  volume =       "34",
  number =       "2",
  pages =        "7:1--7:33",
  month =        mar,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1326548.1326549",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 12 12:47:31 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "PyTrilinos is a collection of Python modules that are
                 useful for serial and parallel scientific computing.
                 This collection contains modules that cover serial and
                 parallel dense linear algebra, serial and parallel
                 sparse linear algebra, direct and iterative linear
                 solution techniques, domain decomposition and
                 multilevel preconditioners, nonlinear solvers, and
                 continuation algorithms. Also included are a variety of
                 related utility functions and classes, including
                 distributed I/O, coloring algorithms, and matrix
                 generation. PyTrilinos vector objects are integrated
                 with the popular NumPy Python module, gathering
                 together a variety of high-level distributed computing
                 operations with serial vector
                 operations.\par

                 PyTrilinos is a set of interfaces to existing, compiled
                 libraries. This hybrid framework uses Python as
                 front-end, and efficient precompiled libraries for all
                 computationally expensive tasks. Thus, we take
                 advantage of both the flexibility and ease of use of
                 Python, and the efficiency of the underlying C++, C,
                 and FORTRAN numerical kernels. Out numerical results
                 show that, for many important problem classes, the
                 overhead required by the Python interpreter is
                 negligible.\par

                 To run in parallel, PyTrilinos simply requires a
                 standard Python interpreter. The fundamental MPI calls
                 are encapsulated under an abstract layer that manages
                 all interprocessor communications. This makes serial
                 and parallel scripts using PyTrilinos virtually
                 identical.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "direct solvers; multilevel preconditioners; nonlinear
                 solvers; object-oriented programming; script
                 languages",
}

@Article{Avron:2008:PUP,
  author =       "Haim Avron and Gil Shklarski and Sivan Toledo",
  title =        "Parallel unsymmetric-pattern multifrontal sparse {LU}
                 with column preordering",
  journal =      j-TOMS,
  volume =       "34",
  number =       "2",
  pages =        "8:1--8:31",
  month =        mar,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1326548.1326550",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 12 12:47:31 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a new parallel sparse LU factorization
                 algorithm and code. The algorithm uses a
                 column-preordering partial-pivoting unsymmetric-pattern
                 multifrontal approach. Our baseline sequential
                 algorithm is based on UMFPACK 4, but is somewhat
                 simpler and is often somewhat faster than UMFPACK
                 version 4.0. Our parallel algorithm is designed for
                 shared-memory machines with a small or moderate number
                 of processors (we tested it on up to 32 processors). We
                 experimentally compare our algorithm with SuperLU\_MT,
                 an existing shared-memory sparse LU factorization with
                 partial pivoting. SuperLU\_MT scales better than our
                 new algorithm, but our algorithm is more reliable and
                 is usually faster. More specifically, on matrices that
                 are costly to factor, our algorithm is usually faster
                 on up to 4 processors, and is usually faster on 8 and
                 16. We were not able to run SuperLU\_MT on 32. The main
                 contribution of this article is showing that the
                 column-preordering partial-pivoting unsymmetric-pattern
                 multifrontal approach, developed as a sequential
                 algorithm by Davis in several recent versions of
                 UMFPACK, can be effectively parallelized.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Gaussian elimination; multifrontal; unsymmetric",
}

@Article{Sala:2008:DIS,
  author =       "Marzio Sala and Kendall S. Stanley and Michael A.
                 Heroux",
  title =        "On the design of interfaces to sparse direct solvers",
  journal =      j-TOMS,
  volume =       "34",
  number =       "2",
  pages =        "9:1--9:22",
  month =        mar,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1326548.1326551",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 12 12:47:31 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We discuss the design of general, flexible,
                 consistent, reusable, and efficient interfaces to
                 software libraries for the direct solution of systems
                 of linear equations on both serial and distributed
                 memory architectures. We introduce a set of abstract
                 classes to access the linear system matrix elements and
                 their distribution, access vector elements, and control
                 the solution of the linear system.\par

                 We describe a concrete implementation of the proposed
                 interfaces, and report examples of applications and
                 numerical results showing that the overhead induced by
                 the object-oriented design is negligible under typical
                 conditions of usage. We include examples of
                 applications, and we comment on the advantages and
                 limitations of the design.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "direct solver libraries; distributed linear algebra;
                 object-oriented design",
}

@Article{VanZee:2008:SPF,
  author =       "Field G. {Van Zee} and Paolo Bientinesi and Tze Meng
                 Low and Robert A. van de Geijn",
  title =        "Scalable parallelization of {FLAME} code via the
                 workqueuing model",
  journal =      j-TOMS,
  volume =       "34",
  number =       "2",
  pages =        "10:1--10:29",
  month =        mar,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1326548.1326552",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 12 12:47:31 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We discuss the OpenMP parallelization of linear
                 algebra algorithms that are coded using the Formal
                 Linear Algebra Methods Environment (FLAME) API. This
                 API expresses algorithms at a higher level of
                 abstraction, avoids the use loop and array indices, and
                 represents these algorithms as they are formally
                 derived and presented. We report on two implementations
                 of the workqueuing model, neither of which requires the
                 use of explicit indices to specify parallelism. The
                 first implementation uses the experimental {\tt taskq}
                 pragma, which may influence the adoption of a similar
                 construct into OpenMP 3.0. The second workqueuing
                 implementation is domain-specific to FLAME but allows
                 us to illustrate the benefits of sorting tasks
                 according to their computational cost prior to parallel
                 execution. In addition, we discuss how scalable
                 parallelization of dense linear algebra algorithms via
                 OpenMP will require a two-dimensional partitioning of
                 operands much like a 2D data distribution is needed on
                 distributed memory architectures. We illustrate the
                 issues and solutions by discussing the parallelization
                 of the symmetric rank-$k$ update and report impressive
                 performance on an SGI system with 14 Itanium2
                 processors.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "FLAME; OpenMP; parallel; scalability; SMP;
                 workqueuing",
}

@Article{Rojas:2008:ALM,
  author =       "Marielba Rojas and Sandra A. Santos and Danny C.
                 Sorensen",
  title =        "{Algorithm 873}: {LSTRS}: {MATLAB} software for
                 large-scale trust-region subproblems and
                 regularization",
  journal =      j-TOMS,
  volume =       "34",
  number =       "2",
  pages =        "11:1--11:28",
  month =        mar,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1326548.1326553",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 12 12:47:31 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A MATLAB 6.0 implementation of the LSTRS method is
                 presented. LSTRS was described in Rojas et al. [2000].
                 LSTRS is designed for large-scale quadratic problems
                 with one norm constraint. The method is based on a
                 reformulation of the trust-region subproblem as a
                 parameterized eigenvalue problem, and consists of an
                 iterative procedure that finds the optimal value for
                 the parameter. The adjustment of the parameter requires
                 the solution of a large-scale eigenvalue problem at
                 each step. LSTRS relies on matrix-vector products only
                 and has low and fixed storage requirements, features
                 that make it suitable for large-scale computations. In
                 the MATLAB implementation, the Hessian matrix of the
                 quadratic objective function can be specified either
                 explicitly, or in the form of a matrix-vector
                 multiplication routine. Therefore, the implementation
                 preserves the matrix-free nature of the method. A
                 description of the LSTRS method and of the MATLAB
                 software, version 1.2, is presented. Comparisons with
                 other techniques and applications of the method are
                 also included. A guide for using the software and
                 examples are provided.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "ARPACK; constrained quadratic optimization; Lanczos
                 method; MATLAB; regularization; trust-region",
}

@Article{Goto:2008:AHP,
  author =       "Kazushige Goto and Robert A. van de Geijn",
  title =        "Anatomy of high-performance matrix multiplication",
  journal =      j-TOMS,
  volume =       "34",
  number =       "3",
  pages =        "12:1--12:25",
  month =        may,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1356052.1356053",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 12 12:53:20 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present the basic principles that underlie the
                 high-performance implementation of the matrix-matrix
                 multiplication that is part of the widely used GotoBLAS
                 library. Design decisions are justified by successively
                 refining a model of architectures with multilevel
                 memories. A simple but effective algorithm for
                 executing this operation results. Implementations on a
                 broad selection of architectures are shown to achieve
                 near-peak performance.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Basic Linear Algebra Subprograms; linear algebra;
                 matrix multiplication",
}

@Article{Piiroinen:2008:EDM,
  author =       "Petri T. Piiroinen and Yuri A. Kuznetsov",
  title =        "An event-driven method to simulate {Filippov} systems
                 with accurate computing of sliding motions",
  journal =      j-TOMS,
  volume =       "34",
  number =       "3",
  pages =        "13:1--13:24",
  month =        may,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1356052.1356054",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 12 12:53:20 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article describes how to use smooth solvers for
                 simulation of a class of piecewise smooth systems of
                 ordinary differential equations, called Filippov
                 systems, with discontinuous vector fields. In these
                 systems constrained motion along a discontinuity
                 surface (so-called sliding) is possible and requires
                 special treatment numerically. The introduced
                 algorithms are based on an extension to Filippov's
                 method to stabilize the sliding flow together with
                 accurate detection of the entrance and exit of sliding
                 regions. The methods are implemented in a general way
                 in MATLAB and sufficient details are given to enable
                 users to modify the code to run on arbitrary examples.
                 Here, the method is used to compute the dynamics of
                 three example systems, a dry-friction oscillator, a
                 relay feedback system and a model of an oil well
                 drill-string.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Filippov systems; Numerical simulation;
                 piecewise-smooth differential equations; sliding
                 solutions",
}

@Article{Howell:2008:CEB,
  author =       "Gary W. Howell and James W. Demmel and Charles T.
                 Fulton and Sven Hammarling and Karen Marmol",
  title =        "Cache efficient bidiagonalization using {BLAS 2.5}
                 operators",
  journal =      j-TOMS,
  volume =       "34",
  number =       "3",
  pages =        "14:1--14:33",
  month =        may,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1356052.1356055",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 12 12:53:20 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "On cache based computer architectures using current
                 standard algorithms, Householder bidiagonalization
                 requires a significant portion of the execution time
                 for computing matrix singular values and vectors. In
                 this paper we reorganize the sequence of operations for
                 Householder bidiagonalization of a general $m \times n$
                 matrix, so that two (\_GEMV) vector-matrix
                 multiplications can be done with one pass of the
                 unreduced trailing part of the matrix through cache.
                 Two new BLAS operations approximately cut in half the
                 transfer of data from main memory to cache, reducing
                 execution times by up to 25 per cent. We give detailed
                 algorithm descriptions and compare timings with the
                 current LAPACK bidiagonalization algorithm.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "bidiagonalization; BLAS 2.5; cache-efficient;
                 Householder reflections; matrix factorization; singular
                 values; SVD",
}

@Article{Wang:2008:ABS,
  author =       "R. Wang and P. Keast and P. H. Muir",
  title =        "{Algorithm 874}: {BACOLR}-spatial and temporal error
                 control software for {PDEs} based on high-order
                 adaptive collocation",
  journal =      j-TOMS,
  volume =       "34",
  number =       "3",
  pages =        "15:1--15:28",
  month =        may,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1356052.1356056",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 12 12:53:20 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this article we discuss a new software package,
                 BACOLR, for the numerical solution of a general class
                 of time-dependent 1-D PDEs. This package employs
                 high-order adaptive methods in time and space within a
                 method-of-lines approach and provides tolerance control
                 of the spatial and temporal errors. The DAEs resulting
                 from the spatial discretization (based on B-spline
                 collocation) are handled by a substantially modified
                 version of the Runge--Kutta solver, RADAU5. For each
                 time step, the RADAU5 code computes an estimate of the
                 temporal error and requires it to satisfy the user
                 tolerance. After each time step BACOLR then computes a
                 high-order estimate of the spatial error and requires
                 this error estimate to satisfy the user tolerance.
                 BACOLR was developed through a substantial modification
                 of the adaptive method-of-lines package, BACOL. In this
                 article we introduce the BACOLR package and present
                 numerical results to show that the performance of
                 BACOLR is comparable to and in some cases significantly
                 superior to that of BACOL, which was shown in previous
                 work to be more efficient, reliable and robust than
                 other existing codes, especially for problems with
                 solutions exhibiting narrow spikes or boundary
                 layers.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "1-D PDEs; adaptive method-of-lines;
                 differential-algebraic equations; Numerical software;
                 Runge--Kutta methods; spatial error control",
}

@Article{Benson:2008:ADS,
  author =       "Steven J. Benson and Yinyu Ye",
  title =        "{Algorithm 875}: {DSDP5}-software for semidefinite
                 programming",
  journal =      j-TOMS,
  volume =       "34",
  number =       "3",
  pages =        "16:1--16:20",
  month =        may,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1356052.1356057",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 12 12:53:20 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "DSDP implements the dual-scaling algorithm for
                 semidefinite programming. The source code for this
                 interior-point algorithm, written entirely in ANSI C,
                 is freely available under an open source license. The
                 solver can be used as a subroutine library, as a
                 function within the Matlab environment, or as an
                 executable that reads and writes to data files.
                 Initiated in 1997, DSDP has developed into an efficient
                 and robust general-purpose solver for semidefinite
                 programming. Its features include a convergence proof
                 with polynomially bounded worst-case complexity, primal
                 and dual feasible solutions when they exist,
                 certificates of infeasibility when solutions do not
                 exist, initial points that can be feasible or
                 infeasible, relatively low memory requirements for an
                 interior-point method, sparse and low-rank data
                 structures, extensibility that allows applications to
                 customize the solver and improve its performance, a
                 subroutine library that enables it to be linked to
                 larger applications, scalable performance for large
                 problems on parallel architectures, and a
                 well-documented interface and examples of its use. The
                 package has been used in many applications and tested
                 for efficiency, robustness, and ease of use.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "conic programming; dual-scaling algorithm;
                 interior-point methods; linear matrix inequalities;
                 semidefinite programming",
}

@Article{Buttari:2008:UMP,
  author =       "Alfredo Buttari and Jack Dongarra and Jakub Kurzak and
                 Piotr Luszczek and Stanimir Tomov",
  title =        "Using Mixed Precision for Sparse Matrix Computations
                 to Enhance the Performance while Achieving 64-bit
                 Accuracy",
  journal =      j-TOMS,
  volume =       "34",
  number =       "4",
  pages =        "17:1--17:22",
  month =        jul,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377596.1377597",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 16 11:30:01 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "By using a combination of 32-bit and 64-bit floating
                 point arithmetic, the performance of many sparse linear
                 algebra algorithms can be significantly enhanced while
                 maintaining the 64-bit accuracy of the resulting
                 solution. These ideas can be applied to sparse
                 multifrontal and supernodal direct techniques and
                 sparse iterative techniques such as Krylov subspace
                 methods. The approach presented here can apply not only
                 to conventional processors but also to exotic
                 technologies such as Field Programmable Gate Arrays
                 (FPGA), Graphical Processing Units (GPU), and the Cell
                 BE processor.",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "floating point; iterative refinement; linear systems;
                 precision",
}

@Article{Utke:2008:OFM,
  author =       "Jean Utke and Uwe Naumann and Mike Fagan and Nathan
                 Tallent and Michelle Strout and Patrick Heimbach and
                 Chris Hill and Carl Wunsch",
  title =        "{OpenAD\slash F}: a Modular Open-Source Tool for
                 Automatic Differentiation of {Fortran} Codes",
  journal =      j-TOMS,
  volume =       "34",
  number =       "4",
  pages =        "18:1--18:36",
  month =        jul,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377596.1377598",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 16 11:30:01 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The Open/ADF tool allows the evaluation of derivatives
                 of functions defined by a Fortran program. The
                 derivative evaluation is performed by a Fortran code
                 resulting from the analysis and transformation of the
                 original program that defines the function of interest.
                 Open/ADF has been designed with a particular emphasis
                 on modularity, flexibility, and the use of open source
                 components. While the code transformation follows the
                 basic principles of automatic differentiation, the tool
                 implements new algorithmic approaches at various
                 levels, for example, for basic block preaccumulation
                 and call graph reversal. Unlike most other automatic
                 differentiation tools, Open/ADF uses components
                 provided by the Open/AD framework, which supports a
                 comparatively easy extension of the code
                 transformations in a language-independent fashion. It
                 uses code analysis results implemented in the
                 OpenAnalysis component. The interface to the
                 language-independent transformation engine is an
                 XML-based format, specified through an XML schema. The
                 implemented transformation algorithms allow efficient
                 derivative computations using locally optimized
                 cross-country sequences of vertex, edge, and face
                 elimination steps. Specifically, for the generation of
                 adjoint codes, Open/ADF supports various code reversal
                 schemes with hierarchical checkpointing at the
                 subroutine level. As an example from geophysical fluid
                 dynamics, a nonlinear time-dependent scalable, yet
                 simple, barotropic ocean model is considered.
                 OpenAD/F's reverse mode is applied to compute
                 sensitivities of some of the model's transport
                 properties with respect to gridded fields such as
                 bottom topography as independent (control) variables.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "adjoint compiler; Automatic differentiation; source
                 transformation",
}

@Article{Goldani-Moghaddam:2008:ECU,
  author =       "Hassan Goldani-Moghaddam and Wayne H. Enright",
  title =        "Efficient Contouring on Unstructured Meshes for
                 Partial Differential Equations",
  journal =      j-TOMS,
  volume =       "34",
  number =       "4",
  pages =        "19:1--19:25",
  month =        jul,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377596.1377599",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 16 11:30:01 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We introduce three fast contouring algorithms for
                 visualizing the solution of partial differential
                 equations based on the PCI (pure cubic interpolant).
                 The PCI is a particular piecewise bicubic polynomial
                 interpolant defined over an unstructured mesh. Unlike
                 standard contouring approaches, our contouring
                 algorithms do not need a fine-structured approximation
                 and work efficiently with the original scattered data.
                 The basic idea is to first identify the intersection
                 points between contour curves and the sides of each
                 triangle and then draw smooth contour curves connecting
                 these points. We compare these contouring algorithms
                 with the built-in Matlab {\em contour\/} procedure and
                 other contouring algorithms. We demonstrate that our
                 algorithms are both more accurate and faster than the
                 others.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "contour; PDE; scattered data; unstructured mesh;
                 Visualization",
}

@Article{Gao:2008:IEA,
  author =       "Weiguo Gao and Xiaoye S. Li and Chao Yang and Zhaojun
                 Bai",
  title =        "An Implementation and Evaluation of the {AMLS} Method
                 for Sparse Eigenvalue Problems",
  journal =      j-TOMS,
  volume =       "34",
  number =       "4",
  pages =        "20:1--20:28",
  month =        jul,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377596.1377600",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 16 11:30:01 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe an efficient implementation and present a
                 performance study of an automated multi-level
                 substructuring (AMLS) method for sparse eigenvalue
                 problems. We assess the time and memory requirements
                 associated with the key steps of the algorithm, and
                 compare it with the shift-and-invert Lanczos algorithm.
                 Our eigenvalue problems come from two very different
                 application areas: accelerator cavity design and
                 normal-mode vibrational analysis of polyethylene
                 particles. We show that the AMLS method, when
                 implemented carefully, outperforms the traditional
                 method in broad application areas when large numbers of
                 eigenvalues are sought, with relatively low accuracy.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "multilevel substructuring; performance evaluation;
                 Sparse eigenvalue problems",
}

@Article{Atkinson:2008:ASF,
  author =       "Kendall E. Atkinson and Lawrence F. Shampine",
  title =        "{Algorithm 876}: Solving {Fredholm} Integral Equations
                 of the Second Kind in {Matlab}",
  journal =      j-TOMS,
  volume =       "34",
  number =       "4",
  pages =        "21:1--21:20",
  month =        jul,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377596.1377601",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65R20",
  MRnumber =     "MR2474526 (2010a:65281)",
  bibdate =      "Tue Mar 30 17:06:44 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present here the algorithms and user interface of a
                 Matlab program, Fie, that solves numerically Fredholm
                 integral equations of the second kind on an interval
                 $[a,b]$ to a specified, modest accuracy. The kernel
                 function $K(s,t)$ is moderately smooth on $[a,b] \times
                 [a,b]$ except possibly across the diagonal $s = t$. If
                 the interval is finite, provides for kernel functions
                 that behave in a variety of ways across the diagonal,
                 that is, $K(s,t)$ may be smooth, have a discontinuity
                 in a low-order derivative, have a logarithmic
                 singularity, or have an algebraic singularity. Fie also
                 solves a large class of integral equations with
                 moderately smooth kernel function on $[0,\infty)$.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Matlab; Numerical solution",
}

@Article{Kodama:2008:ASP,
  author =       "Masao Kodama",
  title =        "{Algorithm 877}: a Subroutine Package for Cylindrical
                 Functions of Complex Order and Nonnegative Argument",
  journal =      j-TOMS,
  volume =       "34",
  number =       "4",
  pages =        "22:1--22:21",
  month =        jul,
  year =         "2008",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377596.1377602",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 16 11:30:01 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The algorithm presented provides a package of
                 subroutines for calculating the cylindrical functions
                 $J_\nu(x)$, $N_\nu(x)$, $H_\nu^{1}(x)$, $H_\nu^{2}(x)$
                 where the order $\nu$ is complex and the real argument
                 $x$ is nonnegative. The algorithm is written in Fortran
                 95 and calculates the functions using single, double,
                 or quadruple precision according to the value of a
                 parameter defined in the algorithm. The methods of
                 calculating the functions are based on a series
                 expansion, Debye's asymptotic expansions, Olver's
                 asymptotic expansions, and recurrence methods (Miller's
                 algorithms). The relative errors of the functional
                 values computed by this algorithm using double
                 precision are less than $2.4 \times 10^{-13}$ in the
                 region $0 \leq \mbox{Re}(\nu) \leq 64$, $0 \leq
                 \mbox{Im}(\nu) \leq 63$, $0.024 \leq x \leq 97$.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Bessel functions; complex order; Cylindrical
                 functions; Debye's asymptotic expansions; Hankel
                 functions; Miller's algorithms; Neumann functions;
                 nonnegative argument; numerical calculation; Olver's
                 asymptotic expansions",
}

@Article{Bartlett:2009:HDS,
  author =       "Roscoe A. Bartlett and Bart G. {Van Bloemen Waanders}
                 and Martin Berggren",
  title =        "Hybrid differentiation strategies for simulation and
                 analysis of applications in {C++}",
  journal =      j-TOMS,
  volume =       "35",
  number =       "1",
  pages =        "1:1--1:29",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377603.1377604",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:12:48 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Computationally efficient and accurate derivatives are
                 important to the success of many different types of
                 numerical methods. Automatic differentiation (AD)
                 approaches compute truncation-free derivatives and can
                 be efficient in many cases. Although present AD tools
                 can provide a convenient implementation mechanism, the
                 computational efficiency rarely compares to
                 analytically derived versions that have been carefully
                 implemented. The focus of this work is to combine the
                 strength of these methods into a hybrid strategy that
                 attempts to achieve an optimal balance of
                 implementation and computational efficiency by
                 selecting the appropriate components of the target
                 algorithms for AD and analytical derivation. Although
                 several AD approaches can be considered, our focus is
                 on the use of template overloading forward AD tools in
                 C++ applications. We demonstrate this hybrid strategy
                 for a system of partial differential equations in gas
                 dynamics. These methods apply however to other systems
                 of differentiable equations, including DAEs and ODEs.",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "automatic differentiation; Euler equations; finite
                 volume methods; hybrid differentiation methods;
                 template overloading",
}

@Article{Naumann:2009:OVE,
  author =       "Uwe Naumann and Yuxiao Hu",
  title =        "Optimal vertex elimination in single-expression-use
                 graphs",
  journal =      j-TOMS,
  volume =       "35",
  number =       "1",
  pages =        "2:1--2:20",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377603.1377605",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:12:48 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The source transformation tool for automatic
                 differentiation of Fortran programs ADIFOR uses a
                 preaccumulation technique to speed up tangent-linear
                 codes significantly compared to the standard forward
                 mode. Reverse mode automatic differentiation is applied
                 to all scalar assignments to generate efficient code
                 for the computation of local gradients. It has been
                 well known for some time that reverse mode is not
                 necessarily the optimal choice for the computation of
                 these statement-level gradients as it does not minimize
                 the number of operations required. This article
                 presents an efficient algorithm for the solution of
                 this combinatorial optimization problem. The
                 corresponding software is freely available for
                 downloading on our website. Developers of software for
                 automatic differentiation are invited to integrate the
                 algorithm into their tools.\par

                 Gradients of scalar multivariate functions can be
                 computed by elimination methods on the linearized
                 computational graph. The combinatorial optimization
                 problem that aims to minimize the number of arithmetic
                 operations performed by the elimination algorithm is
                 known to be NP-complete. In this article we present a
                 polynomial algorithm for solving a relevant subclass of
                 this problem's instances. The proposed method relies on
                 the ability to compute vertex covers in bipartite
                 graphs in polynomial time. A simplified version of this
                 graph algorithm is used in a research prototype of the
                 differentiation-enabled NAGWare Fortran compiler for
                 the preaccumulation of local gradients of scalar
                 assignments in the context of automatic generation of
                 efficient tangent-linear code for numerical programs.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "single-expression-use graph; vertex elimination",
}

@Article{Bientinesi:2009:FAR,
  author =       "Paolo Bientinesi and Brian Gunter and Robert A. van de
                 Geijn",
  title =        "Families of algorithms related to the inversion of a
                 {Symmetric Positive Definite} matrix",
  journal =      j-TOMS,
  volume =       "35",
  number =       "1",
  pages =        "3:1--3:22",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377603.1377606",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:12:48 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We study the high-performance implementation of the
                 inversion of a Symmetric Positive Definite (SPD) matrix
                 on architectures ranging from sequential processors to
                 Symmetric MultiProcessors to distributed memory
                 parallel computers. This inversion is traditionally
                 accomplished in three ``sweeps'': a Cholesky
                 factorization of the SPD matrix, the inversion of the
                 resulting triangular matrix, and finally the
                 multiplication of the inverted triangular matrix by its
                 own transpose. We state different algorithms for each
                 of these sweeps as well as algorithms that compute the
                 result in a single sweep. One algorithm outperforms the
                 current ScaLAPACK implementation by 20--30 percent due
                 to improved load-balance on a distributed memory
                 architecture.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "inversion; libraries; linear algebra; symmetric
                 positive definite",
}

@Article{Goto:2009:HPI,
  author =       "Kazushige Goto and Robert {Van De Geijn}",
  title =        "High-performance implementation of the level-3
                 {BLAS}",
  journal =      j-TOMS,
  volume =       "35",
  number =       "1",
  pages =        "4:1--4:14",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377603.1377607",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:12:48 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A simple but highly effective approach for
                 transforming high-performance implementations on
                 cache-based architectures of matrix-matrix
                 multiplication into implementations of other commonly
                 used matrix-matrix computations (the level-3 BLAS) is
                 presented. Exceptional performance is demonstrated on
                 various architectures.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "basic linear algebra subprograms; libraries; linear
                 algebra; matrix-matrix operations",
}

@Article{Jonasson:2009:EEV,
  author =       "Kristjan Jonasson and Sebastian E. Ferrando",
  title =        "Evaluating exact {VARMA} likelihood and its gradient
                 when data are incomplete",
  journal =      j-TOMS,
  volume =       "35",
  number =       "1",
  pages =        "5:1--5:16",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377603.1377608",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:12:48 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A detailed description of an algorithm for the
                 evaluation and differentiation of the likelihood
                 function for VARMA processes in the general case of
                 missing values is presented. The method is based on
                 combining the Cholesky decomposition method for
                 complete data VARMA evaluation and the
                 Sherman--Morrison--Woodbury formula. Potential saving
                 for pure VAR processes is discussed and formulae for
                 the estimation of missing values and shocks are
                 provided. A theorem on the determinant of a low rank
                 update is proved. Matlab implementation of the
                 algorithm is in a companion article.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "ARMA; determinant of low rank update; exact likelihood
                 function; incomplete data; matrix derivative; matrix
                 differentiation; missing values; VARMA; vector
                 autoregressive moving average model",
}

@Article{Jonasson:2009:AEV,
  author =       "Kristjan Jonasson",
  title =        "{Algorithm 878}: {Exact VARMA} likelihood and its
                 gradient for complete and incomplete data with
                 {Matlab}",
  journal =      j-TOMS,
  volume =       "35",
  number =       "1",
  pages =        "6:1--6:11",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377603.1377609",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:12:48 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Matlab functions for the evaluation of the exact
                 log-likelihood of VAR and VARMA time series models are
                 presented (vector autoregressive moving average). The
                 functions accept incomplete data, and calculate
                 analytical gradients, which may be used in parameter
                 estimation with numerical likelihood maximization.
                 Allowance is made for possible savings when estimating
                 seasonal, structured or distributed lag models. Also
                 provided is a function for creating simulated VARMA
                 time series that have an accurate distribution from
                 term one (they are {\em spin-up\/} free). The functions
                 are accompanied by a simple example driver, a program
                 demonstrating their use for real parameter fitting, as
                 well as a test suite for verifying their correctness
                 and aid further development. The article concludes with
                 description of numerical results obtained with the
                 algorithm.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "ARMA; exact likelihood function; incomplete data;
                 missing values; VARMA; vector autoregressive moving
                 average model",
}

@Article{Lee:2009:AET,
  author =       "Che-Rung Lee and G. W. Stewart",
  title =        "{Algorithm 879}: {EIGENTEST} --- a test matrix
                 generator for large-scale eigenproblems",
  journal =      j-TOMS,
  volume =       "35",
  number =       "1",
  pages =        "7:1--7:11",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377603.1377610",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:12:48 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Eigentest is a package that produces real test
                 matrices with known eigensystems. A test matrix, called
                 an eigenmat, is generated in a factored form, in which
                 the user can specify the eigenvalues and has some
                 control over the condition of the eigenvalues and
                 eigenvectors. An eigenmat $A$ of order $n$ requires
                 only $O(n)$ storage for its representation. Auxiliary
                 programs permit the computation of $(A - sI) b$, $(A -
                 sI)^T b$, $(A - sI)^{-1} b$, and $(A - sI)^{-T} b$ in
                 $O(n)$ operations. A special routine computes specified
                 eigenvectors of an eigenmat and the condition of its
                 eigenvalue. Thus eigenmats are suitable for testing
                 algorithms based on Krylov sequences, as well as others
                 based on matrix-vector products. This article
                 introduces the eigenmat and describes implementations
                 in Fortran 77, Fortran 95, C, and Matlab.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "eigensystem; test matrix generation",
}

@Article{Marques:2009:ATI,
  author =       "Osni A. Marques and Christof V{\"o}mel and James W.
                 Demmel and Beresford N. Parlett",
  title =        "{Algorithm 880}: a testing infrastructure for
                 symmetric tridiagonal eigensolvers",
  journal =      j-TOMS,
  volume =       "35",
  number =       "1",
  pages =        "8:1--8:13",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377603.1377611",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:12:48 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "LAPACK is often mentioned as a positive example of a
                 software library that encapsulates complex, robust, and
                 widely used numerical algorithms for a wide range of
                 applications. At installation time, the user has the
                 option of running a (limited) number of test cases to
                 verify the integrity of the installation process. On
                 the algorithm developer's side, however, more
                 exhaustive tests are usually performed to study
                 algorithm behavior on a variety of problem settings and
                 also computer architectures. In this process, difficult
                 test cases need to be found that reflect particular
                 challenges of an application or push algorithms to
                 extreme behavior. These tests are then assembled into a
                 comprehensive collection, therefore making it possible
                 for any new or competing algorithm to be stressed in a
                 similar way. This article describes an infrastructure
                 for exhaustively testing the symmetric tridiagonal
                 eigensolvers implemented in LAPACK. It consists of two
                 parts: a selection of carefully chosen test matrices
                 with particular idiosyncrasies and a portable testing
                 framework that allows for easy testing and data
                 processing. The tester facilitates experiments with
                 algorithmic choices, parameter and threshold studies,
                 and performance comparisons on different
                 architectures.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accuracy; design; eigenvalues; eigenvectors;
                 implementation; LAPACK; numerical software;
                 performance; symmetric matrix; test matrices; testing",
}

@Article{Huyer:2009:SSN,
  author =       "Waltraud Huyer and Arnold Neumaier",
  title =        "{SNOBFIT} -- {Stable Noisy Optimization by Branch and
                 Fit}",
  journal =      j-TOMS,
  volume =       "35",
  number =       "2",
  pages =        "9:1--9:25",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377612.1377613",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:13:00 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The software package SNOBFIT for bound-constrained
                 (and soft-constrained) noisy optimization of an
                 expensive objective function is described. It combines
                 global and local search by branching and local fits.
                 The program is made robust and flexible for practical
                 use by allowing for hidden constraints, batch function
                 evaluations, change of search regions, etc.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "branch-and-bound; derivative-free; expensive function
                 values; hidden constraints; noisy function values;
                 parallel evaluation; soft constraints; surrogate
                 model",
}

@Article{Kirby:2009:BDS,
  author =       "Robert C. Kirby and Anders Logg",
  title =        "Benchmarking Domain-Specific Compiler Optimizations
                 for Variational Forms",
  journal =      j-TOMS,
  volume =       "35",
  number =       "2",
  pages =        "10:1--10:18",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377612.1377614",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:13:00 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We examine the effect of using complexity-reducing
                 relations [Kirby et al. 2006] to generate optimized
                 code for the evaluation of finite-element variational
                 forms. The optimizations are implemented in a prototype
                 code named FErari, which has been integrated as an
                 optimizing backend to the FEniCS form compiler, FFC
                 [Kirby and Logg 2006; 2007]. In some cases, FErari
                 provides very little speedup, while in other cases we
                 obtain reduced local operation counts by a factor of as
                 much as 7.9 and speedups for the assembly of the global
                 sparse matrix by as much as a factor of 2.8 (see Figure
                 9).",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "compiler; complexity-reducing relations; FErari; FFC;
                 finite element method; optimization; variational form",
}

@Article{Quintana-Orti:2009:ULF,
  author =       "Enrique S. Quintana-Ort{\'\i} and Robert A. {Van De
                 Geijn}",
  title =        "Updating an {LU} Factorization with Pivoting",
  journal =      j-TOMS,
  volume =       "35",
  number =       "2",
  pages =        "11:1--11:16",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377612.1377615",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:13:00 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We show how to compute an LU factorization of a matrix
                 when the factors of a leading principle submatrix are
                 already known. The approach incorporates pivoting akin
                 to partial pivoting, a strategy we call {\em
                 incremental pivoting}. An implementation using the
                 Formal Linear Algebra Methods Environment (FLAME)
                 application programming interface (API) is described.
                 Experimental results demonstrate practical numerical
                 stability and high performance on an Intel Itanium2
                 processor-based server.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "linear systems; LU factorization; pivoting; updating",
}

@Article{Drmac:2009:FRR,
  author =       "Zlatko Drma{\v{c}} and Zvonimir Bujanovi{\'c}",
  title =        "On the Failure of Rank-Revealing {QR} Factorization
                 Software -- a Case Study",
  journal =      j-TOMS,
  volume =       "35",
  number =       "2",
  pages =        "12:1--12:28",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377612.1377616",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:13:00 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article reports an unexpected and rather erratic
                 behavior of the LAPACK software implementation of the
                 QR factorization with Businger--Golub column pivoting.
                 It is shown that, due to finite precision arithmetic,
                 the software implementation of the factorization can
                 catastrophically fail to produce a properly structured
                 triangular factor, thus leading to a potentially severe
                 underestimate of a matrix's numerical rank. The 30-year
                 old problem, dating back to LINPACK, has (undetectedly)
                 badly affected many computational routines and software
                 packages, as well as the study of rank-revealing QR
                 factorizations. We combine computer experiments and
                 numerical analysis to isolate, analyze, and fix the
                 problem. Our modification of the current LAPACK xGEQP3
                 routine is already included in the LAPACK 3.1.0
                 release. The modified routine is numerically more
                 robust and with a negligible overhead. We also provide
                 a new, equally efficient, and provably numerically safe
                 partial-column norm-updating strategy.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "pivoting; QR factorization; rank-revealing",
}

@Article{Fraysse:2009:ASF,
  author =       "Val{\'e}rie Frayss{\'e} and Luc Giraud and Serge
                 Gratton",
  title =        "{Algorithm 881}: a Set of Flexible {GMRES} Routines
                 for Real and Complex Arithmetics on High-Performance
                 Computers",
  journal =      j-TOMS,
  volume =       "35",
  number =       "2",
  pages =        "13:1--13:12",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377612.1377617",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:13:00 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this article we describe our implementations of the
                 FGMRES algorithm for both real and complex, single and
                 double precision arithmetics suitable for serial,
                 shared-memory, and distributed-memory computers. For
                 the sake of portability, simplicity, flexibility, and
                 efficiency, the FGMRES solvers have been implemented in
                 Fortran 77 using the reverse communication mechanism
                 for the matrix-vector product, the preconditioning, and
                 the dot-product computations. For distributed-memory
                 computation, several orthogonalization procedures have
                 been implemented to reduce the cost of the dot-product
                 calculation, which is a well-known bottleneck of
                 efficiency for Krylov methods. Furthermore, either
                 implicit or explicit calculation of the residual at
                 restart is possible depending on the actual cost of the
                 matrix-vector product. Finally, the implemented
                 stopping criterion is based on a normwise backward
                 error.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "distributed memory; FGMRES; flexible Krylov methods;
                 high-performance computing; linear systems; reverse
                 communication",
}

@Article{VanDeun:2009:ANB,
  author =       "Joris {Van Deun} and Karl Deckers and Adhemar Bultheel
                 and J. A. C. Weideman",
  title =        "{Algorithm 882}: Near-Best Fixed Pole Rational
                 Interpolation with Applications in Spectral Methods",
  journal =      j-TOMS,
  volume =       "35",
  number =       "2",
  pages =        "14:1--14:21",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377612.1377618",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:13:00 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a numerical procedure to compute the nodes
                 and weights in rational Gauss--Chebyshev quadrature
                 formulas. Under certain conditions on the poles, these
                 nodes are near best for rational interpolation with
                 prescribed poles (in the same sense that Chebyshev
                 points are near best for polynomial interpolation). As
                 an illustration, we use these interpolation points to
                 solve a differential equation with an interior boundary
                 layer using a rational spectral method.\par

                 The algorithm to compute the interpolation points (and,
                 if required, the quadrature weights) is implemented as
                 a Matlab program.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "quadrature; rational interpolation",
}

@Article{Waki:2009:ASS,
  author =       "Hayato Waki and Sunyoung Kim and Masakazu Kojima and
                 Masakazu Muramatsu and Hiroshi Sugimoto",
  title =        "{Algorithm 883}: {SparsePOP} --- a Sparse Semidefinite
                 Programming Relaxation of Polynomial Optimization
                 Problems",
  journal =      j-TOMS,
  volume =       "35",
  number =       "2",
  pages =        "15:1--15:13",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377612.1377619",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:13:00 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "SparsePOP is a Matlab implementation of the sparse
                 semidefinite programming (SDP) relaxation method for
                 approximating a global optimal solution of a polynomial
                 optimization problem (POP) proposed by Waki et al.
                 [2006]. The sparse SDP relaxation exploits a sparse
                 structure of polynomials in POPs when applying ``a
                 hierarchy of LMI relaxations of increasing dimensions''
                 Lasserre [2006]. The efficiency of SparsePOP to
                 approximate optimal solutions of POPs is thus
                 increased, and larger-scale POPs can be handled.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "global optimization; Matlab software package;
                 polynomial optimization problem; semidefinite
                 programming relaxation; sparsity; sums-of-squares
                 optimization",
}

@Article{Dominguez:2009:ASM,
  author =       "V{\'\i}ctor Dom{\'\i}nguez and Francisco-Javier
                 Sayas",
  title =        "{Algorithm 884}: a Simple {Matlab} Implementation of
                 the {Argyris} Element",
  journal =      j-TOMS,
  volume =       "35",
  number =       "2",
  pages =        "16:1--16:11",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1377612.1377620",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Aug 5 18:13:00 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this work we propose a new algorithm to evaluate
                 the basis functions of the Argyris finite element and
                 their derivatives. The main novelty here is an
                 efficient way to calculate the matrix which gives the
                 change of coordinates between the bases of the Argyris
                 element for the reference and for an arbitrary
                 triangle. This matrix is factored as the product of two
                 rectangular matrices with a strong block structure
                 which makes their computation very easy. We show and
                 comment on an implementation of this algorithm in
                 Matlab. Two numerical experiments, an interpolation of
                 a smooth function on a triangle and the finite-element
                 solution of the Dirichlet problem for the biLaplacian,
                 are presented in the last section to check the
                 performance of our implementation.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Argyris element; finite elements; Matlab",
}

@Article{Jansson:2009:ADS,
  author =       "Johan Jansson and Anders Logg",
  title =        "Algorithms and Data Structures for Multi-Adaptive
                 Time-Stepping",
  journal =      j-TOMS,
  volume =       "35",
  number =       "3",
  pages =        "17:1--17:24",
  month =        oct,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1391989.1391990",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 1 19:57:00 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Multi-adaptive Galerkin methods are extensions of the
                 standard continuous and discontinuous Galerkin methods
                 for the numerical solution of initial value problems
                 for ordinary or partial differential equations. In
                 particular, the multi-adaptive methods allow individual
                 and adaptive time steps to be used for different
                 components or in different regions of space. We present
                 algorithms for efficient multi-adaptive time-stepping,
                 including the recursive construction of time slabs and
                 adaptive time step selection. We also present data
                 structures for efficient storage and interpolation of
                 the multi-adaptive solution. The efficiency of the
                 proposed algorithms and data structures is demonstrated
                 for a series of benchmark problems.",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms; C++; continuous Galerkin; discontinuous
                 Galerkin; DOLFIN; implementation; individual time
                 steps; local time steps; mcgq; mdgq; Multi-adaptivity;
                 multirate; ODE",
}

@Article{Gordon:2009:CRR,
  author =       "Dan Gordon and Rachel Gordon",
  title =        "{CGMN} Revisited: Robust and Efficient Solution of
                 Stiff Linear Systems Derived from Elliptic Partial
                 Differential Equations",
  journal =      j-TOMS,
  volume =       "35",
  number =       "3",
  pages =        "18:1--18:27",
  month =        oct,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1391989.1391991",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 1 19:57:00 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Given a linear system $A x = b$, one can construct a
                 related ``normal equations'' system $A A^T y = b$, $x =
                 A^T y$. Bj{\"o}rck and Elfving have shown that the SSOR
                 algorithm, applied to the normal equations, can be
                 accelerated by the conjugate gradient algorithm (CG).
                 The resulting algorithm, called CGMN, is error-reducing
                 and in theory it always converges even when the
                 equation system is inconsistent and/or nonsquare. SSOR
                 on the normal equations is equivalent to the Kaczmarz
                 algorithm (KACZ), with a fixed relaxation parameter,
                 run in a double (forward and backward) sweep on the
                 original equations. CGMN was tested on nine well-known
                 large and sparse linear systems obtained by
                 central-difference discretization of elliptic
                 convection-diffusion partial differential equations
                 (PDEs). Eight of the PDEs were strongly
                 convection-dominated, and these are known to produce
                 very stiff systems with large off-diagonal elements.
                 CGMN was compared with some of the foremost
                 state-of-the art Krylov subspace methods: restarted
                 GMRES, Bi-CGSTAB, and CGS. These methods were tested
                 both with and without various preconditioners. CGMN
                 converged in all the cases, while none of the preceding
                 algorithm/preconditioner combinations achieved this
                 level of robustness. Furthermore, on varying grid
                 sizes, there was only a gradual increase in the number
                 of iterations as the grid was refined. On the eight
                 convection-dominated cases, the initial convergence
                 rate of CGMN was better than all the other combinations
                 of algorithms and preconditioners, and the residual
                 decreased monotonically. The CGNR algorithm was also
                 tested, and it was as robust as CGMN, but slower.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "CGMN; CGNR; conjugate-gradient; convection-dominated;
                 elliptic equations; Kaczmarz; linear systems; normal
                 equations; partial differential equations; row
                 projections; SOR; sparse linear systems; SSOR; stiff
                 equations",
}

@Article{Dumas:2009:DLA,
  author =       "Jean-Guillaume Dumas and Pascal Giorgi and Cl{\'e}ment
                 Pernet",
  title =        "Dense Linear Algebra over Word-Size Prime Fields: the
                 {FFLAS} and {FFPACK} Packages",
  journal =      j-TOMS,
  volume =       "35",
  number =       "3",
  pages =        "19:1--19:35",
  month =        oct,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1391989.1391992",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 1 19:57:00 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In the past two decades, some major efforts have been
                 made to reduce exact (e.g. integer, rational,
                 polynomial) linear algebra problems to matrix
                 multiplication in order to provide algorithms with
                 optimal asymptotic complexity. To provide efficient
                 implementations of such algorithms one need to be
                 careful with the underlying arithmetic. It is well
                 known that modular techniques such as the Chinese
                 remainder algorithm or the $p$-adic lifting allow very
                 good practical performance, especially when word size
                 arithmetic is used. Therefore, finite field arithmetic
                 becomes an important core for efficient exact linear
                 algebra libraries. In this article, we study high
                 performance implementations of basic linear algebra
                 routines over word size prime fields: especially matrix
                 multiplication; our goal being to provide an exact
                 alternate to the numerical BLAS library. We show that
                 this is made possible by a careful combination of
                 numerical computations and asymptotically faster
                 algorithms. Our kernel has several symbolic linear
                 algebra applications enabled by diverse matrix
                 multiplication reductions: symbolic triangularization,
                 system solving, determinant, and matrix inverse
                 implementations are thus studied.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "BLAS level 1-2-3; determinant; inverse; linear algebra
                 package; matrix factorization; s symbolic matrix
                 multiplication; Winograd' Word size prime fields",
}

@Article{Linhart:2009:ACL,
  author =       "Jean Marie Linhart",
  title =        "{Algorithm 885}: Computing the Logarithm of the Normal
                 Distribution",
  journal =      j-TOMS,
  volume =       "35",
  number =       "3",
  pages =        "20:1--20:10",
  month =        oct,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1391989.1391993",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 1 19:57:00 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present and compare three C functions to compute
                 the logarithm of the cumulative standard normal
                 distribution. The first is a new algorithm derived from
                 Algorithm 304's calculation of the standard normal
                 distribution via a series or continued fraction
                 approximation, and it is good to the accuracy of the
                 machine. The second is based on Algorithm 715's
                 calculation of the standard normal distribution via
                 rational Chebyshev approximation. This is related to,
                 and an improvement on, the algorithm for the logarithm
                 of the normal distribution available in the software
                 package R. The third is a new and simple algorithm that
                 uses the compiler's implementation of the error
                 function, and complement of the error function, to
                 compute the log of the normal distribution.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "error function; logarithm of the standard normal
                 distribution; Normal distribution; normal integral",
}

@Article{Caliari:2009:APL,
  author =       "Marco Caliari and Stefanode Marchi and Marco
                 Vianello",
  title =        "{Algorithm 886}: {Padua$2$D} --- {Lagrange}
                 Interpolation at {Padua} Points on Bivariate Domains",
  journal =      j-TOMS,
  volume =       "35",
  number =       "3",
  pages =        "21:1--21:11",
  month =        oct,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1391989.1391994",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 1 19:57:00 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a stable and efficient Fortran
                 implementation of polynomial interpolation at the Padua
                 points on the square $[-1,1]^2$. These points are
                 unisolvent and their Lebesgue constant has minimal
                 order of growth (log square of the degree). The
                 algorithm is based on the representation of the
                 Lagrange interpolation formula in a suitable orthogonal
                 basis, and takes advantage of a new matrix formulation
                 together with the machine-specific optimized BLAS
                 subroutine for the matrix-matrix product. Extension to
                 interpolation on rectangles, triangles and ellipses is
                 also described.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "bivariate Chebyshev orthogonal basis; Bivariate
                 Lagrange interpolation; Fortran 77; Padua points",
}

@Article{Chen:2009:ACS,
  author =       "Yanqing Chen and Timothy A. Davis and William W. Hager
                 and Sivasankaran Rajamanickam",
  title =        "{Algorithm 887}: {CHOLMOD}, Supernodal Sparse
                 {Cholesky} Factorization and Update\slash Downdate",
  journal =      j-TOMS,
  volume =       "35",
  number =       "3",
  pages =        "22:1--22:14",
  month =        oct,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1391989.1391995",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 1 19:57:00 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "CHOLMOD is a set of routines for factorizing sparse
                 symmetric positive definite matrices of the form $A$ or
                 $AA^T$, updating/downdating a sparse Cholesky
                 factorization, solving linear systems,
                 updating/downdating the solution to the triangular
                 system $Lx = b$, and many other sparse matrix functions
                 for both symmetric and unsymmetric matrices. Its
                 supernodal Cholesky factorization relies on LAPACK and
                 the Level-3 BLAS, and obtains a substantial fraction of
                 the peak performance of the BLAS. Both real and complex
                 matrices are supported. CHOLMOD is written in ANSI/ISO
                 C, with both C and MATLAB$^{\sc TM}$ interfaces. It
                 appears in MATLAB 7.2 as $x = A\backslash b$ when $A$
                 is sparse symmetric positive definite, as well as in
                 several other sparse matrix functions.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Cholesky factorization; linear equations; sparse
                 matrices",
}

@Article{Drake:2009:ASH,
  author =       "John B. Drake and Pat Worley and Eduardo D'Azevedo",
  title =        "{Algorithm 888}: Spherical Harmonic Transform
                 Algorithms",
  journal =      j-TOMS,
  volume =       "35",
  number =       "3",
  pages =        "23:1--23:23",
  month =        oct,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1391989.1404581",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 1 19:57:00 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A collection of MATLAB classes for computing and using
                 spherical harmonic transforms is presented. Methods of
                 these classes compute differential operators on the
                 sphere and are used to solve simple partial
                 differential equations in a spherical geometry. The
                 spectral synthesis and analysis algorithms using fast
                 Fourier transforms and Legendre transforms with the
                 associated Legendre functions are presented in detail.
                 A set of methods associated with a spectral\_field
                 class provides spectral approximation to the
                 differential operators $\nabla \cdot$, $\nabla \times$,
                 $\nabla$, and $\nabla^2$ in spherical geometry. Laplace
                 inversion and Helmholtz equation solvers are also
                 methods for this class. The use of the class and
                 methods in MATLAB is demonstrated by the solution of
                 the barotropic vorticity equation on the sphere. A
                 survey of alternative algorithms is given and
                 implementations for parallel high performance computers
                 are discussed in the context of global climate and
                 weather models.",
  acknowledgement = ack-nhfb,
  articleno =    "23",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "fluid dynamics; geophysical flow; high performance
                 computing; Spectral transform methods; spherical",
}

@Article{Cazals:2009:AJG,
  author =       "Fr{\'e}d{\'e}ric Cazals and Marc Pouget",
  title =        "{Algorithm 889}: {Jet\_fitting\_3}: --- a Generic
                 {C++} Package for Estimating the Differential
                 Properties on Sampled Surfaces via Polynomial Fitting",
  journal =      j-TOMS,
  volume =       "35",
  number =       "3",
  pages =        "24:1--24:20",
  month =        oct,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1391989.1404582",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 1 19:57:00 MDT 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Surfaces of $R^3$ are ubiquitous in science and
                 engineering, and estimating the local differential
                 properties of a surface discretized as a point cloud or
                 a triangle mesh is a central building block in computer
                 graphics, computer aided design, computational
                 geometry, and computer vision. One strategy to perform
                 such an estimation consists of resorting to polynomial
                 fitting, either interpolation or approximation, but
                 this route is difficult for several reasons: choice of
                 the coordinate system, numerical handling of the
                 fitting problem, and extraction of the differential
                 properties.\par

                 This article presents a generic C++ software package
                 solving these problems. On the theoretical side and as
                 established in a companion paper, the interpolation and
                 approximation methods provided achieve the best
                 asymptotic error bounds known to date. On the
                 implementation side and following state-of-the-art
                 coding rules in computational geometry, genericity of
                 the package is achieved thanks to four template classes
                 accounting for, (a) the type of the input points, (b)
                 the internal geometric computations, (c) a conversion
                 mechanism between these two geometries, and (d) the
                 linear algebra operations. An instantiation within the
                 Computational Geometry Algorithms Library (CGAL,
                 version 3.3) and using LAPACK is also provided.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Approximation; C++ design; computational geometry;
                 differential geometry; interpolation; numerical linear
                 algebra; sampled surfaces",
}

@Article{Eijkhout:2009:SSN,
  author =       "Victor Eijkhout and Erika Fuentes",
  title =        "A Standard and Software for Numerical Metadata",
  journal =      j-TOMS,
  volume =       "35",
  number =       "4",
  pages =        "25:1--25:20",
  month =        feb,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1462173.1462174",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Feb 13 18:09:40 MST 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We propose a standard for generating, manipulating,
                 and storing metadata describing numerical problems, in
                 particular properties of matrices and linear systems.
                 The standard comprises:\par

                 --an API for metadata generating and querying software,
                 and\par

                 --an XML format for permanent storage of
                 metadata.\par

                 The API is open-ended, allowing for other parties to
                 define additional metadata categories to be generated
                 and stored within this framework. Furthermore, we
                 present two software libraries, NMD and AnaMod, that
                 implement this standard, and that contain a number of
                 computational modules for numerical metadata. The
                 libraries, more than simply illustrating the use of the
                 standard, provide considerable utility to numerical
                 researchers.",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Taylor:2009:CCT,
  author =       "Alan Taylor and Desmond J. Higham",
  title =        "{CONTEST}: a Controllable Test Matrix Toolbox for
                 {MATLAB}",
  journal =      j-TOMS,
  volume =       "35",
  number =       "4",
  pages =        "26:1--26:17",
  month =        feb,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1462173.1462175",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Feb 13 18:09:40 MST 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Large, sparse networks that describe complex
                 interactions are a common feature across a number of
                 disciplines, giving rise to many challenging matrix
                 computational tasks. Several random graph models have
                 been proposed that capture key properties of real-life
                 networks. These models provide realistic, parametrized
                 matrices for testing linear system and eigenvalue
                 solvers. CONTEST (CONtrollable TEST matrices) is a
                 random network toolbox for MATLAB that implements nine
                 models. The models produce unweighted directed or
                 undirected graphs; that is, symmetric or unsymmetric
                 matrices with elements equal to zero or one. They have
                 one or more parameters that affect features such as
                 sparsity and characteristic pathlength and all can be
                 of arbitrary dimension. Utility functions are supplied
                 for rewiring, adding extra shortcuts and subsampling in
                 order to create further classes of networks. Other
                 utilities convert the adjacency matrices into
                 real-valued coefficient matrices for naturally arising
                 computational tasks that reduce to sparse linear system
                 and eigenvalue problems.",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "clustering; matrix computation; preferential
                 attachment; random graph; rewiring; small-world; sparse
                 matrix",
}

@Article{Davis:2009:DSS,
  author =       "Timothy A. Davis and William W. Hager",
  title =        "Dynamic Supernodes in Sparse {Cholesky} Update\slash
                 Downdate and Triangular Solves",
  journal =      j-TOMS,
  volume =       "35",
  number =       "4",
  pages =        "27:1--27:23",
  month =        feb,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1462173.1462176",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Feb 13 18:09:40 MST 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The supernodal method for sparse Cholesky
                 factorization represents the factor $L$ as a set of
                 supernodes, each consisting of a contiguous set of
                 columns of $L$ with identical nonzero pattern. A
                 conventional supernode is stored as a dense submatrix.
                 While this is suitable for sparse Cholesky
                 factorization where the nonzero pattern of $L$ does not
                 change, it is not suitable for methods that modify a
                 sparse Cholesky factorization after a low-rank change
                 to $A$ (an update\slash downdate, $\bar{A} = A \pm W
                 W^T$). Supernodes merge and split apart during an
                 update\slash downdate. Dynamic supernodes are
                 introduced which allow a sparse Cholesky update\slash
                 downdate to obtain performance competitive with
                 conventional supernodal methods. A dynamic supernodal
                 solver is shown to exceed the performance of the
                 conventional (BLAS-based) supernodal method for solving
                 triangular systems. These methods are incorporated into
                 CHOLMOD, a sparse Cholesky factorization and
                 update\slash downdate package which forms the basis of
                 {\tt $x = A \backslash b$} in MATLAB when {\tt A} is
                 sparse and symmetric positive definite.",
  acknowledgement = ack-nhfb,
  articleno =    "27",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Cholesky factorization; linear equations; sparse
                 matrices",
}

@Article{Demmel:2009:EPI,
  author =       "James Demmel and Yozo Hida and E. Jason Riedy and
                 Xiaoye S. Li",
  title =        "Extra-Precise Iterative Refinement for Overdetermined
                 Least Squares Problems",
  journal =      j-TOMS,
  volume =       "35",
  number =       "4",
  pages =        "28:1--28:32",
  month =        feb,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1462173.1462177",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Feb 13 18:09:40 MST 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/lawn.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present the algorithm, error bounds, and numerical
                 results for extra-precise iterative refinement applied
                 to overdetermined linear least squares (LLS) problems.
                 We apply our linear system refinement algorithm to
                 Bj{\"o}rck's augmented linear system formulation of an
                 LLS problem. Our algorithm reduces the forward normwise
                 and componentwise errors to $ O(\epsilon_w) $, where $
                 \epsilon_w $ is the working precision, unless the
                 system is too ill conditioned. In contrast to linear
                 systems, we provide two separate error bounds for the
                 solution $x$ and the residual $r$. The refinement
                 algorithm requires only limited use of extra precision
                 and adds only $ O(m n)$ work to the $ O(m n^2)$ cost of
                 QR factorization for problems of size $ m \times n$.
                 The extra precision calculation is facilitated by the
                 new extended-precision BLAS standard in a portable way,
                 and the refinement algorithm will be included in a
                 future release of LAPACK and can be extended to the
                 other types of least squares problems.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "BLAS; floating-point arithmetic; LAPACK; Linear
                 algebra",
  remark =       "Journal publication of LAWN 188
                 \cite{Demmel:2007:EPI}.",
}

@Article{vandenBerg:2009:AST,
  author =       "Ewout van den Berg and Michael P. Friedlander and
                 Gilles Hennenfent and Felix J. Herrmann and Rayan Saab
                 and {\"O}zg{\"u}r Yilmaz",
  title =        "{Algorithm 890}: {Sparco}: a Testing Framework for
                 Sparse Reconstruction",
  journal =      j-TOMS,
  volume =       "35",
  number =       "4",
  pages =        "29:1--29:16",
  month =        feb,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1462173.1462178",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Feb 13 18:09:40 MST 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Sparco is a framework for testing and benchmarking
                 algorithms for sparse reconstruction. It includes a
                 large collection of sparse reconstruction problems
                 drawn from the imaging, compressed sensing, and
                 geophysics literature. Sparco is also a framework for
                 implementing new test problems and can be used as a
                 tool for reproducible research. Sparco is implemented
                 entirely in Matlab, and is released as open-source
                 software under the GNU Public License.",
  acknowledgement = ack-nhfb,
  articleno =    "29",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Compressed sensing; linear operators; sparse
                 recovery",
}

@Article{Mayer:2009:NEP,
  author =       "Jan Mayer",
  title =        "A numerical evaluation of preprocessing and {ILU}-type
                 preconditioners for the solution of unsymmetric sparse
                 linear systems using iterative methods",
  journal =      j-TOMS,
  volume =       "36",
  number =       "1",
  pages =        "1:1--1:26",
  month =        mar,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1486525.1486526",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 17 17:22:09 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Recent advances in multilevel LU factorizations and
                 novel preprocessing techniques have led to an extremely
                 large number of possibilities for preconditioning
                 sparse, unsymmetric linear systems for solving with
                 iterative methods. However, not all combinations work
                 well for all systems, so making the right choices is
                 essential for obtaining an efficient solver. The
                 numerical results for 256 matrices presented in this
                 article give an indication of which approaches are
                 suitable for which matrices (based on different
                 criteria, such as total computation time or fill-in)
                 and of the differences between the methods.",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Incomplete LU factorization; iterative methods;
                 preconditioning; sparse linear systems",
}

@Article{Lourakis:2009:SSP,
  author =       "Manolis I. A. Lourakis and Antonis A. Argyros",
  title =        "{SBA}: a software package for generic sparse bundle
                 adjustment",
  journal =      j-TOMS,
  volume =       "36",
  number =       "1",
  pages =        "2:1--2:30",
  month =        mar,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1486525.1486527",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 17 17:22:09 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Bundle adjustment constitutes a large, nonlinear
                 least-squares problem that is often solved as the last
                 step of feature-based structure and motion estimation
                 computer vision algorithms to obtain optimal estimates.
                 Due to the very large number of parameters involved, a
                 general purpose least-squares algorithm incurs high
                 computational and memory storage costs when applied to
                 bundle adjustment. Fortunately, the lack of interaction
                 among certain subgroups of parameters results in the
                 corresponding Jacobian being sparse, a fact that can be
                 exploited to achieve considerable computational
                 savings. This article presents sba, a publicly
                 available C/C++ software package for realizing generic
                 bundle adjustment with high efficiency and flexibility
                 regarding parameterization.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "bundle adjustment; engineering applications;
                 Levenberg--Marquardt; multiple-view geometry; nonlinear
                 least squares; sparse Jacobian; structure and motion
                 estimation; Unconstrained optimization",
}

@Article{DAlberto:2009:AWM,
  author =       "Paolo D'Alberto and Alexandru Nicolau",
  title =        "Adaptive {Winograd}'s matrix multiplications",
  journal =      j-TOMS,
  volume =       "36",
  number =       "1",
  pages =        "3:1--3:23",
  month =        mar,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1486525.1486528",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 17 17:22:09 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Modern architectures have complex memory hierarchies
                 and increasing parallelism (e.g., multicores). These
                 features make achieving and maintaining good
                 performance across rapidly changing architectures
                 increasingly difficult. Performance has become a
                 complex tradeoff, not just a simple matter of counting
                 cost of simple CPU operations.\par

                 We present a novel, hybrid, and adaptive recursive
                 Strassen-Winograd's matrix multiplication (MM) that
                 uses automatically tuned linear algebra software
                 (ATLAS) or GotoBLAS. Our algorithm applies to any size
                 and shape matrices stored in either row or column major
                 layout (in double precision in this work) and thus is
                 efficiently applicable to both C and FORTRAN
                 implementations. In addition, our algorithm divides the
                 computation into equivalent in-complexity sub-MMs and
                 does not require any extra computation to combine the
                 intermediary sub-MM results.\par

                 We achieve up to 22\% execution-time reduction versus
                 GotoBLAS/ATLAS alone for a single core system and up to
                 19\% for a two dual-core processor system. Most
                 importantly, even for small matrices such as $1500
                 \times 1500$, our approach attains already 10\%
                 execution-time reduction and, for MM of matrices larger
                 than $3000 \times 3000$, it delivers performance that
                 would correspond, for a classic $O(n^3)$ algorithm, to
                 faster-than-processor peak performance (i.e., our
                 algorithm delivers the equivalent of 5 GFLOPS
                 performance on a system with 4.4 GFLOPS peak
                 performance and where GotoBLAS achieves only 4 GFLOPS).
                 This is a result of the savings in operations (and thus
                 FLOPS). Therefore, our algorithm is faster than any
                 {\em classic\/} MM algorithms could ever be for
                 matrices of this size. Furthermore, we present
                 experimental evidence based on established
                 methodologies found in the literature that our
                 algorithm is, for a family of matrices, as accurate as
                 the classic algorithms.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "fast algorithms; Winograd's matrix multiplications",
}

@Article{Bangerth:2009:DSR,
  author =       "W. Bangerth and O. Kayser-Herold",
  title =        "Data structures and requirements for {\em hp\/} finite
                 element software",
  journal =      j-TOMS,
  volume =       "36",
  number =       "1",
  pages =        "4:1--4:31",
  month =        mar,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1486525.1486529",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 17 17:22:09 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Finite element methods approximate solutions of
                 partial differential equations by restricting the
                 problem to a finite dimensional function space. In {\em
                 hp\/} adaptive finite element methods, one defines
                 these discrete spaces by choosing different polynomial
                 degrees for the shape functions defined on a locally
                 refined mesh.\par

                 Although this basic idea is quite simple, its
                 implementation in algorithms and data structures is
                 challenging. It has apparently not been documented in
                 the literature in its most general form. Rather, most
                 existing implementations appear to be for special
                 combinations of finite elements, or for discontinuous
                 Galerkin methods.\par

                 In this article, we discuss generic data structures and
                 algorithms used in the implementation of {\em hp\/}
                 methods for arbitrary elements, and the complications
                 and pitfalls one encounters. As a consequence, we list
                 the information a description of a finite element has
                 to provide to the generic algorithms for it to be used
                 in an {\em hp\/} context. We support our claim that our
                 reference implementation is efficient using numerical
                 examples in two dimensions and three dimensions, and
                 demonstrate that the {\em hp\/} -specific parts of the
                 program do not dominate the total computing time. This
                 reference implementation is also made available as part
                 of the Open Source deal. II finite element library.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "data structures; finite element software; hp finite
                 element methods; Object orientation; software design",
}

@Article{Reid:2009:AFV,
  author =       "John K. Reid and Jennifer A. Scott",
  title =        "{Algorithm 891}: a {Fortran} virtual memory system",
  journal =      j-TOMS,
  volume =       "36",
  number =       "1",
  pages =        "5:1--5:12",
  month =        mar,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1486525.1486530",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 17 17:22:09 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Fortran\_Virtual\_Memory is a Fortran 95 package that
                 provides facilities for reading from and writing to
                 direct-access files. A buffer is used to avoid actual
                 input/output operations whenever possible. The data may
                 be spread over many files and for very large data sets
                 these may be held on more than one device. We describe
                 the design of Fortran\_Virtual\_Memory and comment on
                 its use within an out-of-core sparse direct solver.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "direct-access files; Fortran; out-of-core; Virtual
                 memory",
}

@Article{Jonasson:2009:ADF,
  author =       "Kristjan Jonasson",
  title =        "{Algorithm 892}: {DISPMODULE}, a {Fortran 95} module
                 for pretty-printing matrices",
  journal =      j-TOMS,
  volume =       "36",
  number =       "1",
  pages =        "6:1--6:7",
  month =        mar,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1486525.1486531",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 17 17:22:09 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A standard Fortran 95 module for printing scalars,
                 vectors, and matrices to external files is provided.
                 The module can display variables of default kind of all
                 intrinsic types (integer, real, complex, logical, and
                 character), and add-on modules are provided for data of
                 the nondefault kind. The main module is self-contained
                 and incorporating it only requires that it be compiled
                 and linked with a program containing a ``use
                 dispmodule'' statement. A generic interface and
                 optional parameters are used, so that the same
                 subroutine name, DISP, is used to display items of
                 different data type and rank, irrespective of display
                 options. The subroutine is quite versatile, and
                 hopefully can improve Fortran's competitiveness against
                 other array programming languages. The module also
                 contains a function TOSTRING to convert numerical
                 scalars and vectors to strings.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "array programming language; Fortran 95; matrix
                 pretty-printing; matrix printing; output utilities",
}

@Article{Renka:2009:ATT,
  author =       "Robert J. Renka",
  title =        "{Algorithm 893}: {TSPACK}: tension spline package for
                 curve design and data fitting",
  journal =      j-TOMS,
  volume =       "36",
  number =       "1",
  pages =        "7:1--7:8",
  month =        mar,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1486525.1486532",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 17 17:22:09 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "TSPACK is a curve-fitting package based on exponential
                 tension splines with automatic selection of tension
                 factors. It serves both as a method for data fitting
                 with preservation of shape properties or more general
                 constraints, and as a means of computer aided geometric
                 design of curves in two or three dimensions. The
                 package is based on a translation of Algorithm 716 from
                 Fortran 77 into MATLAB. The translation includes bug
                 corrections, vectorization where possible, and
                 extensions, including a B-spline representation,
                 designed to facilitate curve design as opposed to data
                 fitting. An interactive graphical user interface, not
                 part of the algorithm, is available from the author.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Convexity preserving; cubic spline; exponential
                 spline; interpolation; monotonicity preserving;
                 parametric curve; piecewise polynomial; shape
                 preserving; smoothing; spline under tension; tension
                 factor",
}

@Article{Padula:2009:SFA,
  author =       "Anthony D. Padula and Shannon D. Scott and William W.
                 Symes",
  title =        "A software framework for abstract expression of
                 coordinate-free linear algebra and optimization
                 algorithms",
  journal =      j-TOMS,
  volume =       "36",
  number =       "2",
  pages =        "8:1--8:36",
  month =        mar,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1499096.1499097",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Apr 3 17:44:12 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The Rice Vector Library is a collection of C++ classes
                 expressing core concepts (vector, function,\ldots{}) of
                 calculus in Hilbert space with minimal implementation
                 dependence, and providing standardized interfaces
                 behind which to hide application-dependent
                 implementation details (data containers, function
                 objects). A variety of coordinate-free algorithms from
                 linear algebra and optimization, including Krylov
                 subspace methods and various relatives of Newton's
                 method for nonlinear equations and constrained and
                 unconstrained optimization, may be expressed purely in
                 terms of this system of classes. The resulting code may
                 be used {\em without alteration\/} in a wide range of
                 control, design, and parameter estimation applications,
                 in serial and parallel computing environments.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Abstract numerical algorithms; complex simulation;
                 numerical optimization",
}

@Article{Reid:2009:CSC,
  author =       "John K. Reid and Jennifer A. Scott",
  title =        "An out-of-core sparse {Cholesky} solver",
  journal =      j-TOMS,
  volume =       "36",
  number =       "2",
  pages =        "9:1--9:33",
  month =        mar,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1499096.1499098",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Apr 3 17:44:12 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Direct methods for solving large sparse linear systems
                 of equations are popular because of their generality
                 and robustness. Their main weakness is that the memory
                 they require usually increases rapidly with problem
                 size. We discuss the design and development of the
                 first release of a new symmetric direct solver that
                 aims to circumvent this limitation by allowing the
                 system matrix, intermediate data, and the matrix
                 factors to be stored externally. The code, which is
                 written in Fortran and called HSL\_MA77, implements a
                 multifrontal algorithm. The first release is for
                 positive-definite systems and performs a Cholesky
                 factorization. Special attention is paid to the use of
                 efficient dense linear algebra kernel codes that handle
                 the full-matrix operations on the frontal matrix and to
                 the input/output operations. The input/output
                 operations are performed using a separate package that
                 provides a virtual-memory system and allows the data to
                 be spread over many files; for very large problems
                 these may be held on more than one
                 device.\par

                 Numerical results are presented for a collection of 30
                 large real-world problems, all of which were solved
                 successfully.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Cholesky; multifrontal; out-of-core solver; sparse
                 symmetric linear systems",
}

@Article{Yang:2009:KMT,
  author =       "Chao Yang and Juan C. Meza and Byounghak Lee and
                 Lin-Wang Wang",
  title =        "{KSSOLV} --- a {MATLAB} toolbox for solving the
                 {Kohn--Sham} equations",
  journal =      j-TOMS,
  volume =       "36",
  number =       "2",
  pages =        "10:1--10:35",
  month =        mar,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1499096.1499099",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Apr 3 17:44:12 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe the design and implementation of KSSOLV, a
                 MATLAB toolbox for solving a class of nonlinear
                 eigenvalue problems known as the {\em Kohn--Sham
                 equations}. These types of problems arise in electronic
                 structure calculations, which are nowadays essential
                 for studying the microscopic quantum mechanical
                 properties of molecules, solids, and other nanoscale
                 materials. KSSOLV is well suited for developing new
                 algorithms for solving the Kohn--Sham equations and is
                 designed to enable researchers in computational and
                 applied mathematics to investigate the convergence
                 properties of the existing algorithms. The toolbox
                 makes use of the object-oriented programming features
                 available in MATLAB so that the process of setting up a
                 physical system is straightforward and the amount of
                 coding effort required to prototype, test, and compare
                 new algorithms is significantly reduced. All of these
                 features should also make this package attractive to
                 other computational scientists and students who wish to
                 study small- to medium-size systems.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "density functional theory (DFT); direct constrained
                 minimization (DCM); electronic structure calculation;
                 Kohn--Sham equations; nonlinear eigenvalue problem;
                 Planewave discretization; pseudopotential;
                 self-consistent field iteration (SCF)",
}

@Article{Gustavson:2009:DSC,
  author =       "Fred G. Gustavson and Lars Karlsson and Bo
                 K{\aa}gstr{\"o}m",
  title =        "Distributed {SBP Cholesky} factorization algorithms
                 with near-optimal scheduling",
  journal =      j-TOMS,
  volume =       "36",
  number =       "2",
  pages =        "11:1--11:25",
  month =        mar,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1499096.1499100",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Apr 3 17:44:12 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The minimal block storage Distributed Square Block
                 Packed (DSBP) format for distributed memory computing
                 on symmetric and triangular matrices is presented.
                 Three algorithm variants (Basic, Static, and Dynamic)
                 of the blocked right-looking Cholesky factorization are
                 designed for the DSBP format, implemented, and
                 evaluated. On our target machine, all variants
                 outperform standard full-storage implementations while
                 saving almost half the storage. Communication overhead
                 is shown to be virtually eliminated by the Static and
                 Dynamic variants, both of which take advantage of
                 hardware parallelism to hide communication costs. The
                 Basic variant is shown to yield comparable or slightly
                 better performance than the full-storage ScaLAPACK
                 routine PDPOTRF while clearly outperformed by both
                 Static and Dynamic. Models of execution assuming zero
                 communication costs and overhead are developed. For
                 medium- and larger-sized problems, the Static schedule
                 is near optimal on our target machine based on
                 comparisons with these models and measurements of
                 synchronization overhead.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Cholesky factorization; distributed square block
                 format; packed storage; parallel algorithms; parallel
                 computing; positive definite matrices; Real symmetric
                 matrices",
}

@Article{Koikari:2009:ABS,
  author =       "Souji Koikari",
  title =        "{Algorithm 894}: {On} a block {Schur--Parlett}
                 algorithm for $\varphi$-functions based on the
                 sep-inverse estimate",
  journal =      j-TOMS,
  volume =       "36",
  number =       "2",
  pages =        "12:1--12:20",
  month =        mar,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1499096.1499101",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Apr 3 17:44:12 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "FORTRAN 95 software is provided for computing the
                 matrix values of $\varphi$-functions required in
                 exponential integrators. The subroutines in the library
                 accept as their argument a full, diagonal, or upper
                 quasitriangular matrix with real or complex entries in
                 one of four precisions. Two different algorithms are
                 implemented, one is the scaling and squaring method,
                 and the other is a modified block Schur--Parlett
                 algorithm. In the latter algorithm, a recursive
                 three-by-three blocking is applied to the argument
                 based on an estimate of the sep-inverse function. The
                 estimation of the sep-inverse function is carried out
                 by Hager--Higham estimator implemented as the
                 subroutine xLACON in LAPACK. Our modifications to the
                 block Schur--Parlett algorithm are described together
                 with the results of numerical experiments.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "&phiv; -functions; block Schur--Parlett algorithm;
                 exponential integrators; matrix functions",
}

@Article{Baker:2009:ASN,
  author =       "C. G. Baker and U. L. Hetmaniuk and R. B. Lehoucq and
                 H. K. Thornquist",
  title =        "{Anasazi} software for the numerical solution of
                 large-scale eigenvalue problems",
  journal =      j-TOMS,
  volume =       "36",
  number =       "3",
  pages =        "13:1--13:23",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1527286.1527287",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Jul 21 14:09:07 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Anasazi is a package within the Trilinos software
                 project that provides a framework for the iterative,
                 numerical solution of large-scale eigenvalue problems.
                 Anasazi is written in ANSI C++ and exploits modern
                 software paradigms to enable the research and
                 development of eigensolver algorithms. Furthermore,
                 Anasazi provides implementations for some of the most
                 recent eigensolver methods. The purpose of our article
                 is to describe the design and development of the
                 Anasazi framework. A performance comparison of Anasazi
                 and the popular FORTRAN 77 code ARPACK is given.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Eigenvalue problems; generic programming; large-scale
                 scientific computing; numerical algorithms;
                 object-oriented programming",
}

@Article{Quintana-Orti:2009:PMA,
  author =       "Gregorio Quintana-Ort{\'\i} and Enrique S.
                 Quintana-Ort{\'\i} and Robert A. {Van De Geijn} and
                 Field G. {Van Zee} and Ernie Chan",
  title =        "Programming matrix algorithms-by-blocks for
                 thread-level parallelism",
  journal =      j-TOMS,
  volume =       "36",
  number =       "3",
  pages =        "14:1--14:26",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1527286.1527288",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Jul 21 14:09:07 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "With the emergence of thread-level parallelism as the
                 primary means for continued performance improvement,
                 the programmability issue has reemerged as an obstacle
                 to the use of architectural advances. We argue that
                 evolving legacy libraries for dense and banded linear
                 algebra is not a viable solution due to constraints
                 imposed by early design decisions. We propose a
                 philosophy of abstraction and separation of concerns
                 that provides a promising solution in this problem
                 domain. The first abstraction, FLASH, allows algorithms
                 to express computation with matrices consisting of
                 contiguous blocks, facilitating algorithms-by-blocks.
                 Operand descriptions are registered for a particular
                 operation a priori by the library implementor. A
                 runtime system, SuperMatrix, uses this information to
                 identify data dependencies between suboperations,
                 allowing them to be scheduled to threads out-of-order
                 and executed in parallel. But not all classical
                 algorithms in linear algebra lend themselves to
                 conversion to algorithms-by-blocks. We show how our
                 recently proposed LU factorization with incremental
                 pivoting and a closely related algorithm-by-blocks for
                 the QR factorization, both originally designed for
                 out-of-core computation, overcome this difficulty.
                 Anecdotal evidence regarding the development of
                 routines with a core functionality demonstrates how the
                 methodology supports high productivity while
                 experimental results suggest that high performance is
                 abundantly achievable.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "high-performance; libraries; Linear algebra;
                 multithreaded architectures",
}

@Article{Backeljauw:2009:ACF,
  author =       "Franky Backeljauw and Annie Cuyt",
  title =        "{Algorithm 895}: a continued fractions package for
                 special functions",
  journal =      j-TOMS,
  volume =       "36",
  number =       "3",
  pages =        "15:1--15:20",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1527286.1527289",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Jul 21 14:09:07 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The continued fractions for special functions package
                 (in the sequel abbreviated as CFSF package) complements
                 a systematic study of continued fraction
                 representations for special functions. It provides all
                 the functionality to create continued fractions, in
                 particular $k$-periodic or limit $k$-periodic
                 fractions, to compute approximants, make use of
                 continued fraction tails, perform equivalence
                 transformations and contractions, and much more. The
                 package, developed in Maple, includes a library of more
                 than 200 representations of special functions, of which
                 only 10\% can be found in the 1964 NBS {\em Handbook of
                 Mathematical Functions with Formulas, Graphs and
                 Mathematical Tables\/} by M. Abramowitz and I.
                 Stegun.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "CAS software; continued fractions; Maple; special
                 functions",
}

@Article{Luksan:2009:ALA,
  author =       "Ladislav Luk{\v{s}}an and Ctirad Matonoha and Jan
                 Vl{\v{c}}ek",
  title =        "{Algorithm 896}: {LSA}: {Algorithms} for large-scale
                 optimization",
  journal =      j-TOMS,
  volume =       "36",
  number =       "3",
  pages =        "16:1--16:29",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1527286.1527290",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Jul 21 14:09:07 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present 14 basic Fortran subroutines for
                 large-scale unconstrained and box constrained
                 optimization and large-scale systems of nonlinear
                 equations. Subroutines PLIS and PLIP, intended for
                 dense general optimization problems, are based on
                 limited-memory variable metric methods. Subroutine
                 PNET, also intended for dense general optimization
                 problems, is based on an inexact truncated Newton
                 method. Subroutines PNED and PNEC, intended for sparse
                 general optimization problems, are based on
                 modifications of the discrete Newton method.
                 Subroutines PSED and PSEC, intended for partially
                 separable optimization problems, are based on
                 partitioned variable metric updates. Subroutine PSEN,
                 intended for nonsmooth partially separable optimization
                 problems, is based on partitioned variable metric
                 updates and on an aggregation of subgradients.
                 Subroutines PGAD and PGAC, intended for sparse
                 nonlinear least-squares problems, are based on
                 modifications and corrections of the Gauss--Newton
                 method. Subroutine PMAX, intended for minimization of a
                 maximum value (minimax), is based on the primal
                 line-search interior-point method. Subroutine PSUM,
                 intended for minimization of a sum of absolute values,
                 is based on the primal trust-region interior-point
                 method. Subroutines PEQN and PEQL, intended for sparse
                 systems of nonlinear equations, are based on the
                 discrete Newton method and the inverse column-update
                 quasi-Newton method, respectively. Besides the
                 description of methods and codes, we propose
                 computational experiments which demonstrate the
                 efficiency of the proposed algorithms.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "discrete Newton methods; large-scale nonlinear least
                 squares; large-scale nonlinear minimax; large-scale
                 nonsmooth optimization; Large-scale optimization;
                 large-scale systems of nonlinear equations;
                 limited-memory methods; partially separable problems;
                 primal interior-point methods; quasi-Newton methods;
                 sparse problems",
}

@Article{He:2009:AVS,
  author =       "Jian He and Layne T. Watson and Masha Sosonkina",
  title =        "{Algorithm 897}: {VTDIRECT95}: {Serial} and parallel
                 codes for the global optimization algorithm direct",
  journal =      j-TOMS,
  volume =       "36",
  number =       "3",
  pages =        "17:1--17:24",
  month =        jul,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1527286.1527291",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Jul 21 14:09:07 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Sosonkina:2015:RAV}.",
  abstract =     "VTDIRECT95 is a Fortran 95 implementation of D. R.
                 Jones' deterministic global optimization algorithm
                 called {\em DIRECT}, which is widely used in
                 multidisciplinary engineering design, biological
                 science, and physical science applications. The package
                 includes both a serial code and a data-distributed
                 massively parallel code for different problem scales
                 and optimization (exploration vs. exploitation) goals.
                 Dynamic data structures are used to organize local
                 data, handle unpredictable memory requirements, reduce
                 the memory usage, and share the data across multiple
                 processors. The parallel code employs a multilevel
                 functional and data parallelism to boost concurrency
                 and mitigate the data dependency, thus improving the
                 load balancing and scalability. In addition,
                 checkpointing features are integrated into both
                 versions to provide fault tolerance and hot restarts.
                 Important algorithm modifications and design
                 considerations are discussed regarding data structures,
                 parallel schemes, error handling, and portability.
                 Using several benchmark functions and real-world
                 applications, the software is evaluated on different
                 systems in terms of optimization effectiveness, data
                 structure efficiency, parallel performance, and
                 checkpointing overhead. The package organization and
                 usage are also described in detail.",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "checkpointing; data structures; DIRECT; global
                 optimization; parallel schemes",
}

@Article{Ramachandran:2009:OOD,
  author =       "Prabhu Ramachandran and M. Ramakrishna",
  title =        "An Object-Oriented Design for Two-Dimensional Vortex
                 Particle Methods",
  journal =      j-TOMS,
  volume =       "36",
  number =       "4",
  pages =        "18:1--18:28",
  month =        aug,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1555386.1555387",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 31 15:04:00 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Vortex methods offer a grid-free alternative to
                 simulating incompressible, viscous, fluid flows. They
                 require the use of fairly sophisticated algorithms and
                 can be complicated to implement for general flows. This
                 article describes an object-oriented design used to
                 implement a vortex particle based flow solver in two
                 dimensions. We provide an overview of the various
                 abstractions that arose as a result of this design.
                 Several of the algorithms have common components that
                 may be abstracted and reused. We demonstrate how the
                 design allowed us to derive the traditional benefits of
                 OOD. In addition, we show how the design directly
                 suggested elegant generalizations of existing
                 algorithms. Finally, we show the benefits of using
                 software testing techniques and building a powerful
                 scripting layer for the library.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Keiner:2009:UNS,
  author =       "Jens Keiner and Stefan Kunis and Daniel Potts",
  title =        "Using {NFFT 3} --- a Software Library for Various
                 Nonequispaced {Fast Fourier Transforms}",
  journal =      j-TOMS,
  volume =       "36",
  number =       "4",
  pages =        "19:1--19:30",
  month =        aug,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1555386.1555388",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 31 15:04:00 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "NFFT 3 is a software library that implements the
                 nonequispaced fast Fourier transform (NFFT) and a
                 number of related algorithms, for example,
                 nonequispaced fast Fourier transforms on the sphere and
                 iterative schemes for inversion. This article provides
                 a survey on the mathematical concepts behind the NFFT
                 and its variants, as well as a general guideline for
                 using the library. Numerical examples for a number of
                 applications are given.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Martins:2009:POO,
  author =       "Joaquim R. R. A. Martins and Christopher Marriage and
                 Nathan Tedford",
  title =        "{pyMDO}: An Object-Oriented Framework for
                 Multidisciplinary Design Optimization",
  journal =      j-TOMS,
  volume =       "36",
  number =       "4",
  pages =        "20:1--20:25",
  month =        aug,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1555386.1555389",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 31 15:04:00 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present pyMDO, an object-oriented framework that
                 facilitates the usage and development of algorithms for
                 multidisciplinary optimization (MDO). The resulting
                 implementation of the MDO methods is efficient and
                 portable. The main advantage of the proposed framework
                 is that it is flexible, with a strong emphasis on
                 object-oriented classes and operator overloading, and
                 it is therefore useful for the rapid development and
                 evaluation of new MDO methods. The top layer interface
                 is programmed in Python and it allows for the layers
                 below the interface to be programmed in C, C++,
                 Fortran, and other languages. We describe an
                 implementation of pyMDO and demonstrate that we can
                 take advantage of object-oriented programming to obtain
                 intuitive, easy-to-read, and easy-to-develop codes that
                 are at the same time efficient. This allows developers
                 to focus on the new algorithms they are developing and
                 testing, rather than on implementation details.
                 Examples demonstrate the user interface and the
                 corresponding results show that the various MDO methods
                 yield the correct solutions.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Garcia-Alonso:2009:ANI,
  author =       "Fernando Garc{\'\i}a-Alonso and Jos{\'e} A. Reyes and
                 Jos{\'e} M. Ferr{\'a}ndiz and Jes{\'u}s Vigo-Aguiar",
  title =        "Accurate Numerical Integration of Perturbed
                 Oscillatory Systems in Two Frequencies",
  journal =      j-TOMS,
  volume =       "36",
  number =       "4",
  pages =        "21:1--21:34",
  month =        aug,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1555386.1555390",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 31 15:04:00 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Highly accurate long-term numerical integration of
                 nearly oscillatory systems of ordinary differential
                 equations (ODEs) is a common problem in astrodynamics.
                 Scheifele's algorithm is one of the excellent
                 integrators developed in the past years to take
                 advantage of special transformations of variables such
                 as the K-S set. It is based on using expansions in
                 series of the so-called G-functions, and generalizes
                 the Taylor series integrators but with the remarkable
                 property of integrating without truncation error
                 oscillations in one basic known frequency. A
                 generalization of Scheifele's method capable of
                 integrating exactly harmonic oscillations in two known
                 frequencies is developed here, after introducing a two
                 parametric family of analytical $\varphi$-functions.
                 Moreover, the local error contains the perturbation
                 parameter as a factor when the algorithm is applied to
                 perturbed problems. The good behavior and the long-term
                 accuracy of the new method are shown through several
                 examples, including systems with low- and
                 high-frequency constituents and a perturbed satellite
                 orbit. The new methods provide significantly higher
                 accuracy and efficiency than a selection of
                 well-reputed general-purpose integrators and even
                 recent symplectic or symmetric integrators, whose good
                 behavior in the long-term integration of the Kepler
                 problem and the other oscillatory systems is well
                 stated in recent literature.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Meerbergen:2009:CBE,
  author =       "Karl Meerbergen and Kresimir Fresl and Toon Knapen",
  title =        "{C++} Bindings to External Software Libraries with
                 Examples from {BLAS}, {LAPACK}, {UMFPACK}, and
                 {MUMPS}",
  journal =      j-TOMS,
  volume =       "36",
  number =       "4",
  pages =        "22:1--22:23",
  month =        aug,
  year =         "2009",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1555386.1555391",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Aug 31 15:04:00 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "FORTRAN and C software packages are often used in
                 generic C++ software. Calling nongeneric functions in
                 generic code is not straightforward. The bindings in
                 this article help the C++ programmer using external
                 software with a small effort. The bindings provide a
                 mechanism to keep external software interfaces and
                 specific vector and matrix containers orthogonal. We
                 show examples using BLAS, LAPACK, UMFPACK, and MUMPS
                 functions and subroutines.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Vomel:2010:SMA,
  author =       "Christof V{\"o}mel",
  title =        "{ScaLAPACK}'s {MRRR} algorithm",
  journal =      j-TOMS,
  volume =       "37",
  number =       "1",
  pages =        "1:1--1:35",
  month =        jan,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1644001.1644002",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Mar 15 10:45:33 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The (sequential) algorithm of Multiple Relatively
                 Robust Representations, MRRR, is a more efficient
                 variant of inverse iteration that does not require
                 reorthogonalization. It solves the eigenproblem of an
                 unreduced symmetric tridiagonal matrix $T \in R^{n
                 \times n}$ at $O(n^2)$ cost. The computed normalized
                 eigenvectors are numerically orthogonal in the sense
                 that the dot product between different vectors is $O(n
                 \epsilon)$, where $\epsilon$ refers to the relative
                 machine precision.\par

                 This article describes the design of ScaLAPACK's
                 parallel MRRR algorithm. One emphasis is on the
                 critical role of the representation tree in achieving
                 both adequate accuracy and parallel scalability. A
                 second point concerns the favorable properties of this
                 code: subset computation, the use of static memory, and
                 scalability.\par

                 Unlike ScaLAPACK's Divide \& Conquer and QR, MRRR can
                 compute subsets of eigenpairs at reduced cost. And in
                 contrast to inverse iterations which can fail, it is
                 guaranteed to produce a satisfactory answer while
                 maintaining memory scalability.\par

                 ParEig, the parallel MRRR algorithm for PLAPACK, uses
                 dynamic memory allocation. This is avoided by our code
                 at marginal additional cost. We also use a different
                 representation tree criterion that allows for more
                 accurate computation of the eigenvectors but can make
                 parallelization more difficult.",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "design; implementation; Multiple relatively robust
                 representations; numerical software; parallel
                 computation; ScaLAPACK; symmetric eigenvalue problem",
}

@Article{Daumas:2010:CBE,
  author =       "Marc Daumas and Guillaume Melquiond",
  title =        "Certification of bounds on expressions involving
                 rounded operators",
  journal =      j-TOMS,
  volume =       "37",
  number =       "1",
  pages =        "2:1--2:20",
  month =        jan,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1644001.1644003",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Mar 15 10:45:33 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Gappa is a tool designed to formally verify the
                 correctness of numerical software and hardware. It uses
                 interval arithmetic and forward error analysis to bound
                 mathematical expressions that involve rounded as well
                 as exact operators. It then generates a theorem and its
                 proof for each verified enclosure. This proof can be
                 automatically checked with a proof assistant, such as
                 Coq or HOL Light. It relies on a large companion
                 library of facts that we have developed. This Coq
                 library provides theorems dealing with addition,
                 multiplication, division, and square root, for both
                 fixed- and floating-point arithmetics. Gappa uses
                 multiple-precision dyadic fractions for the endpoints
                 of intervals and performs forward error analysis on
                 rounded operators when necessary. When asked, Gappa
                 reports the best bounds it is able to reach for a given
                 expression in a given context. This feature can be used
                 to identify where the set of facts and automatic
                 techniques implemented in Gappa becomes insufficient.
                 Gappa handles seamlessly additional properties
                 expressed as interval properties or rewriting rules in
                 order to establish more intricate bounds. Recent work
                 showed that Gappa is suited to discharge proof
                 obligations generated for small pieces of software.
                 They may be produced by third-party tools and the first
                 applications of Gappa use proof obligations written by
                 designers or obtained from traces of execution.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Coq; dyadic fraction; floating point; Forward error
                 analysis; HOL Light; interval arithmetic; proof
                 obligation; proof system; PVS",
}

@Article{Rouson:2010:DPM,
  author =       "Damian W. I. Rouson and Helgi Adalsteinsson and Jim
                 Xia",
  title =        "Design patterns for multiphysics modeling in {Fortran
                 2003} and {C++}",
  journal =      j-TOMS,
  volume =       "37",
  number =       "1",
  pages =        "3:1--3:30",
  month =        jan,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1644001.1644004",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Mar 15 10:45:33 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present three new object-oriented software design
                 patterns in Fortran 2003 and C++. These patterns
                 integrate coupled differential equations, facilitating
                 the flexible swapping of physical and numerical
                 software abstractions at compile-time and runtime. The
                 Semi-Discrete pattern supports the time advancement of
                 a dynamical system encapsulated in a single abstract
                 data type (ADT). The Puppeteer pattern combines ADTs
                 into a multiphysics package, mediates interabstraction
                 communications, and enables implicit marching even when
                 nonlinear terms couple separate ADTs with private data.
                 The Surrogate pattern emulates C++ forward references
                 in Fortran 2003. After code demonstrations using the
                 Lorenz equations, we provide architectural descriptions
                 of our use of the new patterns in extending the Rouson
                 et al. [2008a] Navier--Stokes solver to simulate
                 multiphysics phenomena. We also describe the
                 relationships between the new patterns and two
                 previously developed architectural elements: the
                 Strategy pattern of Gamma et al. [1995] and the
                 template emulation technique of Akin [2003]. This
                 report demonstrates how these patterns manage
                 complexity by providing logical separation between
                 individual physics models and the control logic that
                 bridges between them. Additionally, it shows how
                 language features such as operator overloading and
                 automated memory management enable a clear mathematical
                 notation for model bridging and system evolution.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Design patterns; Lorenz equations; multiphysics
                 modeling",
}

@Article{Kornerup:2010:CCR,
  author =       "Peter Kornerup and Christoph Lauter and Vincent
                 Lef{\`e}vre and Nicolas Louvet and Jean-Michel Muller",
  title =        "Computing correctly rounded integer powers in
                 floating-point arithmetic",
  journal =      j-TOMS,
  volume =       "37",
  number =       "1",
  pages =        "4:1--4:23",
  month =        jan,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1644001.1644005",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Mar 15 10:45:33 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We introduce several algorithms for accurately
                 evaluating powers to a positive integer in
                 floating-point arithmetic, assuming a {\em fused
                 multiply-add\/} (fma) instruction is available. For
                 bounded, yet very large values of the exponent, we aim
                 at obtaining correctly rounded results in
                 round-to-nearest mode, that is, our algorithms return
                 the floating-point number that is nearest the exact
                 value.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Correct rounding; floating-point arithmetic; integer
                 power function",
}

@Article{Kirby:2010:SFE,
  author =       "Robert C. Kirby",
  title =        "Singularity-free evaluation of collapsed-coordinate
                 orthogonal polynomials",
  journal =      j-TOMS,
  volume =       "37",
  number =       "1",
  pages =        "5:1--5:16",
  month =        jan,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1644001.1644006",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Mar 15 10:45:33 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The $L^2$ -orthogonal polynomials used in finite and
                 spectral element methods on nonrectangular elements may
                 be defined in terms of {\em collapsed\/} coordinates,
                 wherein the shapes are mapped to a square or cube by
                 means of a singular change of variables. The orthogonal
                 basis is a product of specific Jacobi polynomials in
                 these new coordinates. Implementations of these
                 polynomials require special handling of the coordinate
                 singularities. We derive new recurrence relations for
                 these polynomials on triangles and tetrahedra that work
                 directly in the original coordinates. These relations,
                 also applicable to pyramids and prisms, do not require
                 any special treatment of singular points. These
                 recurrences are seen to speed up both symbolic and
                 numerical computation of the orthogonal polynomials.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "nonrectangular domain; Orthogonal polynomial;
                 recurrence relation",
}

@Article{Alnaes:2010:ESC,
  author =       "Martin Sandve Aln{\ae}s and Kent-Andr{\'e} Mardal",
  title =        "On the efficiency of symbolic computations combined
                 with code generation for finite element methods",
  journal =      j-TOMS,
  volume =       "37",
  number =       "1",
  pages =        "6:1--6:26",
  month =        jan,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1644001.1644007",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Mar 15 10:45:33 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Efficient and easy implementation of variational forms
                 for finite element discretization can be accomplished
                 with metaprogramming. Using a high-level language like
                 Python and symbolic mathematics makes an abstract
                 problem definition possible, but the use of a low-level
                 compiled language is vital for run-time efficiency. By
                 generating low-level C++ code based on symbolic
                 expressions for the discrete weak form, it is possible
                 to accomplish a high degree of abstraction in the
                 problem definition while surpassing the run-time
                 efficiency of traditional hand written C++ codes. We
                 provide several examples where we demonstrate orders of
                 magnitude in speedup.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "automation; code generation; compiler; finite element;
                 metaprogramming; Variational forms",
}

@Article{Savage:2010:COA,
  author =       "John E. Savage and Mohammad Zubair",
  title =        "Cache-optimal algorithms for option pricing",
  journal =      j-TOMS,
  volume =       "37",
  number =       "1",
  pages =        "7:1--7:30",
  month =        jan,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1644001.1644008",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Mar 15 10:45:33 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Today computers have several levels of memory
                 hierarchy. To obtain good performance on these
                 processors it is necessary to design algorithms that
                 minimize I/O traffic to slower memories in the
                 hierarchy. In this article, we study the computation of
                 option pricing using the binomial and trinomial models
                 on processors with a multilevel memory hierarchy. We
                 derive lower bounds on memory traffic between different
                 levels of the hierarchy for these two models. We also
                 develop algorithms for the binomial and trinomial
                 models that have near-optimal memory traffic between
                 levels. We have implemented these algorithms on an
                 UltraSparc IIIi processor with a 4-level of memory
                 hierarchy and demonstrated that our algorithms
                 outperform algorithms without cache blocking by a
                 factor of up to 5 and operate at 70\% of peak
                 performance.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "cache blocking; Memory hierarchy",
}

@Article{Olgaard:2010:OQR,
  author =       "Kristian B. {\O}lgaard and Garth N. Wells",
  title =        "Optimizations for quadrature representations of finite
                 element tensors through automated code generation",
  journal =      j-TOMS,
  volume =       "37",
  number =       "1",
  pages =        "8:1--8:23",
  month =        jan,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1644001.1644009",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Mar 15 10:45:33 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We examine aspects of the computation of finite
                 element matrices and vectors that are made possible by
                 automated code generation. Given a variational form in
                 a syntax that resembles standard mathematical notation,
                 the low-level computer code for building finite element
                 tensors, typically matrices, vectors and scalars, can
                 be generated automatically via a form compiler. In
                 particular, the generation of code for computing finite
                 element matrices using a quadrature approach is
                 addressed. For quadrature representations, a number of
                 optimization strategies which are made possible by
                 automated code generation are presented. The relative
                 performance of two different automatically generated
                 representations of finite element matrices is examined,
                 with a particular emphasis on complicated variational
                 forms. It is shown that approaches which perform best
                 for simple forms are not tractable for more complicated
                 problems in terms of run-time performance, the time
                 required to generate the code or the size of the
                 generated code. The approach and optimizations
                 elaborated here are effective for a range of
                 variational forms.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "code generation; Finite element method",
}

@Article{Albrecht:2010:AEM,
  author =       "Martin Albrecht and Gregory Bard and William Hart",
  title =        "{Algorithm 898}: {Efficient} multiplication of dense
                 matrices over {GF(2)}",
  journal =      j-TOMS,
  volume =       "37",
  number =       "1",
  pages =        "9:1--9:14",
  month =        jan,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1644001.1644010",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Mar 15 10:45:33 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe an efficient implementation of a hierarchy
                 of algorithms for multiplication of dense matrices over
                 the field with two elements (F$_2$). In particular we
                 present our implementation --- in the M4RI library ---
                 of Strassen--Winograd matrix multiplication and the
                 ``Method of the Four Russians for Multiplication''
                 (M4RM) and compare it against other available
                 implementations. Good performance is demonstrated on
                 AMD's Opteron processor and particularly good
                 performance on Intel's Core 2 duo processor. The
                 open-source M4RI library is available as a stand-alone
                 package as well as part of the Sage mathematics
                 system.\par

                 In machine terms, addition in F$_2$ is logical-XOR, and
                 multiplication is logical-AND, thus a machine word of
                 64 bits allows one to operate on 64 elements of F$_2$
                 in parallel: at most one CPU cycle for 64 parallel
                 additions or multiplications. As such, element-wise
                 operations over F$_2$ are relatively cheap. In fact, in
                 this paper, we conclude that the actual bottlenecks are
                 memory reads and writes and issues of data locality. We
                 present our empirical findings in relation to
                 minimizing these and give an analysis thereof.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "GF(2); greasing; linear algebra; matrix;
                 multiplication; Strassen",
}

@Article{Sarra:2010:AMP,
  author =       "Scott A. Sarra",
  title =        "{Algorithm 899}: {The Matlab} postprocessing toolkit",
  journal =      j-TOMS,
  volume =       "37",
  number =       "1",
  pages =        "10:1--10:15",
  month =        jan,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1644001.1644011",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Mar 15 10:45:33 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Global polynomial approximation methods applied to
                 piecewise continuous functions exhibit the well-known
                 Gibbs phenomenon. We summarize known methods to remove
                 the Gibbs oscillations and present a collection of
                 Matlab programs that implement the methods. The
                 software features a Graphical User Interface that
                 allows easy access to the postprocessing algorithms for
                 benchmarking and educational purposes.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Gibbs phenomenon; Matlab; postprocessing;
                 Pseudospectral methods",
}

@Article{Torres:2010:ADT,
  author =       "Germ{\'a}n A. Torres",
  title =        "{Algorithm 900}: a discrete time {Kalman} filter
                 package for large scale problems",
  journal =      j-TOMS,
  volume =       "37",
  number =       "1",
  pages =        "11:1--11:16",
  month =        jan,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1644001.1644012",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Mar 15 10:45:33 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Data assimilation is the process of feeding a
                 partially unknown prediction model with available
                 information from observations, with the objective of
                 correcting and improving the modeled results. One of
                 the most important mathematical tools to perform data
                 assimilation is the Kalman filter. This is essentially
                 a predictor-corrector algorithm that is optimal in the
                 sense of minimizing the trace of the covariance matrix
                 of the errors. Unfortunately, the computational cost of
                 applying the filter to large scale problems is
                 enormous, and the programming of the filter is highly
                 dependent on the model and the format of the data
                 involved. The first objective of this article is to
                 present a set of Fortran 90 modules that implement the
                 reduced rank square root versions of the Kalman filter,
                 adapted for the assimilation of a very large number of
                 variables. The second objective is to present a Kalman
                 filter implementation whose code is independent of both
                 the model and observations and is easy to use. A
                 detailed description of the algorithms, structure,
                 parallelization is given along with examples of using
                 the package to solve practical problems.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "data assimilation; Kalman filter; Large scale
                 problems",
}

@Article{Vlachos:2010:ALP,
  author =       "D. S. Vlachos and T. E. Simos",
  title =        "{Algorithm 901}: {LMEF} --- a program for the
                 construction of linear multistep methods with
                 exponential fitting for the numerical solution of
                 ordinary differential equations",
  journal =      j-TOMS,
  volume =       "37",
  number =       "1",
  pages =        "12:1--12:10",
  month =        jan,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1644001.1644013",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Mar 15 10:45:33 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "LMEF is a program written in MATLAB, to calculate the
                 coefficients of a linear multi-step method (explicit,
                 implicit or backward differentiation formulas) with
                 algebraic and/or exponential fitting, for the numerical
                 solution of first order ordinary differential
                 equations. Moreover, LMEF calculates the local
                 truncation error and in the case of exponential
                 fitting, the Taylor expansions of the coefficients that
                 are necessary for the implementation of the method.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "backward differentiation formulas; exponential
                 fitting; Linear multistep methods",
}

@Article{Rasch:2010:EIE,
  author =       "Arno Rasch and H. Martin B{\"u}cker",
  title =        "{EFCOSS}: an interactive environment facilitating
                 optimal experimental design",
  journal =      j-TOMS,
  volume =       "37",
  number =       "2",
  pages =        "13:1--13:37",
  month =        apr,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1731022.1731023",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Apr 21 11:39:57 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "An interactive software environment is proposed that
                 combines numerical simulation codes with optimization
                 software packages in an automated and modular way. It
                 simplifies the experimentation with varying objective
                 functions for common optimization problems such as
                 parameter estimation and optimal experimental design
                 that are frequently encountered in computational
                 science and engineering. The design philosophy takes
                 into consideration the need for derivatives of
                 potentially large-scale simulation codes via automatic
                 differentiation as well as distributed computing in a
                 heterogeneous environment via CORBA.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "automatic differentiation; distributed computing;
                 optimal experimental design; parameter estimation;
                 Problem solving environments",
}

@Article{Chen:2010:ECF,
  author =       "Wei Chen and Gabor T. Herman",
  title =        "Efficient controls for finitely convergent sequential
                 algorithms",
  journal =      j-TOMS,
  volume =       "37",
  number =       "2",
  pages =        "14:1--14:23",
  month =        apr,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1731022.1731024",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Apr 21 11:39:57 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Finding a feasible point that satisfies a set of
                 constraints is a common task in scientific computing;
                 examples are the linear feasibility problem and the
                 convex feasibility problem. Finitely convergent
                 sequential algorithms can be used for solving such
                 problems; an example of such an algorithm is ART3,
                 which is defined in such a way that its control is
                 cyclic in the sense that during its execution it
                 repeatedly cycles through the given constraints.
                 Previously we found a variant of ART3 whose control is
                 no longer cyclic, but which is still finitely
                 convergent and in practice usually converges faster
                 than ART3. In this article we propose a general
                 methodology for automatic transformation of finitely
                 convergent sequential algorithms in such a way that (1)
                 finite convergence is retained, and (2) the speed of
                 convergence is improved. The first of these properties
                 is proven by mathematical theorems, the second is
                 illustrated by applying the algorithms to a practical
                 problem.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Algebraic reconstruction technique; cyclic subgradient
                 projections; feasibility problem; finite convergence;
                 sequential algorithm",
}

@Article{Krogh:2010:SSO,
  author =       "Fred T. Krogh",
  title =        "Stepsize selection for ordinary differential
                 equations",
  journal =      j-TOMS,
  volume =       "37",
  number =       "2",
  pages =        "15:1--15:21",
  month =        apr,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1731022.1731025",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Apr 21 11:39:57 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This note offers a new approach based on a least
                 squares fit to past data in order to select the
                 stepsize when solving an ordinary differential
                 equation. The approach used may have applicability to
                 other situations where one wants to repeatedly make
                 short term predictions given somewhat noisy data.
                 Additional ad hoc rules help significantly for
                 reliability and efficiency. Comparisons with some
                 Runge--Kutta codes, an Adams code, and an extrapolation
                 code are also included.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "ODE; prediction; stepsize",
}

@Article{Rutten:2010:EFP,
  author =       "Luc Rutten and Marko {Van Eekelen}",
  title =        "Efficient and formally proven reduction of large
                 integers by small moduli",
  journal =      j-TOMS,
  volume =       "37",
  number =       "2",
  pages =        "16:1--16:21",
  month =        apr,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1731022.1731026",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Apr 21 11:39:57 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "On $w$-bit processors which are much faster at
                 multiplying two $w$-bit integers than at dividing
                 $2w$-bit integers by $w$-bit integers, reductions of
                 large integers by moduli $M$ smaller than $2^{w-1}$ are
                 often implemented suboptimally, leading applications to
                 take excessive processing time.\par

                 We present a modular reduction algorithm implementing
                 division by a modulus through multiplication by a
                 reciprocal of that modulus, a well-known method for
                 moduli larger than $2^{w-1}$. We show that application
                 of this method to smaller moduli makes it possible to
                 express certain modular sums and differences without
                 having to compensate for word overflows.\par

                 By embedding the algorithm in a loop and applying a few
                 transformations to the loop, we obtain an algorithm for
                 reduction of large integers by moduli up to $2^{w -
                 1}$. Implementations of this algorithm can run
                 considerably faster than implementations of similar
                 algorithms that allow for moduli up to $2^w$. This is
                 substantiated by measurements on processors with
                 relatively fast multiplication instructions.\par

                 It is notoriously hard to specify efficient
                 mathematical algorithms on the level of abstract
                 machine instructions in an error-free manner. In order
                 to eliminate the chance of errors as much as possible,
                 we have created formal correctness proofs of our
                 algorithms, checked by a mechanized proof assistant.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Computer arithmetic; machine-checked proofs; modular
                 reduction; optimization",
}

@Article{Hogg:2010:FRM,
  author =       "J. D. Hogg and J. A. Scott",
  title =        "A fast and robust mixed-precision solver for the
                 solution of sparse symmetric linear systems",
  journal =      j-TOMS,
  volume =       "37",
  number =       "2",
  pages =        "17:1--17:24",
  month =        apr,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1731022.1731027",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Apr 21 11:39:57 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "On many current and emerging computing architectures,
                 single-precision calculations are at least twice as
                 fast as double-precision calculations. In addition, the
                 use of single precision may reduce pressure on memory
                 bandwidth. The penalty for using single precision for
                 the solution of linear systems is a potential loss of
                 accuracy in the computed solutions. For sparse linear
                 systems, the use of mixed precision in which
                 double-precision iterative methods are preconditioned
                 by a single-precision factorization can enable the
                 recovery of high-precision solutions more quickly and
                 use less memory than a sparse direct solver run using
                 double-precision arithmetic.\par

                 In this article, we consider the use of single
                 precision within direct solvers for sparse symmetric
                 linear systems, exploiting both the reduction in memory
                 requirements and the performance gains. We develop a
                 practical algorithm to apply a mixed-precision approach
                 and suggest parameters and techniques to minimize the
                 number of solves required by the iterative recovery
                 process. These experiments provide the basis for our
                 new code HSL\_MA79 --- a fast, robust, mixed-precision
                 sparse symmetric solver that is included in the
                 mathematical software library HSL.\par

                 Numerical results for a wide range of problems from
                 practical applications are presented.",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "FGMRES; Fortran 95; Gaussian elimination; iterative
                 refinement; mixed precision; multifrontal method;
                 sparse symmetric linear systems",
}

@Article{Gustavson:2010:RFP,
  author =       "Fred G. Gustavson and Jerzy Wa{\'s}niewski and Jack J.
                 Dongarra and Julien Langou",
  title =        "Rectangular full packed format for {Cholesky}'s
                 algorithm: factorization, solution, and inversion",
  journal =      j-TOMS,
  volume =       "37",
  number =       "2",
  pages =        "18:1--18:21",
  month =        apr,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1731022.1731028",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Apr 21 11:39:57 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe a new data format for storing triangular,
                 symmetric, and Hermitian matrices called {\em
                 Rectangular Full Packed Format\/} (RFPF). The standard
                 two-dimensional arrays of Fortran and C (also known as
                 {\em full format\/}) that are used to represent
                 triangular and symmetric matrices waste nearly half of
                 the storage space but provide high performance via the
                 use of Level 3 BLAS. Standard packed format arrays
                 fully utilize storage (array space) but provide low
                 performance as there is no Level 3 packed BLAS. We
                 combine the good features of packed and full storage
                 using RFPF to obtain high performance via using Level 3
                 BLAS as RFPF is a standard full-format representation.
                 Also, RFPF requires exactly the same minimal storage as
                 the packed format. Each LAPACK full and/or packed
                 triangular, symmetric, and Hermitian routine becomes a
                 single new RFPF routine based on eight possible data
                 layouts of RFPF. This new RFPF routine usually consists
                 of two calls to the corresponding LAPACK full-format
                 routine and two calls to Level 3 BLAS routines. This
                 means {\em no\/} new software is required. As examples,
                 we present LAPACK routines for Cholesky factorization,
                 Cholesky solution, and Cholesky inverse computation in
                 RFPF to illustrate this new work and to describe its
                 performance on several commonly used computer
                 platforms. Performance of LAPACK full routines using
                 RFPF versus LAPACK full routines using the standard
                 format for both serial and SMP parallel processing is
                 about the same while using half the storage.
                 Performance gains are roughly one to a factor of 43 for
                 serial and one to a factor of 97 for SMP parallel times
                 faster using vendor LAPACK full routines with RFPF than
                 with using vendor and/or reference packed routines.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "BLAS; Cholesky factorization and solution; complex
                 Hermitian matrices; LAPACK; linear algebra libraries;
                 novel packed matrix data structures; positive definite
                 matrices; Real symmetric matrices; Rectangular Full
                 Packed Format; recursive algorithms",
}

@Article{Scott:2010:SPC,
  author =       "Jennifer A. Scott",
  title =        "Scaling and pivoting in an out-of-core sparse direct
                 solver",
  journal =      j-TOMS,
  volume =       "37",
  number =       "2",
  pages =        "19:1--19:23",
  month =        apr,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1731022.1731029",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Apr 21 11:39:57 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Out-of-core sparse direct solvers reduce the amount of
                 main memory needed to factorize and solve large sparse
                 linear systems of equations by holding the matrix data,
                 the computed factors, and some of the work arrays in
                 files on disk. The efficiency of the factorization and
                 solution phases is dependent upon the number of entries
                 in the factors. For a given pivot sequence, the level
                 of fill in the factors beyond that predicted on the
                 basis of the sparsity pattern alone depends on the
                 number of pivots that are delayed (i.e., the number of
                 pivots that are used later than expected because of
                 numerical stability considerations). Our aim is to
                 limit the number of delayed pivots, while maintaining
                 robustness and accuracy. In this article, we consider a
                 new out-of-core multifrontal solver HSL\_MA78 from the
                 HSL mathematical software library that is designed to
                 solve the unsymmetric sparse linear systems that arise
                 from finite element applications. We consider how
                 equilibration can be built into the solver without
                 requiring the system matrix to be held in main memory.
                 We also examine the effects of different pivoting
                 strategies, including threshold partial pivoting,
                 threshold rook pivoting, and static pivoting. Numerical
                 experiments on problems arising from a range of
                 practical applications illustrate the importance of
                 scaling and show that, in some cases, rook pivoting can
                 be more efficient than partial pivoting in terms of
                 both the factorization time and the sparsity of the
                 computed factors.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "element problems; Large sparse unsymmetric linear
                 systems; multifrontal; out-of-core solver; partial
                 pivoting; rook pivoting; scaling",
}

@Article{Logg:2010:DAF,
  author =       "Anders Logg and Garth N. Wells",
  title =        "{DOLFIN}: {Automated} finite element computing",
  journal =      j-TOMS,
  volume =       "37",
  number =       "2",
  pages =        "20:1--20:28",
  month =        apr,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1731022.1731030",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Apr 21 11:39:57 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe here a library aimed at automating the
                 solution of partial differential equations using the
                 finite element method. By employing novel techniques
                 for automated code generation, the library combines a
                 high level of expressiveness with efficient
                 computation. Finite element variational forms may be
                 expressed in near mathematical notation, from which
                 low-level code is automatically generated, compiled,
                 and seamlessly integrated with efficient
                 implementations of computational meshes and
                 high-performance linear algebra. Easy-to-use
                 object-oriented interfaces to the library are provided
                 in the form of a C++ library and a Python module. This
                 article discusses the mathematical abstractions and
                 methods used in the design of the library and its
                 implementation. A number of examples are presented to
                 demonstrate the use of the library in application
                 code.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "code generation; DOLFIN; FEniCS project; form
                 compiler",
}

@Article{Stathopoulos:2010:PPI,
  author =       "Andreas Stathopoulos and James R. McCombs",
  title =        "{PRIMME}: preconditioned iterative multimethod
                 eigensolver --- methods and software description",
  journal =      j-TOMS,
  volume =       "37",
  number =       "2",
  pages =        "21:1--21:30",
  month =        apr,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1731022.1731031",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Apr 21 11:39:57 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article describes the PRIMME software package for
                 solving large, sparse Hermitian standard eigenvalue
                 problems. The difficulty and importance of these
                 problems have increased over the years, necessitating
                 the use of preconditioning and near optimally
                 converging iterative methods. However, the complexity
                 of tuning or even using such methods has kept them
                 outside the reach of many users. Responding to this
                 problem, we have developed PRIMME, a comprehensive
                 package that brings state-of-the-art methods from
                 ``bleeding edge'' to production, with the best possible
                 robustness, efficiency, and a flexible, yet highly
                 usable interface that requires minimal or no tuning. We
                 describe (1) the PRIMME multimethod framework that
                 implements a variety of algorithms, including the near
                 optimal methods GD+$k$ and JDQMR; (2) a host of
                 algorithmic innovations and implementation techniques
                 that endow the software with its robustness and
                 efficiency; (3) a multilayer interface that captures
                 our experience and addresses the needs of both expert
                 and end users.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "block; conjugate gradient; Davidson; eigenvalues;
                 eigenvectors; Hermitian; iterative; Jacobi--Davidson;
                 Lanczos; locking; preconditioning; software package",
}

@Article{Rao:2010:AGM,
  author =       "Anil V. Rao and David A. Benson and Christopher Darby
                 and Michael A. Patterson and Camila Francolin and
                 Ilyssa Sanders and Geoffrey T. Huntington",
  title =        "{Algorithm 902}: {GPOPS}, a {MATLAB} software [sic]
                 for solving multiple-phase optimal control problems
                 using the {Gauss} pseudospectral method",
  journal =      j-TOMS,
  volume =       "37",
  number =       "2",
  pages =        "22:1--22:39",
  month =        apr,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1731022.1731032",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Apr 21 11:39:57 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See corrigendum \cite{Rao:2011:CAG}.",
  abstract =     "An algorithm is described to solve multiple-phase
                 optimal control problems using a recently developed
                 numerical method called the {\em Gauss pseudospectral
                 method}. The algorithm is well suited for use in modern
                 vectorized programming languages such as FORTRAN 95 and
                 MATLAB. The algorithm discretizes the cost functional
                 and the differential-algebraic equations in each phase
                 of the optimal control problem. The phases are then
                 connected using linkage conditions on the state and
                 time. A large-scale nonlinear programming problem (NLP)
                 arises from the discretization and the significant
                 features of the NLP are described in detail. A
                 particular reusable MATLAB implementation of the
                 algorithm, called {\em GPOPS}, is applied to three
                 classical optimal control problems to demonstrate its
                 utility. The algorithm described in this article will
                 provide researchers and engineers a useful software
                 tool and a reference when it is desired to implement
                 the Gauss pseudospectral method in other programming
                 languages.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "computational methods; Dynamic optimization; nonlinear
                 optimization; nonlinear programming; optimal control;
                 phases",
}

@Article{Celledoni:2010:AFF,
  author =       "Elena Celledoni and Antonella Zanna",
  title =        "{Algorithm 903}: {FRB} --- {Fortran} routines for the
                 exact computation of free rigid body motions",
  journal =      j-TOMS,
  volume =       "37",
  number =       "2",
  pages =        "23:1--23:24",
  month =        apr,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1731022.1731033",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Apr 21 11:39:57 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present two algorithms and their corresponding
                 Fortran routines for the exact computation of free
                 rigid body motions. The methods use the same
                 description of the angular momentum part $m$ by Jacobi
                 elliptic functions, and suitably chosen frames for the
                 attitude matrix\slash quaternion $ Q / q $,
                 respectively. The frame transformation requires the
                 computation of elliptic integrals of the third kind.
                 Implementation and usage of the routines are described,
                 and some examples of drivers are included. Accuracy and
                 performance are also tested to provide reliable
                 numerical results.",
  acknowledgement = ack-nhfb,
  articleno =    "23",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "attitude rotation; Jacobi elliptic integrals;
                 numerical methods; Rigid body; splitting methods",
}

@Article{Haggard:2010:CTP,
  author =       "Gary Haggard and David J. Pearce and Gordon Royle",
  title =        "Computing {Tutte} Polynomials",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "24:1--24:17",
  month =        sep,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1824802",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The Tutte polynomial of a graph, also known as the
                 partition function of the $q$-state Potts model is a
                 2-variable polynomial graph invariant of considerable
                 importance in both combinatorics and statistical
                 physics. It contains several other polynomial
                 invariants, such as the chromatic polynomial and flow
                 polynomial as partial evaluations, and various
                 numerical invariants such as the number of spanning
                 trees as complete evaluations. However despite its
                 ubiquity, there are no widely available effective
                 computational tools able to compute the Tutte
                 polynomial of a general graph of reasonable size. In
                 this article we describe the implementation of a
                 program that exploits isomorphisms in the computation
                 tree to extend the range of graphs for which it is
                 feasible to compute their Tutte polynomials, and we
                 demonstrate the utility of the program by finding
                 counterexamples to a conjecture of Welsh on the
                 location of the real flow roots of a graph.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Chromatic polynomial; flow polynomial; graph
                 polynomial; graph theory; Tutte polynomial",
}

@Article{Gonzalez-Pinto:2010:CBT,
  author =       "Severiano Gonz{\'a}lez-Pinto and Rogel Rojas-Bello",
  title =        "A Code Based on the Two-Stage {Runge--Kutta Gauss}
                 Formula for Second-Order Initial Value Problems",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "25:1--25:30",
  month =        sep,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1824803",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A code based on the two-stage Gauss formula (order
                 four) for second-order initial value problems of a
                 special type is developed. This code can be used to
                 obtain a low- to medium-precision integration for a
                 wide range of problems in the class of oscillatory
                 type, Hamiltonian problems, and time-dependent partial
                 differential equations discretized in space by finite
                 differences or finite elements. The iteration process
                 used in solving for the stage values of the Gauss
                 formula, the selection of the initial step size, and
                 the choice of an appropriate local error estimator for
                 determining the step size change according to a
                 particular tolerance specified by the user are studied.
                 Moreover, a global error estimate and a dense output at
                 equidistant points in the integration interval are
                 supplied with the code. Numerical experiments and some
                 comparisons with certain standard codes on relevant
                 test problems are also given.",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "implicit Runge--Kutta Nystr{\"o} initial step size;
                 local error estimators; m methods; predictors;
                 Second-order problems; stage values",
}

@Article{Gonnet:2010:IRA,
  author =       "Pedro Gonnet",
  title =        "Increasing the Reliability of Adaptive Quadrature
                 Using Explicit Interpolants",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "26:1--26:32",
  month =        sep,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1824804",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present two new adaptive quadrature routines. Both
                 routines differ from previously published algorithms in
                 many aspects, most significantly in how they represent
                 the integrand, how they treat nonnumerical values of
                 the integrand, how they deal with improper divergent
                 integrals, and how they estimate the integration error.
                 The main focus of these improvements is to increase the
                 {\em reliability\/} of the algorithms without
                 significantly impacting their {\em efficiency}. Both
                 algorithms are implemented in MATLAB and tested using
                 both the ``families'' suggested by Lyness and Kaganove
                 and the battery test used by Gander and Gautschi and
                 Kahaner. They are shown to be more reliable, albeit in
                 some cases less efficient, than other commonly-used
                 adaptive integrators.",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Adaptive quadrature; error estimation; interpolation;
                 orthogonal polynomials",
}

@Article{Yamazaki:2010:APS,
  author =       "Ichitaro Yamazaki and Zhaojun Bai and Horst Simon and
                 Lin-Wang Wang and Kesheng Wu",
  title =        "Adaptive Projection Subspace Dimension for the
                 Thick-Restart {Lanczos} Method",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "27:1--27:18",
  month =        sep,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1824805",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The Thick-Restart Lanczos (TRLan) method is an
                 effective method for solving large-scale Hermitian
                 eigenvalue problems. The performance of the method
                 strongly depends on the dimension of the projection
                 subspace used at each restart. In this article, we
                 propose an objective function to quantify the
                 effectiveness of the selection of subspace dimension,
                 and then introduce an adaptive scheme to dynamically
                 select the dimension to optimize the performance. We
                 have developed an open-source software package
                 $a$-TRLan to include this adaptive scheme in the TRLan
                 method. When applied to calculate the electronic
                 structure of quantum dots, $a$-TRLan runs up to 2.3x
                 faster than a state-of-the-art preconditioned conjugate
                 gradient eigensolver.",
  acknowledgement = ack-nhfb,
  articleno =    "27",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Adaptive subspace dimension; electronic structure
                 calculation; Lanczos; thick-restart",
}

@Article{Anand:2010:UTE,
  author =       "Christopher Kumar Anand and Anuroop Sharma",
  title =        "Unified Tables for Exponential and Logarithm
                 Families",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "28:1--28:23",
  month =        sep,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1824806",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Accurate table methods allow for very accurate and
                 efficient evaluation of elementary functions. We
                 present new single-table approaches to logarithm and
                 exponential evaluation, by which we mean that a single
                 table of values works for both $\log(x)$ and $log(1 +
                 x)$, and a single table for $e^x$ and $e^x - 1$. This
                 approach eliminates special cases normally required to
                 evaluate $\log(1 + x)$ and $e^x - 1$ accurately near
                 zero, which will significantly improve performance on
                 architectures which use SIMD parallelism, or on which
                 data-dependent branching is expensive.\par

                 We have implemented it on the Cell/B.E. SPU (SIMD
                 compute engine) and found the resulting functions to be
                 up to twice as fast as the conventional implementations
                 distributed in the IBM Mathematical Acceleration
                 Subsystem (MASS). We include the literate code used to
                 generate all the variants of exponential and log
                 functions in the article, and discuss relevant language
                 and hardware features.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Accurate tables method; Cell/B.E; IEEE arithmetic;
                 SIMD; vector library",
}

@Article{Ollivier-Gooch:2010:IDS,
  author =       "Carl Ollivier-Gooch and Lori Diachin and Mark S.
                 Shephard and Timothy Tautges and Jason Kraftcheck and
                 Vitus Leung and Xiaojuan Luo and Mark Miller",
  title =        "An Interoperable, Data-Structure-Neutral Component for
                 Mesh Query and Manipulation",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "29:1--29:28",
  month =        sep,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1864430",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Much of the effort required to create a new simulation
                 code goes into developing infrastructure for mesh data
                 manipulation, adaptive refinement, design optimization,
                 and so forth. This infrastructure is an obvious target
                 for code reuse, except that implementations of these
                 functionalities are typically tied to specific data
                 structures. In this article, we describe a software
                 component---an abstract data model and programming
                 interface---designed to provide low-level mesh query
                 and manipulation support for meshing and solution
                 algorithms. The component's data model provides a data
                 abstraction, completely hiding all details of how mesh
                 data is stored, while its interface defines how
                 applications can interact with that data. Because the
                 component has been carefully designed to be general
                 purpose and efficient, it provides a practical platform
                 for implementing high-level mesh operations
                 independently of the underlying mesh data structures.
                 After describing the data model and interface, we
                 provide several usage examples, each of which has been
                 used successfully with multiple implementations of the
                 interface functionality. The overhead due to accessing
                 mesh data through the interface rather than directly
                 accessing the underlying mesh data is shown to be
                 acceptably small.",
  acknowledgement = ack-nhfb,
  articleno =    "29",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Data structure independence; mesh modification;
                 mesh-based simulations; software components",
}

@Article{DAmbra:2010:MPP,
  author =       "Pasqua D'Ambra and Daniela {Di Serafino} and Salvatore
                 Filippone",
  title =        "{MLD2P4}: a Package of Parallel Algebraic Multilevel
                 Domain Decomposition Preconditioners in {Fortran 95}",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "30:1--30:23",
  month =        sep,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1824808",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/domain-decomp.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Domain decomposition ideas have long been an essential
                 tool for the solution of PDEs on parallel computers. In
                 recent years many research efforts have been focused on
                 recursively employing domain decomposition methods to
                 obtain multilevel preconditioners to be used with
                 Krylov solvers. In this context, we developed MLD2P4
                 (MultiLevel Domain Decomposition Parallel
                 Preconditioners Package based on PSBLAS), a package of
                 parallel multilevel preconditioners that combines
                 additive Schwarz domain decomposition methods with a
                 smoothed aggregation technique to build a hierarchy of
                 coarse-level corrections in an algebraic way. The
                 design of MLD2P4 was guided by objectives such as
                 extensibility, flexibility, performance, portability,
                 and ease of use. They were achieved by following an
                 object-based approach while using the Fortran 95
                 language, as well as by employing the PSBLAS library as
                 a basic framework. In this article, we present MLD2P4
                 focusing on its design principles, software
                 architecture, and use.",
  acknowledgement = ack-nhfb,
  articleno =    "30",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algebraic multilevel; domain decomposition;
                 Mathematics of computing; object-based design; parallel
                 preconditioners",
}

@Article{Wendykier:2010:PCH,
  author =       "Piotr Wendykier and James G. Nagy",
  title =        "{Parallel Colt}: a High-Performance {Java} Library for
                 Scientific Computing and Image Processing",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "31:1--31:22",
  month =        sep,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1824809",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Major breakthroughs in chip and software design have
                 been observed for the last nine years. In October 2001,
                 IBM released the world's first multicore processor:
                 POWER4. Six years later, in February 2007, NVIDIA made
                 a public release of CUDA SDK, a set of development
                 tools to write algorithms for execution on Graphic
                 Processing Units (GPUs). Although software vendors have
                 started working on parallelizing their products, the
                 vast majority of existing code is still sequential and
                 does not effectively utilize modern multicore CPUs and
                 manycore GPUs.\par

                 This article describes Parallel Colt, a multithreaded
                 Java library for scientific computing and image
                 processing. In addition to describing the design and
                 functionality of Parallel Colt, a comparison to MATLAB
                 is presented. Two ImageJ plugins for iterative image
                 deblurring and motion correction of PET brain images
                 are described as typical applications of this library.
                 Performance comparisons with MATLAB, including GPU
                 computations via AccelerEyes' Jacket toolbox are also
                 given.",
  acknowledgement = ack-nhfb,
  articleno =    "31",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Deconvolution; FFT; inverse problems; iterative
                 methods; motion correction; multithreading; PET;
                 regularization",
}

@Article{Granat:2010:PSS,
  author =       "Robert Granat and Bo Kagstrom",
  title =        "Parallel Solvers for {Sylvester}-Type Matrix Equations
                 with Applications in Condition Estimation, {Part I}:
                 Theory and Algorithms",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "32:1--32:32",
  month =        sep,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1824810",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Parallel ScaLAPACK-style algorithms for solving eight
                 common standard and generalized Sylvester-type matrix
                 equations and various sign and transposed variants are
                 presented. All algorithms are blocked variants based on
                 the Bartels--Stewart method and involve four major
                 steps: reduction to triangular form, updating the
                 right-hand side with respect to the reduction,
                 computing the solution to the reduced triangular
                 problem, and transforming the solution back to the
                 original coordinate system. Novel parallel algorithms
                 for solving reduced triangular matrix equations based
                 on wavefront-like traversal of the right-hand side
                 matrices are presented together with a generic
                 scalability analysis. These algorithms are used in
                 condition estimation and new robust parallel sep$^{ -
                 1}$ -estimators are developed. Experimental results
                 from three parallel platforms, including results from a
                 mixed OpenMP/MPI platform, are presented and analyzed
                 using several performance and accuracy metrics. The
                 analysis includes results regarding general and
                 triangular parallel solvers as well as parallel
                 condition estimators.",
  acknowledgement = ack-nhfb,
  articleno =    "32",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "condition estimation; Eigenvalue problems; library
                 software; Sylvester matrix equations",
}

@Article{Granat:2010:ASL,
  author =       "Robert Granat and Bo K{\aa}gstr{\"o}m",
  title =        "{Algorithm 904}: {The SCASY Library} -- Parallel
                 Solvers for {Sylvester}-Type Matrix Equations with
                 Applications in Condition Estimation, {Part II}",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "33:1--33:4",
  month =        sep,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1824811",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We continue our presentation of parallel
                 ScaLAPACK-style algorithms for solving Sylvester-type
                 matrix equations. In Part II, we present SCASY
                 (SCAlable SYlvester solvers), a state-of-the-art HPC
                 software library for solving 44 sign and transpose
                 variants of eight common standard and generalized
                 Sylvester-type matrix equations.",
  acknowledgement = ack-nhfb,
  articleno =    "33",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "condition estimation; Eigenvalue problems; parallel
                 algorithms; Parallel computing; Sylvester matrix
                 equations",
}

@Article{Thacker:2010:AMS,
  author =       "William I. Thacker and Jingwei Zhang and Laynet Watson
                 and Jeffrey B. Birch and Manjula A. Iyer and Michael W.
                 Berry",
  title =        "{Algorithm 905}: Modified {Shepard} Algorithm for
                 Interpolation of Scattered Multivariate Data",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "34:1--34:20",
  month =        sep,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1824812",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Scattered data interpolation problems arise in many
                 applications. Shepard's method for constructing a
                 global interpolant by blending local interpolants using
                 local-support weight functions usually creates
                 reasonable approximations. SHEPPACK is a Fortran 95
                 package containing five versions of the modified
                 Shepard algorithm: quadratic (Fortran 95 translations
                 of Algorithms 660, 661, and 798), cubic (Fortran 95
                 translation of Algorithm 791), and linear variations of
                 the original Shepard algorithm. An option to the linear
                 Shepard code is a statistically robust fit, intended to
                 be used when the data is known to contain outliers.
                 SHEPPACK also includes a hybrid robust piecewise linear
                 estimation algorithm RIPPLE (residual initiated
                 polynomial-time piecewise linear estimation) intended
                 for data from piecewise linear functions in arbitrary
                 dimension $m$. The main goal of SHEPPACK is to provide
                 users with a single consistent package containing most
                 existing polynomial variations of Shepard's algorithm.
                 The algorithms target data of different dimensions. The
                 linear Shepard algorithm, robust linear Shepard
                 algorithm, and RIPPLE are the only algorithms in the
                 package that are applicable to arbitrary dimensional
                 data.",
  acknowledgement = ack-nhfb,
  articleno =    "34",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "M-estimation; RIPPLE; Shepard's algorithm",
}

@Article{Li:2010:AET,
  author =       "Tiancheng Li and Ian Robinson",
  title =        "{Algorithm 906}: {{\em elrint3d}} --- a
                 Three-Dimensional Nonadaptive Automatic Cubature
                 Routine Using a Sequence of Embedded Lattice Rules",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "35:1--35:17",
  month =        sep,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1824813",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A three-dimensional automatic cubature routine, called
                 {\em elrint3d}, is described and numerical results are
                 presented that demonstrate its applicability across a
                 wide range of domains and integrand types. The
                 underlying algorithm is based on a $2 s$-copy lattice
                 augmentation sequence, the seed lattice for which has
                 been determined by exhaustive search based on
                 optimization of index of merit and trigonometric degree
                 of precision.",
  acknowledgement = ack-nhfb,
  articleno =    "35",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "2s-copy lattice augmentation sequence; Automatic
                 cubature routine; index of merit; seed lattice;
                 trigonometric degree of precision",
}

@Article{Davis:2010:AKD,
  author =       "Timothy A. Davis and Ekanathan Palamadai Natarajan",
  title =        "{Algorithm 907}: {KLU}, a Direct Sparse Solver for
                 Circuit Simulation Problems",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "36:1--36:17",
  month =        sep,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1824814",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "KLU is a software package for solving sparse
                 unsymmetric linear systems of equations that arise in
                 circuit simulation applications. It relies on a
                 permutation to Block Triangular Form (BTF), several
                 methods for finding a fill-reducing ordering (variants
                 of approximate minimum degree and nested dissection),
                 and Gilbert/Peierls' sparse left-looking LU
                 factorization algorithm to factorize each block. The
                 package is written in C and includes a MATLAB
                 interface. Performance results comparing KLU with
                 SuperLU, Sparse 1.3, and UMFPACK on circuit simulation
                 matrices are presented. KLU is the default sparse
                 direct solver in the Xyce$^{TM}$ circuit simulation
                 package developed by Sandia National Laboratories.",
  acknowledgement = ack-nhfb,
  articleno =    "36",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "circuit simulation; LU factorization; sparse
                 matrices",
}

@Article{Zhu:2010:AOE,
  author =       "Yong-Kang Zhu and Wayne B. Hayes",
  title =        "{Algorithm 908}: Online Exact Summation of
                 Floating-Point Streams",
  journal =      j-TOMS,
  volume =       "37",
  number =       "3",
  pages =        "37:1--37:13",
  month =        sep,
  year =         "2010",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1824801.1824815",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 27 10:15:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a novel, online algorithm for exact
                 summation of a stream of floating-point numbers. By
                 ``online'' we mean that the algorithm needs to see only
                 one input at a time, and can take an arbitrary length
                 input stream of such inputs while requiring only
                 constant memory. By ``exact'' we mean that the sum of
                 the internal array of our algorithm is exactly equal to
                 the sum of all the inputs, and the returned result is
                 the correctly-rounded sum. The proof of correctness is
                 valid for all inputs (including nonnormalized numbers
                 but modulo intermediate overflow), and is independent
                 of the number of summands or the condition number of
                 the sum. The algorithm asymptotically needs only 5
                 FLOPs per summand, and due to instruction-level
                 parallelism runs only about 2--3 times slower than the
                 obvious, fast-but-dumb ``ordinary recursive summation''
                 loop when the number of summands is greater than
                 10,000. Thus, to our knowledge, it is the fastest, most
                 accurate, and most memory efficient among known
                 algorithms. Indeed, it is difficult to see how a faster
                 algorithm or one requiring significantly fewer FLOPs
                 could exist without hardware improvements. An
                 application for a large number of summands is
                 provided.",
  acknowledgement = ack-nhfb,
  articleno =    "37",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "Floating-point summation; rounding error",
}

@Article{Rozloznik:2011:PTT,
  author =       "Miroslav Rozlo{\v{z}}n{\'\i}k and Gil Shklarski and
                 Sivan Toledo",
  title =        "Partitioned Triangular Tridiagonalization",
  journal =      j-TOMS,
  volume =       "37",
  number =       "4",
  pages =        "38:1--38:16",
  month =        feb,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1916461.1916462",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 16:05:18 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a partitioned algorithm for reducing a
                 symmetric matrix to a tridiagonal form, with partial
                 pivoting. That is, the algorithm computes a
                 factorization $P A P^T = L T L^T$, where, $P$ is a
                 permutation matrix, $L$ is lower triangular with a unit
                 diagonal and entries' magnitudes bounded by 1, and $T$
                 is symmetric and tridiagonal. The algorithm is based on
                 the basic (nonpartitioned) methods of Parlett and Reid
                 and of Aasen. We show that our factorization algorithm
                 is componentwise backward stable (provided that the
                 growth factor is not too large), with a similar
                 behavior to that of Aasen's basic algorithm. Our
                 implementation also computes the QR factorization of
                 $T$ and solves linear systems of equations using the
                 computed factorization.",
  acknowledgement = ack-nhfb,
  articleno =    "38",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cook:2011:SVS,
  author =       "William Cook and Daniel E. Steffy",
  title =        "Solving Very Sparse Rational Systems of Equations",
  journal =      j-TOMS,
  volume =       "37",
  number =       "4",
  pages =        "39:1--39:21",
  month =        feb,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1916461.1916463",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 16:05:18 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Efficient methods for solving linear-programming
                 problems in exact precision rely on the solution of
                 sparse systems of linear equations over the rational
                 numbers. We consider a test set of instances arising
                 from exact-precision linear programming and use this
                 test set to compare the performance of several
                 techniques designed for symbolic sparse linear-system
                 solving. We compare a direct exact solver based on LU
                 factorization, Wiedemann's method for black-box linear
                 algebra, Dixon's p-adic-lifting algorithm, and the use
                 of iterative numerical methods and rational
                 reconstruction as developed by Wan.",
  acknowledgement = ack-nhfb,
  articleno =    "39",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lin:2011:SAS,
  author =       "Lin Lin and Chao Yang and Juan C. Meza and Jianfeng Lu
                 and Lexing Ying and Weinan E",
  title =        "{SelInv}---An Algorithm for Selected Inversion of a
                 Sparse Symmetric Matrix",
  journal =      j-TOMS,
  volume =       "37",
  number =       "4",
  pages =        "40:1--40:19",
  month =        feb,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1916461.1916464",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 16:05:18 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe an efficient implementation of an
                 algorithm for computing selected elements of a general
                 sparse symmetric matrix $A$ that can be decomposed as
                 $A = L D L^T$, where $L$ is lower triangular and $D$ is
                 diagonal. Our implementation, which is called SelInv,
                 is built on top of an efficient supernodal left-looking
                 $L D L^T$ factorization of $A$. We discuss how
                 computational efficiency can be gained by making use of
                 a relative index array to handle indirect addressing.
                 We report the performance of SelInv on a collection of
                 sparse matrices of various sizes and nonzero
                 structures.",
  acknowledgement = ack-nhfb,
  articleno =    "40",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Taylor:2011:CAS,
  author =       "Ken Taylor and Scott Rickard and Konstantinos
                 Drakakis",
  title =        "{Costas} Arrays: Survey, Standardization, and {MATLAB}
                 Toolbox",
  journal =      j-TOMS,
  volume =       "37",
  number =       "4",
  pages =        "41:1--41:31",
  month =        feb,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1916461.1916465",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 16:05:18 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A Costas array is an arrangement of N dots on an
                 N-by-N grid, one per row, one per column, such that no
                 two dots share the same displacement vector with any
                 other pair. Costas arrays have applications in
                 SONAR\slash RADAR systems, communication systems,
                 cryptography, and other areas. We present a
                 standardization of notation and language which can be
                 used to discuss Costas array generation techniques and
                 array manipulations. Using this standardization we can
                 concisely and clearly state various theorems about
                 Costas arrays, including several new theorems about the
                 symmetries of Costas arrays. We also define labels for
                 each array (generated, emergent, and sporadic), which
                 describe whether the array is generated using a known
                 technique, generated using a semiempirical variation of
                 a known technique, or of unexplained origin.",
  acknowledgement = ack-nhfb,
  articleno =    "41",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Silvester:2011:OIS,
  author =       "David J. Silvester and Valeria Simoncini",
  title =        "An Optimal Iterative Solver for Symmetric Indefinite
                 Systems Stemming from Mixed Approximation",
  journal =      j-TOMS,
  volume =       "37",
  number =       "4",
  pages =        "42:1--42:22",
  month =        feb,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1916461.1916466",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 16:05:18 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We discuss the design and implementation of a suite of
                 functions for solving symmetric indefinite linear
                 systems associated with mixed approximation of systems
                 of PDEs. The novel feature of our iterative solver is
                 the incorporation of error control in the natural
                 ``energy'' norm in combination with an a posteriori
                 estimator for the PDE approximation error. This leads
                 to a robust and optimally efficient stopping criterion:
                 the iteration is terminated as soon as the algebraic
                 error is insignificant compared to the approximation
                 error. We describe a ``proof of concept'' MATLAB
                 implementation of this algorithm, which we call
                 EST\_MINRES, and we illustrate its effectiveness when
                 integrated into the Incompressible Flow Iterative
                 Solution Software (IFISS) package (cf. ACM Transactions
                 on Mathematical Software 33, Article 14, 2007).",
  acknowledgement = ack-nhfb,
  articleno =    "42",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Li:2011:SAI,
  author =       "Xiaoye S. Li and Meiyue Shao",
  title =        "A Supernodal Approach to Incomplete {LU} Factorization
                 with Partial Pivoting",
  journal =      j-TOMS,
  volume =       "37",
  number =       "4",
  pages =        "43:1--43:20",
  month =        feb,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1916461.1916467",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 16:05:18 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a new supernode-based incomplete LU
                 factorization method to construct a preconditioner for
                 solving sparse linear systems with iterative methods.
                 The new algorithm is primarily based on the ILUTP
                 approach by Saad, and we incorporate a number of
                 techniques to improve the robustness and performance of
                 the traditional ILUTP method. These include new
                 dropping strategies that accommodate the use of
                 supernodal structures in the factored matrix and an
                 area-based fill control heuristic for the secondary
                 dropping strategy.",
  acknowledgement = ack-nhfb,
  articleno =    "43",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{LeDigabel:2011:ANN,
  author =       "S{\'e}bastien {Le Digabel}",
  title =        "{Algorithm 909}: {NOMAD}: Nonlinear Optimization with
                 the {MADS} Algorithm",
  journal =      j-TOMS,
  volume =       "37",
  number =       "4",
  pages =        "44:1--44:15",
  month =        feb,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1916461.1916468",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 16:05:18 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "NOMAD is software that implements the Mesh Adaptive
                 Direct Search (MADS) algorithm for blackbox
                 optimization under general nonlinear constraints.
                 Blackbox optimization is about optimizing functions
                 that are usually given as costly programs with no
                 derivative information and no function values returned
                 for a significant number of calls attempted. NOMAD is
                 designed for such problems and aims for the best
                 possible solution with a small number of evaluations.
                 The objective of this article is to describe the
                 underlying algorithm, the software's functionalities,
                 and its implementation.",
  acknowledgement = ack-nhfb,
  articleno =    "44",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kormanyos:2011:APC,
  author =       "Christopher Kormanyos",
  title =        "{Algorithm 910}: a Portable {C++} Multiple-Precision
                 System for Special-Function Calculations",
  journal =      j-TOMS,
  volume =       "37",
  number =       "4",
  pages =        "45:1--45:27",
  month =        feb,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1916461.1916469",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 16:05:18 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
                 https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article presents a portable C++ system for
                 multiple precision calculations of special functions
                 called {\tt e\_float}. It has an extendable
                 architecture with a uniform C++ layer which can be used
                 with any suitably prepared MP type. The system
                 implements many high-precision special functions and
                 extends some of these to very large parameter ranges.
                 It supports calculations with 30 \ldots{} 300 decimal
                 digits of precision. Interoperabilities with
                 Microsoft's CLR, Python, and Mathematica{\reg} are
                 supported. The {\tt e\_float} system and its usage are
                 described in detail. Implementation notes, testing
                 results, and performance measurements are provided.",
  acknowledgement = ack-nhfb,
  articleno =    "45",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Smith:2011:AMP,
  author =       "David M. Smith",
  title =        "{Algorithm 911}: Multiple-Precision Exponential
                 Integral and Related Functions",
  journal =      j-TOMS,
  volume =       "37",
  number =       "4",
  pages =        "46:1--46:16",
  month =        feb,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1916461.1916470",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 16:05:18 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article describes a collection of Fortran-95
                 routines for evaluating the exponential integral
                 function, error function, sine and cosine integrals,
                 Fresnel integrals, Bessel functions, and related
                 mathematical special functions using the FM
                 multiple-precision arithmetic package.",
  acknowledgement = ack-nhfb,
  articleno =    "46",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kodama:2011:AMC,
  author =       "Masao Kodama",
  title =        "{Algorithm 912}: a Module for Calculating Cylindrical
                 Functions of Complex Order and Complex Argument",
  journal =      j-TOMS,
  volume =       "37",
  number =       "4",
  pages =        "47:1--47:25",
  month =        feb,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/1916461.1916471",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 16:05:18 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The present algorithm provides a module for
                 calculating the cylindrical functions $ J_\nu (z) $, $
                 Y_\nu (z) $, $ H_{\nu (1)}(z) $, and $ H_{\nu (2)}(z)
                 $, where the order $ \nu $ is complex and the complex
                 argument $z$ satisfies $ - \pi < \arg z \leq \pi $. The
                 algorithm is written in Fortran 90 and calculates the
                 functions using real and complex numbers of any
                 intrinsic data type whose kind type parameter the
                 user's Fortran system accepts. The methods of
                 calculating the functions are based on two kinds of
                 series expansions and numerical integration. Wronskian
                 tests examine the functional values computed by this
                 algorithm with double precision at 4,100,625
                 pseudorandom test points in the region $ | \Re \nu |
                 \leq 60 $, $ | \Im \nu | \leq 60 $, $ | \Re z| \leq 300
                 $, $ | \Im z| \leq 300 $.",
  acknowledgement = ack-nhfb,
  articleno =    "47",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Davis:2011:UFS,
  author =       "Timothy A. Davis and Yifan Hu",
  title =        "The {University of Florida} sparse matrix collection",
  journal =      j-TOMS,
  volume =       "38",
  number =       "1",
  pages =        "1:1--1:25",
  month =        nov,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049662.2049663",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 15 08:59:34 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe the University of Florida Sparse Matrix
                 Collection, a large and actively growing set of sparse
                 matrices that arise in real applications. The
                 Collection is widely used by the numerical linear
                 algebra community for the development and performance
                 evaluation of sparse matrix algorithms. It allows for
                 robust and repeatable experiments: robust because
                 performance results with artificially generated
                 matrices can be misleading, and repeatable because
                 matrices are curated and made publicly available in
                 many formats. Its matrices cover a wide spectrum of
                 domains, include those arising from problems with
                 underlying 2D or 3D geometry (as structural
                 engineering, computational fluid dynamics, model
                 reduction, electromagnetics, semiconductor devices,
                 thermodynamics, materials, acoustics, computer
                 graphics/vision, robotics/kinematics, and other
                 discretizations) and those that typically do not have
                 such geometry (optimization, circuit simulation,
                 economic and financial modeling, theoretical and
                 quantum chemistry, chemical process simulation,
                 mathematics and statistics, power networks, and other
                 networks and graphs).",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Dalberto:2011:EPM,
  author =       "Paolo D'alberto and Marco Bodrato and Alexandru
                 Nicolau",
  title =        "Exploiting parallelism in matrix-computation kernels
                 for symmetric multiprocessor systems:
                 Matrix-multiplication and matrix-addition algorithm
                 optimizations by software pipelining and threads
                 allocation",
  journal =      j-TOMS,
  volume =       "38",
  number =       "1",
  pages =        "2:1--2:30",
  month =        nov,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049662.2049664",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 15 08:59:34 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a simple and efficient methodology for the
                 development, tuning, and installation of matrix
                 algorithms such as the hybrid Strassen's and Winograd's
                 fast matrix multiply or their combination with the 3M
                 algorithm for complex matrices (i.e., hybrid: a
                 recursive algorithm as Strassen's until a highly tuned
                 BLAS matrix multiplication allows performance
                 advantages). We investigate how modern Symmetric
                 Multiprocessor (SMP) architectures present old and new
                 challenges that can be addressed by the combination of
                 an algorithm design with careful and natural
                 parallelism exploitation at the function level
                 (optimizations) such as function-call parallelism,
                 function percolation, and function software pipelining.
                 We have three contributions: first, we present a
                 performance overview for double- and
                 double-complex-precision matrices for state-of-the-art
                 SMP systems; second, we introduce new algorithm
                 implementations: a variant of the 3M algorithm and two
                 new different schedules of Winograd's matrix
                 multiplication (achieving up to 20\% speedup with
                 respect to regular matrix multiplication).",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cazals:2011:CVU,
  author =       "Frederic Cazals and Harshad Kanhere and S{\'e}bastien
                 Loriot",
  title =        "Computing the volume of a union of balls: a certified
                 algorithm",
  journal =      j-TOMS,
  volume =       "38",
  number =       "1",
  pages =        "3:1--3:20",
  month =        nov,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049662.2049665",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 15 08:59:34 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Balls and spheres are amongst the simplest 3D modeling
                 primitives, and computing the volume of a union of
                 balls is an elementary problem. Although a number of
                 strategies addressing this problem have been
                 investigated in several communities, we are not aware
                 of any robust algorithm, and present the first such
                 algorithm. Our calculation relies on the decomposition
                 of the volume of the union into convex regions, namely
                 the restrictions of the balls to their regions in the
                 power diagram. Theoretically, we establish a formula
                 for the volume of a restriction, based on Gauss'
                 divergence theorem. The proof being constructive, we
                 develop the associated algorithm.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{VanDeGeijn:2011:HPD,
  author =       "Robert A. {Van De Geijn} and Field G. {Van Zee}",
  title =        "High-performance up-and-downdating via
                 {Householder}-like transformations",
  journal =      j-TOMS,
  volume =       "38",
  number =       "1",
  pages =        "4:1--4:17",
  month =        nov,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049662.2049666",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 15 08:59:34 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present high-performance algorithms for
                 up-and-downdating a Cholesky factor or QR
                 factorization. The method uses Householder-like
                 transformations, sometimes called hyperbolic
                 Householder transformations, that are accumulated so
                 that most computation can be cast in terms of
                 high-performance matrix-matrix operations. The
                 resulting algorithms can then be used as building
                 blocks for an algorithm-by-blocks that allows
                 computation to be conveniently scheduled to
                 multithreaded architectures like multicore processors.
                 Performance is shown to be similar to that achieved by
                 a blocked QR factorization via Householder
                 transformations.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{VanGijzen:2011:AEI,
  author =       "Martin B. {Van Gijzen} and Peter Sonneveld",
  title =        "{Algorithm 913}: an elegant {IDR($s$)} variant that
                 efficiently exploits biorthogonality properties",
  journal =      j-TOMS,
  volume =       "38",
  number =       "1",
  pages =        "5:1--5:19",
  month =        nov,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049662.2049667",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 15 08:59:34 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The IDR(s) method that is proposed in Sonneveld and
                 van Gijzen [2008] is a very efficient limited memory
                 method for solving large nonsymmetric systems of linear
                 equations. IDR(s) is based on the induced dimension
                 reduction theorem, that provides a way to construct
                 subsequent residuals that lie in a sequence of
                 shrinking subspaces. The IDR(s) algorithm that is given
                 in Sonneveld and van Gijzen [2008] is a direct
                 translation of the theorem into an algorithm. This
                 translation is not unique. This article derives a new
                 IDR(s) variant, that imposes (one-sided)
                 biorthogonalization conditions on the iteration
                 vectors. The resulting method has lower overhead in
                 vector operations than the original IDR(s)
                 algorithms.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gil:2011:APC,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 914}: {Parabolic} cylinder function {$ W(a,
                 x) $} and its derivative",
  journal =      j-TOMS,
  volume =       "38",
  number =       "1",
  pages =        "6:1--6:5",
  month =        nov,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049662.2049668",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 15 08:59:34 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A Fortran 90 program for the computation of the real
                 parabolic cylinder functions $W(a, \pm x)$, $x \geq 0$
                 and their derivatives is presented. The code also
                 computes scaled functions for $a > 50$. The functions
                 $W(a, \pm x)$ are a numerically satisfactory pair of
                 solutions of the parabolic cylinder equation $y^\prime
                 + (x^2/4 - a)y = 0$, $x \geq 0$. Using Wronskian tests,
                 we claim a relative accuracy better than $5 \times
                 10^{-13}$ in the computable range of unscaled
                 functions, while for scaled functions the aimed
                 relative accuracy is better than $5 \times 10^{-14}$.
                 This code, together with the algorithm and related
                 software described in Gil et al.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Morales:2011:RAB,
  author =       "Jos{\'e} Luis Morales and Jorge Nocedal",
  title =        "Remark on {``Algorithm 778: L-BFGS-B: Fortran
                 subroutines for large-scale bound constrained
                 optimization''}",
  journal =      j-TOMS,
  volume =       "38",
  number =       "1",
  pages =        "7:1--7:4",
  month =        nov,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049662.2049669",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 15 08:59:34 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Zhu:1997:ALF}.",
  abstract =     "This remark describes an improvement and a correction
                 to Algorithm 778. It is shown that the performance of
                 the algorithm can be improved significantly by making a
                 relatively simple modification to the subspace
                 minimization phase. The correction concerns an error
                 caused by the use of routine dpmeps to estimate machine
                 precision.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Davis:2011:ASM,
  author =       "Timothy A. Davis",
  title =        "{Algorithm 915}, {SuiteSparseQR}: {Multifrontal}
                 multithreaded rank-revealing sparse {QR}
                 factorization",
  journal =      j-TOMS,
  volume =       "38",
  number =       "1",
  pages =        "8:1--8:22",
  month =        nov,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049662.2049670",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 15 08:59:34 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/multithreading.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "SuiteSparseQR is a sparse QR factorization package
                 based on the multifrontal method. Within each frontal
                 matrix, LAPACK and the multithreaded BLAS enable the
                 method to obtain high performance on multicore
                 architectures. Parallelism across different frontal
                 matrices is handled with Intel's Threading Building
                 Blocks library. The symbolic analysis and ordering
                 phase pre-eliminates singletons by permuting the input
                 matrix A into the form [R11 R12; 0 A22] where R11 is
                 upper triangular with diagonal entries above a given
                 tolerance. Next, the fill-reducing ordering, column
                 elimination tree, and frontal matrix structures are
                 found without requiring the formation of the pattern of
                 ATA. Approximate rank-detection is performed within
                 each frontal matrix using Heath's method.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rao:2011:CAG,
  author =       "Anil V. Rao and David A. Benson and Christopher Darby
                 and Michael A. Patterson and Camila Francolin and
                 Ilyssa Sanders and Geoffrey T. Huntington",
  title =        "Corrigendum: {Algorithm 902: GPOPS, a MATLAB software
                 for solving multiple-phase optimal control problems
                 using the Gauss pseudospectral method}",
  journal =      j-TOMS,
  volume =       "38",
  number =       "1",
  pages =        "9:1--9:2",
  month =        nov,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049662.2049671",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 15 08:59:34 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Rao:2010:AGM}.",
  abstract =     "An algorithm is described to solve multiple-phase
                 optimal control problems using a recently developed
                 numerical method called the Gauss pseudospectral
                 method. The algorithm is well suited for use in modern
                 vectorized programming languages such as FORTRAN 95 and
                 MATLAB. The algorithm discretizes the cost functional
                 and the differential-algebraic equations in each phase
                 of the optimal control problem. The phases are then
                 connected using linkage conditions on the state and
                 time. A large-scale nonlinear programming problem (NLP)
                 arises from the discretization and the significant
                 features of the NLP are described in detail. A
                 particular reusable MATLAB implementation of the
                 algorithm, called GPOPS, is applied to three classical
                 optimal control problems to demonstrate its utility.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Reid:2011:PFD,
  author =       "John K. Reid and Jennifer A. Scott",
  title =        "Partial factorization of a dense symmetric indefinite
                 matrix",
  journal =      j-TOMS,
  volume =       "38",
  number =       "2",
  pages =        "10:1--10:19",
  month =        dec,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049673.2049674",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 30 17:43:07 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "At the heart of a frontal or multifrontal solver for
                 the solution of sparse symmetric sets of linear
                 equations, there is the need to partially factorize
                 dense matrices (the frontal matrices) and to be able to
                 use their factorizations in subsequent forward and
                 backward substitutions. For a large problem, packing
                 (holding only the lower or upper triangular part) is
                 important to save memory. It has long been recognized
                 that blocking is the key to efficiency and this has
                 become particularly relevant on modern hardware. For
                 stability in the indefinite case, the use of
                 interchanges and $2 \times 2$ pivots as well as $1
                 \times 1$ pivots is equally well established.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Colman:2011:VCC,
  author =       "Michel Colman and Annie Cuyt and Joris {Van Deun}",
  title =        "Validated computation of certain hypergeometric
                 functions",
  journal =      j-TOMS,
  volume =       "38",
  number =       "2",
  pages =        "11:1--11:20",
  month =        dec,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049673.2049675",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 30 17:43:07 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present an efficient algorithm for the validated
                 high-precision computation of real continued fractions,
                 accurate to the last digit. The algorithm proceeds in
                 two stages. In the first stage, computations are done
                 in double precision. A forward error analysis and some
                 heuristics are used to obtain an a priori error
                 estimate. This estimate is used in the second stage to
                 compute the fraction to the requested accuracy in high
                 precision (adaptively incrementing the precision for
                 reasons of efficiency). A running error analysis and
                 techniques from interval arithmetic are used to
                 validate the result.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Beattie:2011:NSH,
  author =       "Christopher Beattie and Zlatko Drmav{\v{c}} and Serkan
                 Gugercin",
  title =        "A note on shifted {Hessenberg} systems and frequency
                 response computation",
  journal =      j-TOMS,
  volume =       "38",
  number =       "2",
  pages =        "12:1--12:16",
  month =        dec,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049673.2049676",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 30 17:43:07 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this article, we propose a numerical algorithm for
                 efficient and robust solution of a sequence of shifted
                 Hessenberg linear systems. In particular, we show how
                 the frequency response ${\cal G}(\sigma) = d - C(A -
                 \sigma \mathbb{I})^{-1} b$ in the single input case can
                 be computed more efficiently than with other
                 state-of-the-art methods. We also provide a backward
                 stability analysis of the proposed algorithm.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Duff:2011:DIA,
  author =       "Iain S. Duff and Kamer Kaya and Bora U{\c{c}}car",
  title =        "Design, implementation, and analysis of maximum
                 transversal algorithms",
  journal =      j-TOMS,
  volume =       "38",
  number =       "2",
  pages =        "13:1--13:31",
  month =        dec,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049673.2049677",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F50 (05C70 05C85)",
  MRnumber =     "2893028",
  bibdate =      "Fri Dec 30 17:43:07 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We report on careful implementations of seven
                 algorithms for solving the problem of finding a maximum
                 transversal of a sparse matrix. We analyze the
                 algorithms and discuss the design choices. To the best
                 of our knowledge, this is the most comprehensive
                 comparison of maximum transversal algorithms based on
                 augmenting paths. Previous papers with the same
                 objective either do not have all the algorithms
                 discussed in this article or they used nonuniform
                 implementations from different researchers. We use a
                 common base to implement all of the algorithms and
                 compare their relative performance on a wide range of
                 graphs and matrices. We systematize, develop, and use
                 several ideas for enhancing performance.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bangerth:2011:ADS,
  author =       "Wolfgang Bangerth and Carsten Burstedde and Timo
                 Heister and Martin Kronbichler",
  title =        "Algorithms and data structures for massively parallel
                 generic adaptive finite element codes",
  journal =      j-TOMS,
  volume =       "38",
  number =       "2",
  pages =        "14:1--14:28",
  month =        dec,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049673.2049678",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 30 17:43:07 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Today's largest supercomputers have 100,000s of
                 processor cores and offer the potential to solve
                 partial differential equations discretized by billions
                 of unknowns. However, the complexity of scaling to such
                 large machines and problem sizes has so far prevented
                 the emergence of generic software libraries that
                 support such computations, although these would lower
                 the threshold of entry and enable many more
                 applications to benefit from large-scale computing. We
                 are concerned with providing this functionality for
                 mesh-adaptive finite element computations. We assume
                 the existence of an ``oracle'' that implements the
                 generation and modification of an adaptive mesh
                 distributed across many processors, and that responds
                 to queries about its structure.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Zaghloul:2011:ACF,
  author =       "Mofreh R. Zaghloul and Ahmed N. Ali",
  title =        "{Algorithm 916}: Computing the {Faddeyeva} and {Voigt}
                 functions",
  journal =      j-TOMS,
  volume =       "38",
  number =       "2",
  pages =        "15:1--15:22",
  month =        dec,
  year =         "2011",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2049673.2049679",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 30 17:43:07 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Zaghloul:2016:RAC}.",
  abstract =     "We present a MATLAB function for the numerical
                 evaluation of the Faddeyeva function $w(z)$. The
                 function is based on a newly developed accurate
                 algorithm. In addition to its higher accuracy, the
                 software provides a flexible accuracy vs efficiency
                 trade-off through a controlling parameter that may be
                 used to reduce accuracy and computational time and vice
                 versa. Verification of the flexibility, reliability,
                 and superior accuracy of the algorithm is provided
                 through comparison with standard algorithms available
                 in other libraries and software packages.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lantoine:2012:UMV,
  author =       "Gregory Lantoine and Ryan P. Russell and Thierry
                 Dargent",
  title =        "Using Multicomplex Variables for Automatic Computation
                 of High-Order Derivatives",
  journal =      j-TOMS,
  volume =       "38",
  number =       "3",
  pages =        "16:1--16:21",
  month =        apr,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2168773.2168774",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu May 3 16:27:26 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The computations of the high-order partial derivatives
                 in a given problem are often cumbersome or not
                 accurate. To combat such shortcomings, a new method for
                 calculating exact high-order sensitivities using
                 multicomplex numbers is presented. Inspired by the
                 recent complex step method that is only valid for
                 first-order sensitivities, the new multicomplex
                 approach is valid to arbitrary order. The mathematical
                 theory behind this approach is revealed, and an
                 efficient procedure for the automatic implementation of
                 the method is described. Several applications are
                 presented to validate and demonstrate the accuracy and
                 efficiency of the algorithm. The results are compared
                 to conventional approaches such as finite differencing,
                 the complex step method, and two separate automatic
                 differentiation tools. The multicomplex method performs
                 favorably in the preliminary comparisons and is
                 therefore expected to be useful for a variety of
                 algorithms that exploit higher order derivatives.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gustavson:2012:PCE,
  author =       "Fred Gustavson and Lars Karlsson and Bo
                 K{\aa}gstr{\"o}m",
  title =        "Parallel and Cache-Efficient In-Place Matrix Storage
                 Format Conversion",
  journal =      j-TOMS,
  volume =       "38",
  number =       "3",
  pages =        "17:1--17:32",
  month =        apr,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2168773.2168775",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu May 3 16:27:26 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Techniques and algorithms for efficient in-place
                 conversion to and from standard and blocked matrix
                 storage formats are described. Such functionality is
                 required by numerical libraries that use different data
                 layouts internally. Parallel algorithms and a software
                 package for in-place matrix storage format conversion
                 based on in-place matrix transposition are presented
                 and evaluated. A new algorithm for in-place
                 transposition which efficiently determines the
                 structure of the transposition permutation a priori is
                 one of the key ingredients. It enables effective load
                 balancing in a parallel environment.",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{DeWitte:2012:IIC,
  author =       "Virginie {De Witte} and Willy Govaerts and Yuri A.
                 Kuznetsov and Mark Friedman",
  title =        "Interactive Initialization and Continuation of
                 Homoclinic and Heteroclinic Orbits in {MATLAB}",
  journal =      j-TOMS,
  volume =       "38",
  number =       "3",
  pages =        "18:1--18:34",
  month =        apr,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2168773.2168776",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu May 3 16:27:26 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "{\tt matcont} is a MATLAB continuation package for the
                 interactive numerical study of a range of parameterized
                 nonlinear dynamical systems, in particular ODEs, that
                 allows to compute curves of equilibria, limit points,
                 Hopf points, limit cycles, flip, fold and torus
                 bifurcation points of limit cycles. It is now possible
                 to continue homoclinic-to-hyperbolic-saddle and
                 homoclinic-to-saddle-node orbits in {\tt matcont}. The
                 implementation is done using the continuation of
                 invariant subspaces, with the Riccati equations
                 included in the defining system. A key feature is the
                 possibility to initiate both types of homoclinic orbits
                 interactively, starting from an equilibrium point and
                 using a homotopy method. All known codimension-two
                 homoclinic bifurcations are tested for during
                 continuation. The test functions for inclination-flip
                 bifurcations are implemented in a new and more
                 efficient way. Heteroclinic orbits can now also be
                 continued and an analogous homotopy method can be used
                 for the initialization.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{More:2012:EDN,
  author =       "Jorge J. Mor{\'e} and Stefan M. Wild",
  title =        "Estimating Derivatives of Noisy Simulations",
  journal =      j-TOMS,
  volume =       "38",
  number =       "3",
  pages =        "19:1--19:21",
  month =        apr,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2168773.2168777",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu May 3 16:27:26 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We employ recent work on computational noise to obtain
                 near-optimal difference estimates of the derivative of
                 a noisy function. Our analysis relies on a stochastic
                 model of the noise without assuming a specific form of
                 distribution. We use this model to derive theoretical
                 bounds for the errors in the difference estimates and
                 obtain an easily computable difference parameter that
                 is provably near-optimal. Numerical results closely
                 resemble the theory and show that we obtain accurate
                 derivative estimates even when the noisy function is
                 deterministic.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lawrence:2012:ACD,
  author =       "Piers W. Lawrence and Robert M. Corless and David J.
                 Jeffrey",
  title =        "{Algorithm 917}: Complex Double-Precision Evaluation
                 of the {Wright} $\omega$ Function",
  journal =      j-TOMS,
  volume =       "38",
  number =       "3",
  pages =        "20:1--20:17",
  month =        apr,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2168773.2168779",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu May 3 16:27:26 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article describes an efficient and robust
                 algorithm and implementation for the evaluation of the
                 Wright $\omega$ function in IEEE double precision
                 arithmetic over the complex plane.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sadkane:2012:ASM,
  author =       "Miloud Sadkane and Ahmed Touhami",
  title =        "{Algorithm 918}: {{\tt specdicho}}: a {MATLAB} Program
                 for the Spectral Dichotomy of Regular Matrix Pencils",
  journal =      j-TOMS,
  volume =       "38",
  number =       "3",
  pages =        "21:1--21:13",
  month =        apr,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2168773.2168780",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu May 3 16:27:26 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Given a regular matrix pencil $ \lambda B - A $ and a
                 positively oriented contour \gamma in the complex
                 plane, the spectral dichotomy methods applied to $
                 \lambda B - A $ and \gamma consist in determining
                 whether $ \lambda B - A $ possesses eigenvalues on or
                 in a neighborhood of $ \gamma $. When no such eigenvalues
                 exist, these methods compute iteratively the spectral
                 projector P onto the right deflating subspace of $
                 \lambda B - A $ associated with the eigenvalues
                 inside/outside $ \gamma $. The computation of the
                 projector is accompanied by the spectral norm $ ||H|| $
                 of a Hermitian positive definite matrix $H$ called the
                 dichotomy condition number, which indicates the
                 numerical quality of the spectral projector P. The
                 smaller $ ||H|| $ is, the better this quality. This
                 article presents a MATLAB program ({\tt specdicho})
                 implementing the main types of spectral dichotomy where
                 $ \gamma $ is a circle, an ellipse, the imaginary axis
                 or a parabola.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Niesen:2012:AKS,
  author =       "Jitse Niesen and Will M. Wright",
  title =        "{Algorithm 919}: a {Krylov} Subspace Algorithm for
                 Evaluating the $\varphi$-Functions Appearing in
                 Exponential Integrators",
  journal =      j-TOMS,
  volume =       "38",
  number =       "3",
  pages =        "22:1--22:19",
  month =        apr,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2168773.2168781",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu May 3 16:27:26 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We develop an algorithm for computing the solution of
                 a large system of linear ordinary differential
                 equations (ODEs) with polynomial inhomogeneity. This is
                 equivalent to computing the action of a certain matrix
                 function on the vector representing the initial
                 condition. The matrix function is a linear combination
                 of the matrix exponential and other functions related
                 to the exponential (the so-called $\varphi$-functions).
                 Such computations are the major computational burden in
                 the implementation of exponential integrators, which
                 can solve general ODEs. Our approach is to compute the
                 action of the matrix function by constructing a Krylov
                 subspace using Arnoldi or Lanczos iteration and
                 projecting the function on this subspace. This is
                 combined with time-stepping to prevent the Krylov
                 subspace from growing too large. The algorithm is fully
                 adaptive: it varies both the size of the time steps and
                 the dimension of the Krylov subspace to reach the
                 required accuracy. We implement this algorithm in the
                 Matlab function {\tt phipm} and we give instructions on
                 how to obtain and use this function. Various numerical
                 experiments show that the {\tt phipm} function is often
                 significantly more efficient than the
                 state-of-the-art.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Filippone:2012:OOT,
  author =       "Salvatore Filippone and Alfredo Buttari",
  title =        "Object-Oriented Techniques for Sparse Matrix
                 Computations in {Fortran 2003}",
  journal =      j-TOMS,
  volume =       "38",
  number =       "4",
  pages =        "23:1--23:20",
  month =        aug,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2331130.2331131",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 30 18:55:10 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The efficiency of a sparse linear algebra operation
                 heavily relies on the ability of the sparse matrix
                 storage format to exploit the computing power of the
                 underlying hardware. Since no format is universally
                 better than the others across all possible kinds of
                 operations and computers, sparse linear algebra
                 software packages should provide facilities to easily
                 implement and integrate new storage formats within a
                 sparse linear algebra application without the need to
                 modify it; it should also allow to dynamically change a
                 storage format at run-time depending on the specific
                 operations to be performed. Aiming at these important
                 features, we present an Object Oriented design model
                 for a sparse linear algebra package which relies on
                 Design Patterns. We show that an implementation of our
                 model can be efficiently achieved through some of the
                 unique features of the Fortran 2003 language.
                 Experimental results show that the proposed software
                 infrastructure improves the modularity and ease of use
                 of the code at no performance loss.",
  acknowledgement = ack-nhfb,
  articleno =    "23",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{George:2012:EAP,
  author =       "Thomas George and Anshul Gupta and Vivek Sarin",
  title =        "An Empirical Analysis of the Performance of
                 Preconditioners for {SPD} Systems",
  journal =      j-TOMS,
  volume =       "38",
  number =       "4",
  pages =        "24:1--24:30",
  month =        aug,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2331130.2331132",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 30 18:55:10 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Preconditioned iterative solvers have the potential to
                 solve very large sparse linear systems with a fraction
                 of the memory used by direct methods. However, the
                 effectiveness and performance of most preconditioners
                 is not only problem dependent, but also fairly
                 sensitive to the choice of their tunable parameters. As
                 a result, a typical practitioner is faced with an
                 overwhelming number of choices of solvers,
                 preconditioners, and their parameters. The diversity of
                 preconditioners makes it difficult to analyze them in a
                 unified theoretical model. A systematic empirical
                 evaluation of existing preconditioned iterative solvers
                 can help in identifying the relative advantages of
                 various implementations. We present the results of a
                 comprehensive experimental study of the most popular
                 preconditioner and iterative solver combinations for
                 symmetric positive-definite systems. We introduce a
                 methodology for a rigorous comparative evaluation of
                 various preconditioners, including the use of some
                 simple but powerful metrics. The detailed comparison of
                 various preconditioner implementations and a
                 state-of-the-art direct solver gives interesting
                 insights into their relative strengths and weaknesses.
                 We believe that these results would be useful to
                 researchers developing preconditioners and iterative
                 solvers as well as practitioners looking for
                 appropriate sparse solvers for their applications.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Quintana-Orti:2012:RSP,
  author =       "Gregorio Quintana-Ort{\'\i} and Francisco D. Igual and
                 Mercedes Marqu{\'e}s and Enrique S. Quintana-Ort{\'\i}
                 and Robert A. van de Geijn",
  title =        "A Runtime System for Programming Out-of-Core Matrix
                 Algorithms-by-Tiles on Multithreaded Architectures",
  journal =      j-TOMS,
  volume =       "38",
  number =       "4",
  pages =        "25:1--25:25",
  month =        aug,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2331130.2331133",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 30 18:55:10 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/multithreading.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Out-of-core implementations of algorithms for dense
                 matrix computations have traditionally focused on
                 optimal use of memory so as to minimize I/O, often
                 trading programmability for performance. In this
                 article we show how the current state of hardware and
                 software allows the programmability problem to be
                 addressed without sacrificing performance. This comes
                 from the realizations that memory is cheap and large,
                 making it less necessary to optimally orchestrate I/O,
                 and that new algorithms view matrices as collections of
                 submatrices and computation as operations with those
                 submatrices. This enables libraries to be coded at a
                 high level of abstraction, leaving the tasks of
                 scheduling the computations and data movement in the
                 hands of a runtime system. This is in sharp contrast to
                 more traditional approaches that leverage optimal use
                 of in-core memory and, at the expense of introducing
                 considerable programming complexity, explicit overlap
                 of I/O with computation. Performance is demonstrated
                 for this approach on multicore architectures as well as
                 platforms equipped with hardware accelerators.",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Birkisson:2012:AFD,
  author =       "Asgeir Birkisson and Tobin A. Driscoll",
  title =        "Automatic {Fr{\'e}chet} Differentiation for the
                 Numerical Solution of Boundary-Value Problems",
  journal =      j-TOMS,
  volume =       "38",
  number =       "4",
  pages =        "26:1--26:29",
  month =        aug,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2331130.2331134",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 30 18:55:10 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A new solver for nonlinear boundary-value problems
                 (BVPs) in Matlab is presented, based on the Chebfun
                 software system for representing functions and
                 operators automatically as numerical objects. The
                 solver implements Newton's method in function space,
                 where instead of the usual Jacobian matrices, the
                 derivatives involved are Fr{\'e}chet derivatives. A
                 major novelty of this approach is the application of
                 automatic differentiation (AD) techniques to compute
                 the operator-valued Fr{\'e}chet derivatives in the
                 continuous context. Other novelties include the use of
                 anonymous functions and numbering of each variable to
                 enable a recursive, delayed evaluation of derivatives
                 with forward mode AD . The AD techniques are applied
                 within a new Chebfun class called which allows users to
                 set up and solve nonlinear BVPs, both scalar and
                 systems of coupled equations, in a few lines of code,
                 using the ``nonlinear backslash'' operator
                 ($\backslash$). This framework enables one to study the
                 behaviour of Newton's method in function space.",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kim:2012:ASS,
  author =       "Sunyoung Kim and Masakazu Kojima and Hayato Waki and
                 Makato Yamashita",
  title =        "{Algorithm 920}: {SFSDP}: a Sparse Version of Full
                 Semidefinite Programming Relaxation for Sensor Network
                 Localization Problems",
  journal =      j-TOMS,
  volume =       "38",
  number =       "4",
  pages =        "27:1--27:19",
  month =        aug,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2331130.2331135",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 30 18:55:10 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "SFSDP is a Matlab package for solving sensor network
                 localization (SNL) problems. These types of problems
                 arise in monitoring and controlling applications using
                 wireless sensor networks. SFSDP implements the
                 semidefinite programming (SDP) relaxation proposed in
                 Kim et al. [2009] for sensor network localization
                 problems, as a sparse version of the full semidefinite
                 programming relaxation (FSDP) by Biswas and Ye [2004].
                 To improve the efficiency of FSDP, SFSDP exploits the
                 aggregated and correlative sparsity of a sensor network
                 localization problem. As a result, SFSDP can handle
                 much larger problems than other software as well as
                 three-dimensional anchor-free problems. SFSDP analyzes
                 the input data of a sensor network localization
                 problem, solves the problem, and displays the computed
                 locations of sensors. SFSDP also includes the features
                 of generating test problems for numerical
                 experiments.",
  acknowledgement = ack-nhfb,
  articleno =    "27",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hauenstein:2012:AAC,
  author =       "Jonathan D. Hauenstein and Frank Sottile",
  title =        "{Algorithm 921}: {alphaCertified}: Certifying
                 Solutions to Polynomial Systems",
  journal =      j-TOMS,
  volume =       "38",
  number =       "4",
  pages =        "28:1--28:20",
  month =        aug,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2331130.2331136",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 30 18:55:10 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Smale's $\alpha$-theory uses estimates related to the
                 convergence of Newton's method to certify that Newton
                 iterations will converge quadratically to solutions to
                 a square polynomial system. The program alphaCertified
                 implements algorithms based on $\alpha$-theory to
                 certify solutions of polynomial systems using both
                 exact rational arithmetic and arbitrary precision
                 floating point arithmetic. It also implements
                 algorithms that certify whether a given point
                 corresponds to a real solution, and algorithms to
                 heuristically validate solutions to overdetermined
                 systems. Examples are presented to demonstrate the
                 algorithms.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ji:2012:AMF,
  author =       "Xia Ji and Jiguang Sun and Tiara Turner",
  title =        "{Algorithm 922}: a Mixed Finite Element Method for
                 {Helmholtz} Transmission Eigenvalues",
  journal =      j-TOMS,
  volume =       "38",
  number =       "4",
  pages =        "29:1--29:8",
  month =        aug,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2331130.2331137",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 30 18:55:10 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Transmission eigenvalue problem has important
                 applications in inverse scattering. Since the problem
                 is non-self-adjoint, the computation of transmission
                 eigenvalues needs special treatment. Based on a
                 fourth-order reformulation of the transmission
                 eigenvalue problem, a mixed finite element method is
                 applied. The method has two major advantages: (1) the
                 formulation leads to a generalized eigenvalue problem
                 naturally without the need to invert a related linear
                 system, and (2) the nonphysical zero transmission
                 eigenvalue, which has an infinitely dimensional
                 eigenspace, is eliminated. To solve the resulting
                 non-Hermitian eigenvalue problem, an iterative
                 algorithm using restarted Arnoldi method is proposed.
                 To make the computation efficient, the search interval
                 is decided using a Faber--Krahn type inequality for
                 transmission eigenvalues and the interval is updated at
                 each iteration. The algorithm is implemented using
                 Matlab. The code can be easily used in the qualitative
                 methods in inverse scattering and modified to compute
                 transmission eigenvalues for other models such as
                 elasticity problem.",
  acknowledgement = ack-nhfb,
  articleno =    "29",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Wimmer:2012:AEN,
  author =       "M. Wimmer",
  title =        "{Algorithm 923}: Efficient Numerical Computation of
                 the {Pfaffian} for Dense and Banded Skew-Symmetric
                 Matrices",
  journal =      j-TOMS,
  volume =       "38",
  number =       "4",
  pages =        "30:1--30:17",
  month =        aug,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2331130.2331138",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Aug 30 18:55:10 MDT 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
                 https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Computing the Pfaffian of a skew-symmetric matrix is a
                 problem that arises in various fields of physics. Both
                 computing the Pfaffian and a related problem, computing
                 the canonical form of a skew-symmetric matrix under
                 unitary congruence, can be solved easily once the
                 skew-symmetric matrix has been reduced to
                 skew-symmetric tridiagonal form. We develop efficient
                 numerical methods for computing this tridiagonal form
                 based on Gaussian elimination, using a skew-symmetric,
                 blocked form of the Parlett-Reid algorithm, or based on
                 unitary transformations, using block Householder
                 transformations and Givens rotations, that are
                 applicable to dense and banded matrices, respectively.
                 We also give a complete and fully optimized
                 implementation of these algorithms in Fortran
                 (including a C interface), and also provide Python,
                 Matlab and Mathematica implementations for convenience.
                 Finally, we apply these methods to compute the
                 topological charge of a class D nanowire, and show
                 numerically the equivalence of definitions based on the
                 Hamiltonian and the scattering matrix.",
  acknowledgement = ack-nhfb,
  articleno =    "30",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Notz:2012:GBS,
  author =       "Patrick K. Notz and Roger P. Pawlowski and James C.
                 Sutherland",
  title =        "Graph-Based Software Design for Managing Complexity
                 and Enabling Concurrency in Multiphysics {PDE}
                 Software",
  journal =      j-TOMS,
  volume =       "39",
  number =       "1",
  pages =        "1:1--1:21",
  month =        nov,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2382585.2382586",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 6 07:36:30 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Multiphysics simulation software is plagued by
                 complexity stemming from nonlinearly coupled systems of
                 Partial Differential Equations (PDEs). Such software
                 typically supports many models, which may require
                 different transport equations, constitutive laws, and
                 equations of state. Strong coupling and a multiplicity
                 of models leads to complex algorithms (i.e., the
                 properly ordered sequence of steps to assemble a
                 discretized set of coupled PDEs) and rigid software.
                 This work presents a design strategy that shifts focus
                 away from high-level algorithmic concerns to low-level
                 data dependencies. Mathematical expressions are
                 represented as software objects that directly expose
                 data dependencies. The entire system of expressions
                 forms a directed acyclic graph and the high-level
                 assembly algorithm is generated automatically through
                 standard graph algorithms. This approach makes problems
                 with complex dependencies entirely tractable, and
                 removes virtually all logic from the algorithm itself.
                 Changes are highly localized, allowing developers to
                 implement models without detailed understanding of any
                 algorithms (i.e., the overall assembly process).
                 Furthermore, this approach complements existing
                 MPI-based frameworks and can be implemented within them
                 easily. Finally, this approach enables algorithmic
                 parallelization via threads. By exposing dependencies
                 in the algorithm explicitly, thread-based parallelism
                 is implemented through algorithm decomposition,
                 providing a basis for exploiting parallelism
                 independent from domain decomposition approaches.",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{VanZee:2012:FAR,
  author =       "Field G. {Van Zee} and Robert A. van de Geijn and
                 Gregorio Quintana-Ort{\'\i} and G. Joseph Elizondo",
  title =        "Families of Algorithms for Reducing a Matrix to
                 Condensed Form",
  journal =      j-TOMS,
  volume =       "39",
  number =       "1",
  pages =        "2:1--2:32",
  month =        nov,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2382585.2382587",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 6 07:36:30 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In a recent paper it was shown how memory traffic can
                 be diminished by reformulating the classic algorithm
                 for reducing a matrix to bidiagonal form, a preprocess
                 when computing the singular values of a dense matrix.
                 The key is a reordering of the computation so that the
                 most memory-intensive operations can be ``fused.'' In
                 this article, we show that other operations that reduce
                 matrices to condensed form (reduction to upper
                 Hessenberg form and reduction to tridiagonal form) can
                 be similarly reorganized, yielding different sets of
                 operations that can be fused. By developing the
                 algorithms with a common framework and notation, we
                 facilitate the comparing and contrasting of the
                 different algorithms and opportunities for optimization
                 on sequential architectures. We discuss the algorithms,
                 develop a simple model to estimate the speedup
                 potential from fusing, and showcase performance
                 improvements consistent with the what the model
                 predicts.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bell:2012:PSA,
  author =       "Nathan Bell and Anil N. Hirani",
  title =        "{PyDEC}: Software and Algorithms for Discretization of
                 Exterior Calculus",
  journal =      j-TOMS,
  volume =       "39",
  number =       "1",
  pages =        "3:1--3:41",
  month =        nov,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2382585.2382588",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 6 07:36:30 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article describes the algorithms, features, and
                 implementation of PyDEC, a Python library for
                 computations related to the discretization of exterior
                 calculus. PyDEC facilitates inquiry into both physical
                 problems on manifolds as well as purely topological
                 problems on abstract complexes. We describe efficient
                 algorithms for constructing the operators and objects
                 that arise in discrete exterior calculus, lowest-order
                 finite element exterior calculus, and in related
                 topological problems. Our algorithms are formulated in
                 terms of high-level matrix operations which extend to
                 arbitrary dimension. As a result, our implementations
                 map well to the facilities of numerical libraries such
                 as NumPy and SciPy. The availability of such libraries
                 makes Python suitable for prototyping numerical
                 methods. We demonstrate how PyDEC is used to solve
                 physical and topological problems through several
                 concise examples.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Burton:2012:CCN,
  author =       "Benjamin A. Burton and Melih Ozlen",
  title =        "Computing the Crosscap Number of a Knot Using Integer
                 Programming and Normal Surfaces",
  journal =      j-TOMS,
  volume =       "39",
  number =       "1",
  pages =        "4:1--4:18",
  month =        nov,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2382585.2382589",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 6 07:36:30 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The crosscap number of a knot is an invariant
                 describing the nonorientable surface of smallest genus
                 that the knot bounds. Unlike knot genus (its orientable
                 counterpart), crosscap numbers are difficult to compute
                 and no general algorithm is known. We present three
                 methods for computing crosscap number that offer
                 varying trade-offs between precision and speed: (i) an
                 algorithm based on Hilbert basis enumeration and (ii)
                 an algorithm based on exact integer programming, both
                 of which either compute the solution precisely or
                 reduce it to two possible values, and (iii) a fast but
                 limited precision integer programming algorithm that
                 bounds the solution from above. The first two
                 algorithms advance the theoretical state-of-the-art,
                 but remain intractable for practical use. The third
                 algorithm is fast and effective, which we show in a
                 practical setting by making significant improvements to
                 the current knowledge of crosscap numbers in knot
                 tables. Our integer programming framework is general,
                 with the potential for further applications in
                 computational geometry and topology.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Abad:2012:ATT,
  author =       "Alberto Abad and Roberto Barrio and Fernando Blesa and
                 Marcos Rodr{\'\i}guez",
  title =        "{Algorithm 924}: {TIDES}, a {Taylor Series Integrator
                 for Differential EquationS}",
  journal =      j-TOMS,
  volume =       "39",
  number =       "1",
  pages =        "5:1--5:28",
  month =        nov,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2382585.2382590",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 6 07:36:30 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article introduces the software package TIDES and
                 revisits the use of the Taylor series method for the
                 numerical integration of ODEs. The package TIDES
                 provides an easy-to-use interface for standard double
                 precision integrations, but also for quadruple
                 precision and multiple precision integrations. The
                 motivation for the development of this package is that
                 more and more scientific disciplines need very high
                 precision solution of ODEs, and a standard ODE method
                 is not able to reach these precision levels. The TIDES
                 package combines a preprocessor step in M athematica
                 that generates Fortran or C programs with a library in
                 C. Another capability of TIDES is the direct solution
                 of sensitivities of the solution of ODE systems, which
                 means that we can compute the solution of variational
                 equations up to any order without formulating them
                 explicitly. Different options of the software are
                 discussed, and finally it is compared with other
                 well-known available methods, as well as with different
                 options of TIDES. From the numerical tests, TIDES is
                 competitive, both in speed and accuracy, with standard
                 methods, but it also provides new capabilities.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Yamashita:2012:APS,
  author =       "Makoto Yamashita and Katsuki Fujisawa and Mituhiro
                 Fukuda and Kazuhide Nakata and Maho Nakata",
  title =        "{Algorithm 925}: Parallel Solver for Semidefinite
                 Programming Problem having Sparse {Schur} Complement
                 Matrix",
  journal =      j-TOMS,
  volume =       "39",
  number =       "1",
  pages =        "6:1--6:22",
  month =        nov,
  year =         "2012",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2382585.2382591",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Dec 6 07:36:30 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/multithreading.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A SemiDefinite Programming (SDP) problem is one of the
                 most central problems in mathematical optimization. SDP
                 provides an effective computation framework for many
                 research fields. Some applications, however, require
                 solving a large-scale SDP whose size exceeds the
                 capacity of a single processor both in terms of
                 computation time and available memory. SDPARA
                 (SemiDefinite Programming Algorithm paRAllel package)
                 [Yamashita et al. 2003b] was designed to solve such
                 large-scale SDPs. Its parallel performance is
                 outstanding for general SDPs in most cases. However,
                 the parallel implementation is less successful for some
                 sparse SDPs obtained from applications such as
                 Polynomial Optimization Problems (POPs) or Sensor
                 Network Localization (SNL) problems, since this version
                 of SDPARA cannot directly handle sparse Schur
                 Complement Matrices (SCMs). In this article we improve
                 SDPARA by focusing on the sparsity of the SCM and we
                 propose a new parallel implementation using the
                 formula-cost-based distribution along with a
                 replacement of the dense Cholesky factorization. We
                 verify numerically that these features are key to
                 solving SDPs with sparse SCMs more quickly on parallel
                 computing systems. The performance is further enhanced
                 by multithreading and the new SDPARA attains
                 considerable scalability in general. It also finds
                 solutions for extremely large-scale SDPs arising from
                 POPs which cannot be obtained by other solvers.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Betcke:2013:NCN,
  author =       "Timo Betcke and Nicholas J. Higham and Volker Mehrmann
                 and Christian Schr{\"o}der and Fran{\c{c}}oise
                 Tisseur",
  title =        "{NLEVP}: a Collection of Nonlinear Eigenvalue
                 Problems",
  journal =      j-TOMS,
  volume =       "39",
  number =       "2",
  pages =        "7:1--7:28",
  month =        feb,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2427023.2427024",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 20 16:46:13 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a collection of 52 nonlinear eigenvalue
                 problems in the form of a MATLAB toolbox. The
                 collection contains problems from models of real-life
                 applications as well as ones constructed specifically
                 to have particular properties. A classification is
                 given of polynomial eigenvalue problems according to
                 their structural properties. Identifiers based on these
                 and other properties can be used to extract particular
                 types of problems from the collection. A brief
                 description of each problem is given. NLEVP serves both
                 to illustrate the tremendous variety of applications of
                 nonlinear eigenvalue problems and to provide
                 representative problems for testing, tuning, and
                 benchmarking of algorithms and codes.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Baboulin:2013:ALS,
  author =       "Marc Baboulin and Jack Dongarra and Julien Herrmann
                 and Stanimire Tomov",
  title =        "Accelerating Linear System Solutions Using
                 Randomization Techniques",
  journal =      j-TOMS,
  volume =       "39",
  number =       "2",
  pages =        "8:1--8:13",
  month =        feb,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2427023.2427025",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 20 16:46:13 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We illustrate how linear algebra calculations can be
                 enhanced by statistical techniques in the case of a
                 square linear system $A x = b$. We study a random
                 transformation of $A$ that enables us to avoid pivoting
                 and then to reduce the amount of communication.
                 Numerical experiments show that this randomization can
                 be performed at a very affordable computational price
                 while providing us with a satisfying accuracy when
                 compared to partial pivoting. This random
                 transformation called Partial Random Butterfly
                 Transformation (PRBT) is optimized in terms of data
                 storage and flops count. We propose a solver where PRBT
                 and the LU factorization with no pivoting take
                 advantage of the current hybrid multicore\slash GPU
                 machines and we compare its Gflop/s performance with a
                 solver implemented in a current parallel library.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gustavson:2013:LCF,
  author =       "Fred G. Gustavson and Jerzy Wa{\'s}niewski and Jack J.
                 Dongarra and Jos{\'e} R. Herrero and Julien Langou",
  title =        "Level-3 {Cholesky} Factorization Routines Improve
                 Performance of Many {Cholesky} Algorithms",
  journal =      j-TOMS,
  volume =       "39",
  number =       "2",
  pages =        "9:1--9:10",
  month =        feb,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2427023.2427026",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F05 (65Y15)",
  MRnumber =     "3031628",
  bibdate =      "Wed Feb 20 16:46:13 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Four routines called DPOTF3i, $ i = a, b, c, d $, are
                 presented. DPOTF3i are a novel type of level-3 BLAS for
                 use by BPF (Blocked Packed Format) Cholesky
                 factorization and LAPACK routine DPOTRF. Performance of
                 routines DPOTF3i are still increasing when the
                 performance of Level-2 routine DPOTF2 of LAPACK starts
                 decreasing. This is our main result and it implies, due
                 to the use of larger block size $ n_b $, that DGEMM,
                 DSYRK, and DTRSM performance also increases! The four
                 DPOTF3i routines use simple register
                 blocking. Different platforms have different numbers of
                 registers. Thus, our four routines have different
                 register blocking sizes. BPF is introduced. LAPACK
                 routines for POTRF and PPTRF using BPF instead of full
                 and packed format are shown to be trivial modifications
                 of LAPACK POTRF source codes. We call these codes
                 BPTRF. There are two variants of BPF: lower and
                 upper. Upper BPF is ``identical'' to Square Block
                 Packed Format (SBPF). ``LAPACK'' implementations on
                 multicore processors use SBPF. Lower BPF is less
                 efficient than upper BPF. Vector inplace transposition
                 converts lower BPF to upper BPF very
                 efficiently. Corroborating performance results for
                 DPOTF3i versus DPOTF2 on a variety of common platforms
                 are given for $ n \approx n_b $ as well as results for
                 large $ n $ comparing DBPTRF versus DPOTRF.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Knepley:2013:FEI,
  author =       "Matthew G. Knepley and Andy R. Terrel",
  title =        "Finite Element Integration on {GPUs}",
  journal =      j-TOMS,
  volume =       "39",
  number =       "2",
  pages =        "10:1--10:13",
  month =        feb,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2427023.2427027",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 20 16:46:13 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a novel finite element integration method
                 for low-order elements on GPUs. We achieve more than
                 100GF for element integration on first order
                 discretizations of both the Laplacian and Elasticity
                 operators on an NVIDIA GTX285, which has a nominal
                 single precision peak flop rate of 1 TF/s and bandwidth
                 of 159 GB/s, corresponding to a bandwidth limited peak
                 of 40 GF/s.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Boisvert:2013:RKB,
  author =       "Jason J. Boisvert and Paul H. Muir and Raymond J.
                 Spiteri",
  title =        "A {Runge--Kutta} {BVODE} Solver with Global Error and
                 Defect Control",
  journal =      j-TOMS,
  volume =       "39",
  number =       "2",
  pages =        "11:1--11:22",
  month =        feb,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2427023.2427028",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 20 16:46:13 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Boundary value ordinary differential equations
                 (BVODEs) are systems of ODEs with boundary conditions
                 imposed at two or more distinct points. The global
                 error (GE) of a numerical solution to a BVODE is the
                 amount by which the numerical solution differs from the
                 exact solution. The defect is the amount by which the
                 numerical solution fails to satisfy the ODEs and
                 boundary conditions. Although GE control is often
                 familiar to users, the defect controlled numerical
                 solution can be interpreted as the exact solution to a
                 perturbation of the original BVODE. Software packages
                 based on GE control and on defect control are in wide
                 use. The defect control solver, BVP_SOLVER, can provide
                 an a posteriori estimate of the GE using Richardson
                 extrapolation. In this article, we consider three more
                 strategies for GE estimation based on (i) the direct
                 use of a higher-order discretization formula (HO), (ii)
                 the use of a higher-order discretization formula within
                 a deferred correction (DC) framework, and (iii) the
                 product of an estimate of the maximum defect and an
                 estimate of the BVODE conditioning constant, and
                 demonstrate that the HO and DC approaches have superior
                 performance. We also modify BVP_SOLVER to introduce GE
                 control.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Saito:2013:VMT,
  author =       "Mutsuo Saito and Makoto Matsumoto",
  title =        "Variants of {Mersenne Twister} Suitable for Graphic
                 Processors",
  journal =      j-TOMS,
  volume =       "39",
  number =       "2",
  pages =        "12:1--12:20",
  month =        feb,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2427023.2427029",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 20 16:46:13 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article proposes a type of pseudorandom number
                 generator, Mersenne Twister for Graphic Processor
                 (MTGP), for efficient generation on graphic processing
                 units (GPUs). MTGP supports large state sizes such as
                 11213 bits, and uses the high parallelism of GPUs in
                 computing many steps of the recursion in parallel. The
                 second proposal is a parameter-set generator for MTGP,
                 named MTGP Dynamic Creator (MTGPDC). MTGPDC creates up
                 to $2^{32}$ distinct parameter sets which generate
                 sequences with high-dimensional uniformity. This
                 facility is suitable for a large grid of GPUs where
                 each GPU requires separate random number streams. MTGP
                 is based on linear recursion over the two-element
                 field, and has better high-dimensional equidistribution
                 than the Mersenne Twister pseudorandom number
                 generator.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Poulson:2013:ENF,
  author =       "Jack Poulson and Bryan Marker and Robert A. van de
                 Geijn and Jeff R. Hammond and Nichols A. Romero",
  title =        "{Elemental}: a New Framework for Distributed Memory
                 Dense Matrix Computations",
  journal =      j-TOMS,
  volume =       "39",
  number =       "2",
  pages =        "13:1--13:24",
  month =        feb,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2427023.2427030",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 20 16:46:13 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Parallelizing dense matrix computations to distributed
                 memory architectures is a well-studied subject and
                 generally considered to be among the best understood
                 domains of parallel computing. Two packages, developed
                 in the mid 1990s, still enjoy regular use: ScaLAPACK
                 and PLAPACK. With the advent of many-core
                 architectures, which may very well take the shape of
                 distributed memory architectures within a single
                 processor, these packages must be revisited since the
                 traditional MPI-based approaches will likely need to be
                 extended. Thus, this is a good time to review lessons
                 learned since the introduction of these two packages
                 and to propose a simple yet effective alternative.
                 Preliminary performance results show the new solution
                 achieves competitive, if not superior, performance on
                 large clusters.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Thompson:2013:AIG,
  author =       "Ian Thompson",
  title =        "{Algorithm 926}: Incomplete {Gamma} Functions with
                 Negative Arguments",
  journal =      j-TOMS,
  volume =       "39",
  number =       "2",
  pages =        "14:1--14:9",
  month =        feb,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2427023.2427031",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 20 16:46:13 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "An algorithm for accurately computing the lower
                 incomplete gamma function $ \gamma (a, t) $ in the case
                 where $ a = n + 1 / 2 $, $ n \in Z $ and $ t < 0 $ is
                 described. Series expansions and analytic continuation
                 are employed to compute the function for certain
                 critical values of $n$, and these results are used to
                 initiate stable recurrence. The algorithm has been
                 implemented in Fortran 2003, with precomputations
                 carried out in Maple.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cash:2013:AMC,
  author =       "J. R. Cash and D. Hollevoet and F. Mazzia and A. M.
                 Nagy",
  title =        "{Algorithm 927}: The {MATLAB} Code {{\tt bvptwp.m}}
                 for the Numerical Solution of Two Point Boundary Value
                 Problems",
  journal =      j-TOMS,
  volume =       "39",
  number =       "2",
  pages =        "15:1--15:12",
  month =        feb,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2427023.2427032",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 20 16:46:13 MST 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this article we describe the code bvptwp.m, a
                 MATLAB code for the solution of two point boundary
                 value problems. This code is based on the well-known
                 Fortran codes, twpbvp.f, twpbvpl.f and acdc.f, that
                 employ a mesh selection strategy based on the
                 estimation of the local error, and on revisions of
                 these codes, called twpbvpc.f, twpbvplc.f and acdcc.f,
                 that employ a mesh selection strategy based on the
                 estimation of the local error and the estimation of two
                 parameters which characterize the conditioning of the
                 problem. The codes twpbvp.f/tpbvpc.f use a deferred
                 correction scheme based on Mono-Implicit Runge--Kutta
                 methods (MIRK); the other codes use a deferred
                 correction scheme based on Lobatto formulas. The
                 acdc.f/acdcc.f codes implement an automatic
                 continuation strategy. The performance and features of
                 the new solver are checked by performing some numerical
                 tests to show that the new code is robust and able to
                 solve very difficult singularly perturbed problems. The
                 results obtained show that bvptwp.m is often able to
                 solve problems requiring stringent accuracies and
                 problems with very sharp changes in the solution. This
                 code, coupled with the existing boundary value codes
                 such as bvp4c.m, makes the MATLAB BVP section an
                 extremely powerful one for a very wide range of
                 problems.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ltaief:2013:HPB,
  author =       "Hatem Ltaief and Piotr Luszczek and Jack Dongarra",
  title =        "High-performance bidiagonal reduction using tile
                 algorithms on homogeneous multicore architectures",
  journal =      j-TOMS,
  volume =       "39",
  number =       "3",
  pages =        "16:1--16:22",
  month =        apr,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2450153.2450154",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 30 18:50:55 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article presents a new high-performance
                 bidiagonal reduction (BRD) for homogeneous multicore
                 architectures. This article is an extension of the
                 high-performance tridiagonal reduction implemented by
                 the same authors [Luszczek et al., IPDPS 2011] to the
                 BRD case. The BRD is the first step toward computing
                 the singular value decomposition of a matrix, which is
                 one of the most important algorithms in numerical
                 linear algebra due to its broad impact in computational
                 science. The high performance of the BRD described in
                 this article comes from the combination of four
                 important features: (1) tile algorithms with tile data
                 layout, which provide an efficient data representation
                 in main memory; (2) a two-stage reduction approach that
                 allows to cast most of the computation during the first
                 stage (reduction to band form) into calls to Level 3
                 BLAS and reduces the memory traffic during the second
                 stage (reduction from band to bidiagonal form) by using
                 high-performance kernels optimized for cache reuse; (3)
                 a data dependence translation layer that maps the
                 general algorithm with column-major data layout into
                 the tile data layout; and (4) a dynamic runtime system
                 that efficiently schedules the newly implemented
                 kernels across the processing units and ensures that
                 the data dependencies are not violated. A detailed
                 analysis is provided to understand the critical impact
                 of the tile size on the total execution time, which
                 also corresponds to the matrix bandwidth size after the
                 reduction of the first stage. The performance results
                 show a significant improvement over currently
                 established alternatives. The new high-performance BRD
                 achieves up to a 30-fold speedup on a 16-core Intel
                 Xeon machine with a 12000$ \times $ 12000 matrix size
                 against the state-of-the-art open source and commercial
                 numerical software packages, namely LAPACK, compiled
                 with optimized and multithreaded BLAS from MKL as well
                 as Intel MKL version 10.2.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Patterson:2013:EOM,
  author =       "Michael A. Patterson and Matthew Weinstein and Anil V.
                 Rao",
  title =        "An efficient overloaded method for computing
                 derivatives of mathematical functions in {MATLAB}",
  journal =      j-TOMS,
  volume =       "39",
  number =       "3",
  pages =        "17:1--17:36",
  month =        apr,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2450153.2450155",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 30 18:50:55 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "An object-oriented method is presented that computes
                 without truncation the error derivatives of functions
                 defined by MATLAB computer codes. The method implements
                 forward-mode automatic differentiation via operator
                 overloading in a manner that produces a new MATLAB code
                 that computes the derivatives of the outputs of the
                 original function with respect to the differentiation
                 variables. Because the derivative code has the same
                 input as the original function code, the method can be
                 used recursively to generate derivatives of any order
                 desired. In addition, the approach developed in this
                 article has the feature that the derivatives are
                 generated by simply evaluating the function on an
                 instance of the class, thus making the method
                 straightforward to use while simultaneously enabling
                 differentiation of highly complex functions. A detailed
                 description of the method is presented and the approach
                 is illustrated and shown to be efficient on four
                 examples.",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hammarling:2013:ACS,
  author =       "Sven Hammarling and Christopher J. Munro and
                 Fran{\c{c}}oise Tisseur",
  title =        "An algorithm for the complete solution of quadratic
                 eigenvalue problems",
  journal =      j-TOMS,
  volume =       "39",
  number =       "3",
  pages =        "18:1--18:19",
  month =        apr,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2450153.2450156",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 30 18:50:55 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We develop a new algorithm for the computation of all
                 the eigenvalues and optionally the right and left
                 eigenvectors of dense quadratic matrix polynomials. It
                 incorporates scaling of the problem parameters prior to
                 the computation of eigenvalues, a choice of
                 linearization with favorable conditioning and backward
                 stability properties, and a preprocessing step that
                 reveals and deflates the zero and infinite eigenvalues
                 contributed by singular leading and trailing matrix
                 coefficients. The algorithm is backward-stable for
                 quadratics that are not too heavily damped. Numerical
                 experiments show that our MATLAB implementation of the
                 algorithm, quadeig, outperforms the MATLAB function
                 polyeig in terms of both stability and efficiency.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bosner:2013:EGH,
  author =       "Nela Bosner and Zvonimir Bujanovi{\'c} and Zlatko
                 Drma{\v{c}}",
  title =        "Efficient generalized {Hessenberg} form and
                 applications",
  journal =      j-TOMS,
  volume =       "39",
  number =       "3",
  pages =        "19:1--19:19",
  month =        apr,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2450153.2450157",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 30 18:50:55 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article proposes an efficient algorithm for
                 reducing matrices to generalized Hessenberg form by
                 unitary similarity, and recommends using it as a
                 preprocessor in a variety of applications. To
                 illustrate its usefulness, two cases from control
                 theory are analyzed in detail: a solution procedure for
                 a sequence of shifted linear systems with multiple
                 right hand sides (e.g. evaluating the transfer function
                 of a MIMO LTI dynamical system at many points) and
                 computation of the staircase form. The proposed
                 algorithm for the generalized Hessenberg reduction uses
                 two levels of aggregation of Householder reflectors,
                 thus allowing efficient BLAS 3-based computation.
                 Another level of aggregation is introduced when solving
                 many shifted systems by processing the shifts in
                 batches. Numerical experiments confirm that the
                 proposed methods have superior efficiency.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hascoet:2013:TAD,
  author =       "Laurent Hascoet and Val{\'e}rie Pascual",
  title =        "The {Tapenade} automatic differentiation tool:
                 Principles, model, and specification",
  journal =      j-TOMS,
  volume =       "39",
  number =       "3",
  pages =        "20:1--20:43",
  month =        apr,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2450153.2450158",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 30 18:50:55 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Tapenade is an Automatic Differentiation (AD) tool
                 which, given a Fortran or C code that computes a
                 function, creates a new code that computes its tangent
                 or adjoint derivatives. Tapenade puts particular
                 emphasis on adjoint differentiation, which computes
                 gradients at a remarkably low cost. This article
                 describes the principles of Tapenade, a subset of the
                 general principles of AD. We motivate and illustrate
                 with examples the AD model of Tapenade, that is, the
                 structure of differentiated codes and the strategies
                 used to make them more efficient. Along with this
                 informal description, we formally specify this model by
                 means of data-flow equations and rules of Operational
                 Semantics, making this the reference specification of
                 the tangent and adjoint modes of Tapenade. One benefit
                 we expect from this formal specification is the
                 capacity to formally study the AD model itself,
                 especially for the adjoint mode and its sophisticated
                 strategies. This article also describes the
                 architectural choices of the implementation of
                 Tapenade. We describe the current performance of
                 Tapenade on a set of codes that include industrial-size
                 applications. We present the extensions of the tool
                 that are planned in a foreseeable future, deriving from
                 our ongoing research on AD.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rios:2013:AGP,
  author =       "Joseph Rios",
  title =        "{Algorithm 928}: a general, parallel implementation of
                 {Dantzig--Wolfe} decomposition",
  journal =      j-TOMS,
  volume =       "39",
  number =       "3",
  pages =        "21:1--21:10",
  month =        apr,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2450153.2450159",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 30 18:50:55 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Dantzig--Wolfe Decomposition is recognized as a
                 powerful, algorithmic tool for solving linear programs
                 of block-angular form. While use of the approach has
                 been reported in a wide variety of domains, there has
                 not been a general implementation of Dantzig--Wolfe
                 decomposition available. This article describes an
                 open-source implementation of the algorithm. It is
                 general in the sense that any properly decomposed
                 linear program can be provided to the software for
                 solving. While the original description of the
                 algorithm was motivated by its reduced memory usage,
                 modern computers can also take advantage of the
                 algorithm's inherent parallelism. This implementation
                 is parallel and built upon the POSIX threads (pthreads)
                 library. Some computational results are provided to
                 motivate use of such parallel solvers, as this
                 implementation outperforms state-of-the-art commercial
                 solvers in terms of wall-clock runtime by an order of
                 magnitude or more on several problem instances.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Castaldo:2013:SLP,
  author =       "Anthony M. Castaldo and R. Clint Whaley and Siju
                 Samuel",
  title =        "Scaling {LAPACK} panel operations using parallel cache
                 assignment",
  journal =      j-TOMS,
  volume =       "39",
  number =       "4",
  pages =        "22:1--22:30",
  month =        jul,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2491491.2491492",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 19 17:20:56 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In LAPACK many matrix operations are cast as block
                 algorithms which iteratively process a panel using an
                 unblocked algorithm and then update a remainder matrix
                 using the high performance Level 3 BLAS. The Level 3
                 BLAS have excellent scaling, but panel processing tends
                 to be bus bound, and thus scales with bus speed rather
                 than the number of processors ( p ). Amdahl's law
                 therefore ensures that as p grows, the panel
                 computation will become the dominant cost of these
                 LAPACK routines. Our contribution is a novel parallel
                 cache assignment approach to the panel factorization
                 which we show scales well with p. We apply this general
                 approach to the QR, QL, RQ, LQ and LU panel
                 factorizations. We show results for two commodity
                 platforms: an 8-core Intel platform and a 32-core AMD
                 platform. For both platforms and all twenty
                 implementations (five factorizations each of which is
                 available in 4 types), we present results that
                 demonstrate that our approach yields significant
                 speedup over the existing state of the art.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Khan:2013:EEC,
  author =       "Kamil A. Khan and Paul I. Barton",
  title =        "Evaluating an element of the {Clarke} generalized
                 {Jacobian} of a composite piecewise differentiable
                 function",
  journal =      j-TOMS,
  volume =       "39",
  number =       "4",
  pages =        "23:1--23:28",
  month =        jul,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2491491.2491493",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 19 17:20:56 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Bundle methods for nonsmooth optimization and
                 semismooth Newton methods for nonsmooth equation
                 solving both require computation of elements of the
                 (Clarke) generalized Jacobian, which provides slope
                 information for locally Lipschitz continuous functions.
                 Since the generalized Jacobian does not obey sharp
                 calculus rules, this computation can be difficult. In
                 this article, methods are developed for evaluating
                 generalized Jacobian elements for a nonsmooth function
                 that is expressed as a finite composition of known
                 elemental piecewise differentiable functions. In
                 principle, these elemental functions can include any
                 piecewise differentiable function whose analytical
                 directional derivatives are known. The methods are
                 fully automatable, and are shown to be computationally
                 tractable relative to the cost of a function
                 evaluation. An implementation developed in C++ is
                 discussed, and the methods are applied to several
                 example problems for illustration.",
  acknowledgement = ack-nhfb,
  articleno =    "23",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Dingle:2013:RIT,
  author =       "Nicholas J. Dingle and Nicholas J. Higham",
  title =        "Reducing the influence of tiny normwise relative
                 errors on performance profiles",
  journal =      j-TOMS,
  volume =       "39",
  number =       "4",
  pages =        "24:1--24:11",
  month =        jul,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2491491.2491494",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 19 17:20:56 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "It is a widespread but little-noticed phenomenon that
                 the normwise relative error $ || x - y || / || x || $
                 of vectors $x$ and $y$ of floating point numbers of the
                 same precision, where $y$ is an approximation to x, can
                 be many orders of magnitude smaller than the unit
                 roundoff. We analyze this phenomenon and show that in
                 the $ \infty $-norm it happens precisely when $x$ has
                 components of widely varying magnitude and every
                 component of $x$ of largest magnitude agrees with the
                 corresponding component of $y$. Performance profiles
                 are a popular way to compare competing algorithms
                 according to particular measures of performance. We
                 show that performance profiles based on normwise
                 relative errors can give a misleading impression due to
                 the influence of zero or tiny normwise relative errors.
                 We propose a transformation that reduces the influence
                 of these extreme errors in a controlled manner, while
                 preserving the monotonicity of the underlying data and
                 leaving the performance profile unchanged at its left
                 end-point. Numerical examples with both artificial and
                 genuine data illustrate the benefits of the
                 transformation.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{deDinechin:2013:ZRT,
  author =       "Florent de Dinechin and Christoph Lauter and
                 Jean-Michel Muller and Serge Torres",
  title =        "On {Ziv}'s rounding test",
  journal =      j-TOMS,
  volume =       "39",
  number =       "4",
  pages =        "25:1--25:19",
  month =        jul,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2491491.2491495",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 19 17:20:56 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A very simple test, introduced by Ziv, allows one to
                 determine if an approximation to the value f(x) of an
                 elementary function at a given point x suffices to
                 return the floating-point number nearest f(x). The same
                 test may be used when implementing floating-point
                 operations with input and output operands of different
                 formats, using arithmetic operators tailored for
                 manipulating operands of the same format. That test
                 depends on a ``magic constant'' e. We show how to
                 choose that constant e to make the test reliable and
                 efficient. Various cases are considered, depending on
                 the availability of an fma instruction, and on the
                 range of f(x).",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Russell:2013:OCG,
  author =       "Francis P. Russell and Paul H. J. Kelly",
  title =        "Optimized code generation for finite element local
                 assembly using symbolic manipulation",
  journal =      j-TOMS,
  volume =       "39",
  number =       "4",
  pages =        "26:1--26:29",
  month =        jul,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2491491.2491496",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 19 17:20:56 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Automated code generators for finite element local
                 assembly have facilitated exploration of alternative
                 implementation strategies within generated code.
                 However, even for a theoretical performance indicator
                 such as operation count, an optimal strategy for local
                 assembly is unknown. We explore a code generation
                 strategy based on symbolic integration and polynomial
                 common subexpression elimination (CSE). We present our
                 implementation of a local assembly code generator using
                 these techniques. We systematically evaluate the
                 approach, measuring operation count, execution time and
                 numerical error using a benchmark suite of synthetic
                 variational forms, comparing against the FEniCS Form
                 Compiler (FFC). Our benchmark forms span complexities
                 chosen to expose the performance characteristics of
                 different code generation approaches. We show that it
                 is possible with additional computational cost, to
                 consistently achieve much of, and sometimes
                 substantially exceed, the performance of alternative
                 approaches without compromising precision. Although the
                 approach of using symbolic integration and CSE for
                 optimizing local assembly is not new, we distinguish
                 our work through our strategies for maintaining
                 numerical precision and detecting common
                 subexpressions. We discuss the benefits of the symbolic
                 approach for inferring numerical relationships, and
                 analyze the relationship to other proposed techniques
                 which also have greater computational complexity than
                 those of FFC.",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Mehra:2013:ASW,
  author =       "Mani Mehra and Kavita Goyal",
  title =        "{Algorithm 929}: a suite on wavelet differentiation
                 algorithms",
  journal =      j-TOMS,
  volume =       "39",
  number =       "4",
  pages =        "27:1--27:28",
  month =        jul,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2491491.2491497",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 19 17:20:56 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A collection of the Matlab routines that compute the
                 values of the scaling and wavelet functions ($ \phi (x)
                 $ and $ \psi (x) $ respectively) and the derivative of
                 an arbitrary function (periodic or non periodic) using
                 wavelet bases is presented. Initially, the case of
                 Daubechies wavelets is taken and the procedure is
                 explained for both collocation and Galerkin approaches.
                 For each case a Matlab routine is provided to compute
                 the differentiation matrix and the derivative of the
                 function {$ f^{(d)} = D^{(d)} f $}. Moreover, the
                 convergence of the derivative is shown graphically as a
                 function of different parameters (the wavelet genus,
                 {$D$} and the scale, {$J$}) for two test functions. We
                 then consider the use of spline wavelets.",
  acknowledgement = ack-nhfb,
  articleno =    "27",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Davis:2013:AFO,
  author =       "Timothy A. Davis",
  title =        "{Algorithm 930}: {FACTORIZE}: an object-oriented
                 linear system solver for {MATLAB}",
  journal =      j-TOMS,
  volume =       "39",
  number =       "4",
  pages =        "28:1--28:18",
  month =        jul,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2491491.2491498",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 19 17:20:56 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The MATLAB backslash ({\tt x = A \backslash b}) is an
                 elegant and powerful interface to a suite of
                 high-performance factorization methods for the direct
                 solution of the linear system {$ A x = b $} and the
                 least-squares problem {$ \min_x || b - A x || $}. It is
                 a meta-algorithm that selects the best factorization
                 method for a particular matrix, whether sparse or
                 dense. However, the simplicity and elegance of its
                 single-character interface prohibits the reuse of its
                 factorization for subsequent systems. Requiring MATLAB
                 users to find the best factorization method on their
                 own can lead to suboptimal choices; even MATLAB experts
                 can make the wrong choice. Furthermore, naive MATLAB
                 users have a tendency to translate mathematical
                 expressions from linear algebra directly into MATLAB,
                 so that {$ x = A^{-1} b $} becomes the inferior yet
                 all-too-prevalent {\tt x = inv(A) * b}. To address
                 these issues, an object-oriented FACTORIZE method is
                 presented. Via simple-to-use operator overloading,
                 solving two linear systems can be written as {\tt F =
                 factorize(A); \tt x = F \backslash b; y= F \backslash
                 c}, where {$A$} is factorized only once. The selection
                 of the best factorization method (LU, Cholesky, {$ L D
                 L^T $}, QR, or a complete orthogonal decomposition for
                 rank-deficient matrices) is hidden from the user. The
                 mathematical expression {$ x = A^{-1} b $} directly
                 translates into the MATLAB expression {\tt x =
                 inverse(A) * b}, which does not compute the inverse at
                 all, but does the right thing by factorizing {$A$} and
                 solving the corresponding triangular systems.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gebremedhin:2013:CSG,
  author =       "Assefaw H. Gebremedhin and Duc Nguyen and Md. Mostofa
                 Ali Patwary and Alex Pothen",
  title =        "{ColPack}: Software for graph coloring and related
                 problems in scientific computing",
  journal =      j-TOMS,
  volume =       "40",
  number =       "1",
  pages =        "1:1--1:31",
  month =        sep,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2513109.2513110",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 30 16:05:58 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a suite of fast and effective algorithms,
                 encapsulated in a software package called ColPack, for
                 a variety of graph coloring and related problems. Many
                 of the coloring problems model partitioning needs
                 arising in compression-based computation of Jacobian
                 and Hessian matrices using Algorithmic Differentiation.
                 Several of the coloring problems also find important
                 applications in many areas outside derivative
                 computation, including frequency assignment in wireless
                 networks, scheduling, facility location, and
                 concurrency discovery and data movement operations in
                 parallel and distributed computing. The presentation in
                 this article includes a high-level description of the
                 various coloring algorithms within a common design
                 framework, a detailed treatment of the theory and
                 efficient implementation of known as well as new vertex
                 ordering techniques upon which the coloring algorithms
                 rely, a discussion of the package's software design,
                 and an illustration of its usage. The article also
                 includes an extensive experimental study of the major
                 algorithms in the package using real-world as well as
                 synthetically generated graphs.",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Poppe:2013:CMO,
  author =       "Koen Poppe and Ronald Cools",
  title =        "{CHEBINT}: a {MATLAB\slash Octave} toolbox for fast
                 multivariate integration and interpolation based on
                 {Chebyshev} approximations over hypercubes",
  journal =      j-TOMS,
  volume =       "40",
  number =       "1",
  pages =        "2:1--2:13",
  month =        sep,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2513109.2513111",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 30 16:05:58 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present the fast approximation of multivariate
                 functions based on Chebyshev series for two types of
                 Chebyshev lattices and show how a fast Fourier
                 transform (FFT) based discrete cosine transform (DCT)
                 can be used to reduce the complexity of this operation.
                 Approximating multivariate functions using rank-1
                 Chebyshev lattices can be seen as a one-dimensional DCT
                 while a full-rank Chebyshev lattice leads to a
                 multivariate DCT. We also present a MATLAB/Octave
                 toolbox which uses this fast algorithms to approximate
                 functions on a axis aligned hyper-rectangle. Given a
                 certain accuracy of this approximation, interpolation
                 of the original function can be achieved by evaluating
                 the approximation while the definite integral over the
                 domain can be estimated based on this Chebyshev
                 approximation. We conclude with an example for both
                 operations and actual timings of the two methods
                 presented.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gao:2013:GGA,
  author =       "Mingcen Gao and Thanh-Tung Cao and Ashwin Nanjappa and
                 Tiow-Seng Tan and Zhiyong Huang",
  title =        "{gHull}: a {GPU} algorithm for {$3$D} convex hull",
  journal =      j-TOMS,
  volume =       "40",
  number =       "1",
  pages =        "3:1--3:19",
  month =        sep,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2513109.2513112",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 30 16:05:58 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A novel algorithm is presented to compute the convex
                 hull of a point set in R$^3$ using the graphics
                 processing unit (GPU). By exploiting the relationship
                 between the Voronoi diagram and the convex hull, the
                 algorithm derives the approximation of the convex hull
                 from the former. The other extreme vertices of the
                 convex hull are then found by using a two-round
                 checking in the digital and the continuous space
                 successively. The algorithm does not need explicit
                 locking or any other concurrency control mechanism,
                 thus it can maximize the parallelism available on the
                 modern GPU. The implementation using the CUDA
                 programming model on NVIDIA GPUs is exact and
                 efficient. The experiments show that it is up to an
                 order of magnitude faster than other sequential convex
                 hull implementations running on the CPU for inputs of
                 millions of points. The works demonstrate that the GPU
                 can be used to solve nontrivial computational geometry
                 problems with significant performance benefit.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hogg:2013:PST,
  author =       "Jonathan D. Hogg and Jennifer A. Scott",
  title =        "Pivoting strategies for tough sparse indefinite
                 systems",
  journal =      j-TOMS,
  volume =       "40",
  number =       "1",
  pages =        "4:1--4:19",
  month =        sep,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2513109.2513113",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 30 16:05:58 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The performance of a sparse direct solver is dependent
                 upon the pivot sequence that is chosen before the
                 factorization begins. In the case of symmetric
                 indefinite systems, it may be necessary to modify this
                 sequence during the factorization to ensure numerical
                 stability. These modifications can have serious
                 consequences in terms of time as well as the memory and
                 flops required for the factorization and subsequent
                 solves. This study focuses on hard-to-solve sparse
                 symmetric indefinite problems for which standard
                 threshold partial pivoting leads to significant
                 modifications. We perform a detailed review of pivoting
                 strategies that are aimed at reducing the modifications
                 without compromising numerical stability. Extensive
                 numerical experiments are performed on a set of tough
                 problems arising from practical applications. Based on
                 our findings, we make recommendations on which strategy
                 to use and, in particular, a matching-based approach is
                 recommended for numerically challenging problems.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hao:2013:AAS,
  author =       "Wenrui Hao and Andrew J. Sommese and Zhonggang Zeng",
  title =        "{Algorithm 931}: an algorithm and software for
                 computing multiplicity structures at zeros of nonlinear
                 systems",
  journal =      j-TOMS,
  volume =       "40",
  number =       "1",
  pages =        "5:1--5:16",
  month =        sep,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2513109.2513114",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 30 16:05:58 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A Matlab implementation, multiplicity, of a numerical
                 algorithm for computing the multiplicity structure of a
                 nonlinear system at an isolated zero is presented. The
                 software incorporates a newly developed
                 equation-by-equation strategy that significantly
                 improves the efficiency of the closedness subspace
                 algorithm and substantially reduces the storage
                 requirement. The equation-by-equation strategy is
                 actually based on a variable-by-variable closedness
                 subspace approach. As a result, the algorithm and
                 software can handle much larger nonlinear systems and
                 higher multiplicities than their predecessors, as shown
                 in computational experiments on the included test suite
                 of benchmark problems.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gander:2013:APS,
  author =       "Martin J. Gander and Caroline Japhet",
  title =        "{Algorithm 932}: {PANG}: Software for nonmatching grid
                 projections in {$2$D} and {$3$D} with linear
                 complexity",
  journal =      j-TOMS,
  volume =       "40",
  number =       "1",
  pages =        "6:1--6:25",
  month =        sep,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2513109.2513115",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 30 16:05:58 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We design and analyze an algorithm with linear
                 complexity to perform projections between 2D and 3D
                 nonmatching grids. This algorithm, named the PANG
                 algorithm, is based on an advancing front technique and
                 neighboring information. Its implementation is
                 surprisingly short, and we give the entire Matlab code.
                 For computing the intersections, we use a direct and
                 numerically robust approach. We show numerical
                 experiments both for 2D and 3D grids, which illustrate
                 the optimal complexity and negligible overhead of the
                 algorithm. An outline of this algorithm has already
                 been presented in a short proceedings paper of the 18th
                 International Conference on Domain Decomposition
                 Methods (see Gander and Japhet [2008]).",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Foster:2013:ARC,
  author =       "Leslie V. Foster and Timothy A. Davis",
  title =        "{Algorithm 933}: Reliable calculation of numerical
                 rank, null space bases, pseudoinverse solutions, and
                 basic solutions using {suitesparseQR}",
  journal =      j-TOMS,
  volume =       "40",
  number =       "1",
  pages =        "7:1--7:23",
  month =        sep,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2513109.2513116",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 30 16:05:58 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The SPQR_RANK package contains routines that calculate
                 the numerical rank of large, sparse, numerically
                 rank-deficient matrices. The routines can also
                 calculate orthonormal bases for numerical null spaces,
                 approximate pseudoinverse solutions to least squares
                 problems involving rank-deficient matrices, and basic
                 solutions to these problems. The algorithms are based
                 on SPQR from SuiteSparseQR (ACM Transactions on
                 Mathematical Software 38, Article 8, 2011). SPQR is a
                 high-performance routine for forming QR factorizations
                 of large, sparse matrices. It returns an estimate for
                 the numerical rank that is usually, but not always,
                 correct. The new routines improve the accuracy of the
                 numerical rank calculated by SPQR and reliably
                 determine the numerical rank in the sense that, based
                 on extensive testing with matrices from applications,
                 the numerical rank is almost always accurately
                 determined when our methods report that the numerical
                 rank should be correct. Reliable determination of
                 numerical rank is critical to the other calculations in
                 the package. The routines work well for matrices with
                 either small or large null space dimensions.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Erricolo:2013:AFS,
  author =       "Danilo Erricolo and Giuseppe Carluccio",
  title =        "{Algorithm 934}: {Fortran 90} subroutines to compute
                 {Mathieu} functions for complex values of the
                 parameter",
  journal =      j-TOMS,
  volume =       "40",
  number =       "1",
  pages =        "8:1--8:19",
  month =        sep,
  year =         "2013",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2513109.2513117",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Sep 30 16:05:58 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Software to compute angular and radial Mathieu
                 functions is provided in the case that the parameter q
                 is a complex variable and the independent variable x is
                 real. After an introduction on the notation and the
                 definitions of Mathieu functions and their related
                 properties, Fortran 90 subroutines to compute them are
                 described and validated with some comparisons. A sample
                 application is also provided.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Alnaes:2014:UFL,
  author =       "Martin S. Aln{\ae}s and Anders Logg and Kristian B.
                 {\O}lgaard and Marie E. Rognes and Garth N. Wells",
  title =        "{Unified Form Language}: a domain-specific language
                 for weak formulations of partial differential
                 equations",
  journal =      j-TOMS,
  volume =       "40",
  number =       "2",
  pages =        "9:1--9:37",
  month =        feb,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2566630",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 14 06:30:41 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present the Unified Form Language (UFL), which is a
                 domain-specific language for representing weak
                 formulations of partial differential equations with a
                 view to numerical approximation. Features of UFL
                 include support for variational forms and functionals,
                 automatic differentiation of forms and expressions,
                 arbitrary function space hierarchies for multifield
                 problems, general differential operators and flexible
                 tensor algebra. With these features, UFL has been used
                 to effortlessly express finite element methods for
                 complex systems of partial differential equations in
                 near-mathematical notation, resulting in compact,
                 intuitive and readable programs. We present in this
                 work the language and its construction. An
                 implementation of UFL is freely available as an
                 open-source software library. The library generates
                 abstract syntax tree representations of variational
                 problems, which are used by other software libraries to
                 generate concrete low-level implementations. Some
                 application examples are presented and libraries that
                 support UFL are highlighted.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gower:2014:CSP,
  author =       "Robert Mansel Gower and Margarida Pinheiro Mello",
  title =        "Computing the sparsity pattern of {Hessians} using
                 automatic differentiation",
  journal =      j-TOMS,
  volume =       "40",
  number =       "2",
  pages =        "10:1--10:15",
  month =        feb,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2490254",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 14 06:30:41 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We compare two methods that calculate the sparsity
                 pattern of Hessian matrices using the computational
                 framework of automatic differentiation. The first
                 method is a forward-mode algorithm by Andrea Walther in
                 2008 which has been implemented as the driver called
                 hess\_pat in the automatic differentiation package
                 ADOL-C. The second is edge\_push\_sp, a new reverse
                 mode algorithm descended from the edge\_pushing
                 algorithm for calculating Hessians by Gower and Mello
                 in 2012. We present complexity analysis and perform
                 numerical tests for both algorithms. The results show
                 that the new reverse algorithm is very promising.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Goualard:2014:HDY,
  author =       "Fr{\'e}d{\'e}ric Goualard",
  title =        "How do you compute the midpoint of an interval?",
  journal =      j-TOMS,
  volume =       "40",
  number =       "2",
  pages =        "11:1--11:25",
  month =        feb,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2493882",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 14 06:30:41 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The algorithm that computes the midpoint of an
                 interval with floating-point bounds requires some
                 careful devising to handle all possible inputs
                 correctly. We review several implementations from
                 prominent C/C++ interval arithmetic packages and
                 analyze their potential failure to deliver the expected
                 results. We then show how to amend them to avoid common
                 pitfalls. The results presented are also relevant to
                 noninterval arithmetic computation such as the
                 implementation of bisection methods. Enough background
                 on IEEE 754 floating-point arithmetic is provided for
                 this article to serve as a practical introduction to
                 the analysis of floating-point computation.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Karlsson:2014:OPC,
  author =       "Lars Karlsson and Daniel Kressner and Bruno Lang",
  title =        "Optimally packed chains of bulges in multishift {$QR$}
                 algorithms",
  journal =      j-TOMS,
  volume =       "40",
  number =       "2",
  pages =        "12:1--12:15",
  month =        feb,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2559986",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 14 06:30:41 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The QR algorithm is the method of choice for computing
                 all eigenvalues of a dense nonsymmetric matrix A. After
                 an initial reduction to Hessenberg form, a QR iteration
                 can be viewed as chasing a small bulge from the top
                 left to the bottom right corner along the subdiagonal
                 of A. To increase data locality and create potential
                 for parallelism, modern variants of the QR algorithm
                 perform several iterations simultaneously, which
                 amounts to chasing a chain of several bulges instead of
                 a single bulge. To make effective use of level 3 BLAS,
                 it is important to pack these bulges as tightly as
                 possible within the chain. In this work, we show that
                 the tightness of the packing in existing approaches is
                 not optimal and can be increased. This directly
                 translates into a reduced chain length by 33\% compared
                 to the state-of-the-art LAPACK implementation of the QR
                 algorithm. To demonstrate the impact of our idea, we
                 have modified the LAPACK implementation to make use of
                 the optimal packing. Numerical experiments reveal a
                 uniform reduction of the execution time, without
                 affecting stability or robustness.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Romero:2014:PID,
  author =       "Eloy Romero and Jose E. Roman",
  title =        "A parallel implementation of {Davidson} methods for
                 large-scale eigenvalue problems in {SLEPc}",
  journal =      j-TOMS,
  volume =       "40",
  number =       "2",
  pages =        "13:1--13:29",
  month =        feb,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2543696",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 14 06:30:41 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In the context of large-scale eigenvalue problems,
                 methods of Davidson type such as Jacobi--Davidson can
                 be competitive with respect to other types of
                 algorithms, especially in some particularly difficult
                 situations such as computing interior eigenvalues or
                 when matrix factorization is prohibitive or highly
                 inefficient. However, these types of methods are not
                 generally available in the form of high-quality
                 parallel implementations, especially for the case of
                 non-Hermitian eigenproblems. We present our
                 implementation of various Davidson-type methods in
                 SLEPc, the Scalable Library for Eigenvalue Problem
                 Computations. The solvers incorporate many algorithmic
                 variants for subspace expansion and extraction, and
                 cover a wide range of eigenproblems including standard
                 and generalized, Hermitian and non-Hermitian, with
                 either real or complex arithmetic. We provide
                 performance results on a large battery of test
                 problems.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ratnanather:2014:ATI,
  author =       "J. Tilak Ratnanather and Jung H. Kim and Sirong Zhang
                 and Anthony M. J. Davis and Stephen K. Lucas",
  title =        "{Algorithm 935}: {{\tt IIPBF}}, a {{\tt MATLAB}}
                 toolbox for infinite integral of products of two
                 {Bessel} functions",
  journal =      j-TOMS,
  volume =       "40",
  number =       "2",
  pages =        "14:1--14:12",
  month =        feb,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2508435",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 14 06:30:41 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A {\tt MATLAB} toolbox, {\tt IIPBF}, for calculating
                 infinite integrals involving a product of two Bessel
                 functions $ J_a(\rho x) J_b(\tau x) $, $ J_a(\rho x)
                 Y_b(\tau x) $, and $ Y_a(\rho x) Y_b(\tau x) $, for
                 non-negative integers $a$, $b$, and a well-behaved
                 function $ f(x) $, is described. Based on the Lucas
                 algorithm previously developed for $ J_a(\rho x)
                 J_b(\tau x) $ only, {\tt IIPBF} recasts each product as
                 the sum of two functions whose oscillatory behavior is
                 exploited in the three-step procedure of adaptive
                 integration, summation, and extrapolation. The toolbox
                 uses customised {\tt QUADPACK} and {\tt IMSL} functions
                 from a {\tt MATLAB} conversion of the {\tt SLATEC}
                 library. In addition, {\tt MATLAB}'s own {\tt quadgk}
                 function for adaptive Gauss--Kronrod quadrature results
                 in a significant speed up compared with the original
                 algorithm. Usage of {\tt IIPBF} is described and
                 eighteen test cases illustrate the robustness of the
                 toolbox; five additional ones are used to compare {\tt
                 IIPBF} with the {\tt BESSELINT} code for rational and
                 exponential forms of $ f(x) $ with $ J_a(\rho x)
                 J_b(\tau x) $. Reliability for a broad range of values
                 of $ \rho $ and $ \tau $ for the three different
                 product types as well as different orders in one case
                 is demonstrated. An electronic appendix provides a
                 novel derivation of formulae for five cases.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Krogh:2014:AFM,
  author =       "Fred T. Krogh",
  title =        "{Algorithm 936}: a {Fortran} message processor",
  journal =      j-TOMS,
  volume =       "40",
  number =       "2",
  pages =        "15:1--15:4",
  month =        feb,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2559993",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 14 06:30:41 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Krogh:2017:RAF}.",
  abstract =     "A code is presented which offers a simple clean way to
                 get output that is very easy to read. Special support
                 is given for the output of error messages which are a
                 part of an application package or subprogram library.
                 The code uses many of the features in Fortran 2003, and
                 the ``NEWUNIT='' in an open statement from Fortran
                 2008. The latter can easily be replaced with
                 ``UNIT=99''. One goal here is to illustrate some of the
                 nice features in recent incarnations of Fortran.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Choi:2014:AMQ,
  author =       "Sou-Cheng T. Choi and Michael A. Saunders",
  title =        "{Algorithm 937}: {MINRES-QLP} for symmetric and
                 {Hermitian} linear equations and least-squares
                 problems",
  journal =      j-TOMS,
  volume =       "40",
  number =       "2",
  pages =        "16:1--16:12",
  month =        feb,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2527267",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 14 06:30:41 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe algorithm MINRES-QLP and its FORTRAN 90
                 implementation for solving symmetric or Hermitian
                 linear systems or least-squares problems. If the system
                 is singular, MINRES-QLP computes the unique
                 minimum-length solution (also known as the
                 pseudoinverse solution), which generally eludes MINRES.
                 In all cases, it overcomes a potential instability in
                 the original MINRES algorithm. A positive-definite
                 preconditioner may be supplied. Our FORTRAN 90
                 implementation illustrates a design pattern that allows
                 users to make problem data known to the solver but
                 hidden and secure from other program units. In
                 particular, we circumvent the need for reverse
                 communication. Example test programs input and solve
                 real or complex problems specified in Matrix Market
                 format. While we focus here on a FORTRAN 90
                 implementation, we also provide and maintain MATLAB
                 versions of MINRES and MINRES-QLP.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gunther:2014:ACC,
  author =       "John C. Gunther",
  title =        "{Algorithm 938}: Compressing circular buffers",
  journal =      j-TOMS,
  volume =       "40",
  number =       "2",
  pages =        "17:1--17:12",
  month =        feb,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2559995",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 14 06:30:41 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/java2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Data sequences generated by on-line sensors can become
                 arbitrarily large and must, therefore, be pared down to
                 fit into available memory. For situations where only
                 the most recent data is of interest, this problem can
                 be solved with optimal efficiency by a simple circular
                 buffer: it fills each memory location with useful data,
                 and requires just one write to memory per update. The
                 algorithm presented here provides essentially the same
                 efficiency, but while maintaining a continuously
                 updated, fixed-size, compressed representation of the
                 entire data sequence. Each value in these compressed
                 sequences represents a statistic (an average, maximum,
                 random sample, etc.) computed over a contiguous chunk
                 of the original sequence. Compressing circular buffers
                 gain their efficiency by using an alternative indexing
                 sequence, based on well-known principles of elementary
                 number theory, to ensure that each newly written value
                 gets stored in the unoccupied location created when the
                 two oldest sequential over-sampled values are
                 compressed into one. The associated Java implementation
                 supports a variety of aggregating statistics and is
                 used to compare the algorithm's performance with a more
                 obvious approach (doubling).",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Zee:2014:RTB,
  author =       "Field G. {Van Zee} and Robert A. van de Geijn and
                 Gregorio Quintana-Ort{\'\i}",
  title =        "Restructuring the Tridiagonal and Bidiagonal {QR}
                 Algorithms for Performance",
  journal =      j-TOMS,
  volume =       "40",
  number =       "3",
  pages =        "18:1--18:34",
  month =        apr,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2535371",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Apr 21 17:42:14 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We show how both the tridiagonal and bidiagonal QR
                 algorithms can be restructured so that they become rich
                 in operations that can achieve near-peak performance on
                 a modern processor. The key is a novel, cache-friendly
                 algorithm for applying multiple sets of Givens
                 rotations to the eigenvector/singular vector matrix.
                 This algorithm is then implemented with optimizations
                 that: (1) leverage vector instruction units to increase
                 floating-point throughput, and (2) fuse multiple
                 rotations to decrease the total number of memory
                 operations. We demonstrate the merits of these new QR
                 algorithms for computing the Hermitian eigenvalue
                 decomposition (EVD) and singular value decomposition
                 (SVD) of dense matrices when all eigenvectors/singular
                 vectors are computed. The approach yields vastly
                 improved performance relative to traditional QR
                 algorithms for these problems and is competitive with
                 two commonly used alternatives---Cuppen's
                 Divide-and-Conquer algorithm and the method of Multiple
                 Relatively Robust Representations---while inheriting
                 the more modest O ( n ) workspace requirements of the
                 original QR algorithms. Since the computations
                 performed by the restructured algorithms remain
                 essentially identical to those performed by the
                 original methods, robust numerical properties are
                 preserved.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Awile:2014:PWF,
  author =       "Omar Awile and Ivo F. Sbalzarini",
  title =        "A {Pthreads} Wrapper for {Fortran 2003}",
  journal =      j-TOMS,
  volume =       "40",
  number =       "3",
  pages =        "19:1--19:15",
  month =        apr,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2558889",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Apr 21 17:42:14 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/multithreading.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "With the advent of multicore processors, numerical and
                 mathematical software relies on parallelism in order to
                 benefit from hardware performance increases. We present
                 the design and use of a Fortran 2003 wrapper for POSIX
                 threads, called forthreads. Forthreads is complete in
                 the sense that is provides native Fortran 2003
                 interfaces to all pthreads routines where possible. We
                 demonstrate the use and efficiency of forthreads for
                 SIMD parallelism and task parallelism. We present
                 forthreads/MPI implementations that enable hybrid
                 shared-/distributed-memory parallelism in Fortran 2003.
                 Our benchmarks show that forthreads offers performance
                 comparable to that of OpenMP, but better thread control
                 and more freedom. We demonstrate the latter by
                 presenting a multithreaded Fortran 2003 library for
                 POSIX Internet sockets, enabling interactive numerical
                 simulations with runtime control.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gil:2014:ACM,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 939}: Computation of the {Marcum}
                 {$Q$}-Function",
  journal =      j-TOMS,
  volume =       "40",
  number =       "3",
  pages =        "20:1--20:21",
  month =        apr,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2591004",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Apr 21 17:42:14 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Methods and an algorithm for computing the generalized
                 Marcum $Q$-function $ (Q_\mu (x, y))$ and the
                 complementary function $ (P_\mu (x, y))$ are described.
                 These functions appear in problems of different
                 technical and scientific areas such as, for example,
                 radar detection and communications, statistics, and
                 probability theory, where they are called the
                 noncentral chi-square or the noncentral gamma
                 cumulative distribution functions. The algorithm for
                 computing the Marcum functions combines different
                 methods of evaluation in different regions: series
                 expansions, integral representations, asymptotic
                 expansions, and use of three-term homogeneous
                 recurrence relations. A relative accuracy close to $
                 10^{-12}$ can be obtained in the parameter region $ (x,
                 y, \mu) \in [0, A] \times [0, A] \times [1, A]$, $ A =
                 200$, while for larger parameters the accuracy
                 decreases (close to $ 10^{-11}$ for $ A = 1000$ and
                 close to $ 5 \times 10^{-11}$ for $ A = 10000$).",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Nelson:2014:AOA,
  author =       "Blake Nelson and Robert M. Kirby and Steven Parker",
  title =        "{Algorithm 940}: Optimal Accumulator-Based Expression
                 Evaluation through the Use of Expression Templates",
  journal =      j-TOMS,
  volume =       "40",
  number =       "3",
  pages =        "21:1--21:21",
  month =        apr,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2591005",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Apr 21 17:42:14 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this article we present a compile-time algorithm,
                 implemented using C++ template metaprogramming
                 techniques, that minimizes the use of temporary storage
                 when evaluating expressions. We present the basic
                 building blocks of our algorithm---transformations that
                 act locally on nodes of the expression parse tree---and
                 demonstrate that the application of these local
                 transformations generates a (nonunique) expression that
                 requires a minimum number of temporary storage objects
                 to evaluate. We discuss a C++ implementation of our
                 algorithm using expression templates, and give results
                 demonstrating the effectiveness of our approach.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kressner:2014:AHM,
  author =       "Daniel Kressner and Christine Tobler",
  title =        "{Algorithm 941}: {{\tt htucker}} --- A {Matlab}
                 Toolbox for Tensors in Hierarchical {Tucker} Format",
  journal =      j-TOMS,
  volume =       "40",
  number =       "3",
  pages =        "22:1--22:22",
  month =        apr,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2538688",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Apr 21 17:42:14 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The hierarchical Tucker format is a storage-efficient
                 scheme to approximate and represent tensors of possibly
                 high order. This article presents a Matlab toolbox,
                 along with the underlying methodology and algorithms,
                 which provides a convenient way to work with this
                 format. The toolbox not only allows for the efficient
                 storage and manipulation of tensors in hierarchical
                 Tucker format but also offers a set of tools for the
                 development of higher-level algorithms. Several
                 examples for the use of the toolbox are given.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{delaCruz:2014:ASS,
  author =       "Ra{\'u}l de la Cruz and Mauricio Araya-Polo",
  title =        "{Algorithm 942}: Semi-Stencil",
  journal =      j-TOMS,
  volume =       "40",
  number =       "3",
  pages =        "23:1--23:39",
  month =        apr,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2591006",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Apr 21 17:42:14 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Finite Difference (FD) is a widely used method to
                 solve Partial Differential Equations (PDE). PDEs are
                 the core of many simulations in different scientific
                 fields, such as geophysics, astrophysics, etc. The
                 typical FD solver performs stencil computations for the
                 entire computational domain, thus solving the
                 differential operators. In general terms, the stencil
                 computation consists of a weighted accumulation of the
                 contribution of neighbor points along the cartesian
                 axis. Therefore, optimizing stencil computations is
                 crucial in reducing the application execution time.
                 Stencil computation performance is bounded by two main
                 factors: the memory access pattern and the inefficient
                 reuse of the accessed data. We propose a novel
                 algorithm, named Semi-stencil, that tackles these two
                 problems. The main idea behind this algorithm is to
                 change the way in which the stencil computation
                 progresses within the computational domain. Instead of
                 accessing all required neighbors and adding all their
                 contributions at once, the Semi-stencil algorithm
                 divides the computation into several updates. Then,
                 each update gathers half of the axis neighbors,
                 partially computing at the same time the stencil in a
                 set of closely located points. As Semi-stencil
                 progresses through the domain, the stencil computations
                 are completed on precomputed points. This computation
                 strategy improves the memory access pattern and
                 efficiently reuses the accessed data. Our initial
                 target architecture was the Cell/B.E., where the
                 Semi-stencil in a SPE was 44\% faster than the naive
                 stencil implementation. Since then, we have continued
                 our research on emerging multicore architectures in
                 order to assess and extend this work on homogeneous
                 architectures. The experiments presented combine the
                 Semi-stencil strategy with space- and time-blocking
                 algorithms used in hierarchical memory architectures.
                 Two x86 (Intel Nehalem and AMD Opteron) and two POWER
                 (IBM POWER6 and IBM BG/P) platforms are used as
                 testbeds, where the best improvements for a 25-point
                 stencil range from 1.27 to 1.76$ \times $ faster. The
                 results show that this novel strategy is a feasible
                 optimization method which may be integrated into
                 auto-tuning frameworks. Also, since all current
                 architectures are multicore based, we have introduced a
                 brief section where scalability results on IBM POWER7-,
                 Intel Xeon-, and MIC-based systems are presented. In a
                 nutshell, the algorithm scales as well as or better
                 than other stencil techniques. For instance, the
                 scalability of Semi-stencil on MIC for a certain
                 testcase reached 93.8 $ \times $ over 244 threads.",
  acknowledgement = ack-nhfb,
  articleno =    "23",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Scott:2014:HER,
  author =       "Jennifer Scott and Miroslav Tuma",
  title =        "{HSL\_MI28}: an Efficient and Robust Limited-Memory
                 Incomplete {Cholesky} Factorization Code",
  journal =      j-TOMS,
  volume =       "40",
  number =       "4",
  pages =        "24:1--24:19",
  month =        jun,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2617555",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 2 18:28:58 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article focuses on the design and development of
                 a new robust and efficient general-purpose incomplete
                 Cholesky factorization package HSL\_MI28, which is
                 available within the HSL mathematical software library.
                 It implements a limited memory approach that exploits
                 ideas from the positive semidefinite
                 Tismenetsky-Kaporin modification scheme and, through
                 the incorporation of intermediate memory, is a
                 generalization of the widely used ICFS algorithm of Lin
                 and Mor{\'e}. Both the density of the incomplete factor
                 and the amount of memory used in its computation are
                 under the user's control. The performance of HSL\_MI28
                 is demonstrated using extensive numerical experiments
                 involving a large set of test problems arising from a
                 wide range of real-world applications. The numerical
                 experiments are used to isolate the effects of scaling,
                 ordering, and dropping strategies so as to assess their
                 usefulness in the development of robust algebraic
                 incomplete factorization preconditioners and to select
                 default settings for HSL\_MI28. They also illustrate
                 the significant advantage of employing a modest amount
                 of intermediate memory. Furthermore, the results
                 demonstrate that, with limited memory, high-quality yet
                 sparse general-purpose preconditioners are obtained.
                 Comparisons are made with ICFS, with a level-based
                 incomplete factorization code and, finally, with a
                 state-of-the-art direct solver.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kirby:2014:HPE,
  author =       "Robert C. Kirby",
  title =        "High-Performance Evaluation of Finite Element
                 Variational Forms via Commuting Diagrams and Duality",
  journal =      j-TOMS,
  volume =       "40",
  number =       "4",
  pages =        "25:1--25:24",
  month =        jun,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2559983",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 2 18:28:58 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We revisit the question of optimizing the construction
                 and application of finite element matrices. By using
                 commuting properties of the reference mappings and
                 duality, we reorganize stiffness matrix construction
                 and matrix-free application so that the bulk of the
                 work can be done by optimized matrix multiplication
                 libraries. We provide examples, including numerical
                 experiments, with the Laplace and curl-curl operators
                 as well as develop a general framework. Our techniques
                 are applicable in general geometry and are not
                 restricted to constant coefficient operators.",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hogan:2014:FRM,
  author =       "Robin J. Hogan",
  title =        "Fast Reverse-Mode Automatic Differentiation using
                 Expression Templates in {C++}",
  journal =      j-TOMS,
  volume =       "40",
  number =       "4",
  pages =        "26:1--26:16",
  month =        jun,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2560359",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 2 18:28:58 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Gradient-based optimization problems are encountered
                 in many fields, but the associated task of
                 differentiating large computer algorithms can be
                 formidable. The operator-overloading approach to
                 performing reverse-mode automatic differentiation is
                 the most convenient for the user but current
                 implementations are typically 10--35 times slower than
                 the original algorithm. In this paper a fast new
                 operator-overloading method is presented that uses the
                 expression template programming technique in C++ to
                 provide a compile-time representation of each
                 mathematical expression as a computational graph that
                 can be efficiently traversed in either direction.
                 Benchmarking with four different numerical algorithms
                 shows this approach to be 2.6--9 times faster than
                 current operator-overloading libraries, and 1.3--7.7
                 times more efficient in memory usage. It is typically
                 less than 4 times the computational cost of the
                 original algorithm, although poorer performance is
                 found for all libraries in the case of simple loops
                 containing no mathematical functions. An implementation
                 is freely available in the Adept C++ software
                 library.",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fabregat-Traver:2014:CPT,
  author =       "Diego Fabregat-Traver and Paolo Bientinesi",
  title =        "Computing Petaflops over Terabytes of Data: The Case
                 of Genome-Wide Association Studies",
  journal =      j-TOMS,
  volume =       "40",
  number =       "4",
  pages =        "27:1--27:22",
  month =        jun,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2560421",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 2 18:28:58 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In many scientific and engineering applications, one
                 has to solve not one but multiple instances of the same
                 problem. Often times, these problems are linked in a
                 way that allows intermediate results to be reused. A
                 characteristic example for this class of applications
                 is given by the Genome-Wide Association Studies (GWAS),
                 a widely spread tool in computational biology. GWAS
                 entails the solution of up to trillions (10$^{12}$ ) of
                 correlated generalized least-squares problems, posing a
                 daunting challenge: the performance of petaflops
                 (10$^{15}$ floating-point operations) over terabytes
                 (10$^{12}$ bytes) of data. In this article, we design
                 an algorithm for performing GWAS on multicore
                 architectures. This is accomplished in three steps.
                 First, we show how to exploit the relation among
                 successive problems, thus reducing the overall
                 computational complexity. Then, through an analysis of
                 the required data transfers, we identify how to
                 eliminate any overhead due to input/output operations.
                 Finally, we study how to decompose computation into
                 tasks to be distributed among the available cores, to
                 attain high performance and scalability. With our
                 algorithm, a GWAS that currently requires the use of a
                 supercomputer may now be performed in matter of hours
                 on a single multicore node. The discussion centers
                 around the methodology to develop the algorithm rather
                 than the specific application. We believe this article
                 contributes valuable guidelines of general
                 applicability for computational scientists on how to
                 develop and optimize numerical algorithms.",
  acknowledgement = ack-nhfb,
  articleno =    "27",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Erway:2014:AMM,
  author =       "Jennifer B. Erway and Roummel F. Marcia",
  title =        "Algorithm 943: {MSS}: {MATLAB} Software for {L-BFGS}
                 Trust-Region Subproblems for Large-Scale Optimization",
  journal =      j-TOMS,
  volume =       "40",
  number =       "4",
  pages =        "28:1--28:12",
  month =        jun,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2616588",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 2 18:28:58 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A MATLAB implementation of the Mor{\'e}--Sorensen
                 sequential (MSS) method is presented. The MSS method
                 computes the minimizer of a quadratic function defined
                 by a limited-memory BFGS matrix subject to a two-norm
                 trust-region constraint. This solver is an adaptation
                 of the Mor{\'e}--Sorensen direct method into an L-BFGS
                 setting for large-scale optimization. The MSS method
                 makes use of a recently proposed stable fast direct
                 method for solving large shifted BFGS systems of
                 equations [Erway and Marcia 2012; Erway et al. 2012]
                 and is able to compute solutions to any user-defined
                 accuracy. This MATLAB implementation is a matrix-free
                 iterative method for large-scale optimization.
                 Numerical experiments on the CUTEr [Bongartz et al.
                 1995; Gould et al. 2003] suggest that using the MSS
                 method as a trust-region subproblem solver can require
                 significantly fewer function and gradient evaluations
                 needed by a trust-region method as compared with the
                 Steihaug-Toint method.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Antonelli:2014:ATS,
  author =       "Laura Antonelli and Stefania Corsaro and Zelda Marino
                 and Mariarosaria Rizzardi",
  title =        "Algorithm 944: {Talbot} Suite: Parallel
                 Implementations of {Talbot}'s Method for the Numerical
                 Inversion of {Laplace} Transforms",
  journal =      j-TOMS,
  volume =       "40",
  number =       "4",
  pages =        "29:1--29:18",
  month =        jun,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2616909",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 2 18:28:58 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present Talbot Suite, a C parallel software
                 collection for the numerical inversion of Laplace
                 Transforms, based on Talbot's method. It is designed to
                 fit both single and multiple Laplace inversion
                 problems, which arise in several application and
                 research fields. In our software, we achieve high
                 accuracy and efficiency, making full use of modern
                 architectures and introducing two different levels of
                 parallelism: coarse and fine grained parallelism. They
                 offer a reasonable tradeoff between accuracy, the main
                 aspect for a few inversions, and efficiency, the main
                 aspect for multiple inversions. To take into account
                 modern high-performance computing architectures, Talbot
                 Suite provides different software versions: an
                 OpenMP-based version for shared memory machines and a
                 MPI-based version for distributed memory machines.
                 Moreover, oriented to hybrid architectures, a combined
                 MPI/OpenMP-based implementation is provided too. We
                 describe our parallel algorithms and the software
                 organization. We also report some performance results.
                 Our software includes sample programs to call the
                 Talbot Suite functions from C and from MATLAB.",
  acknowledgement = ack-nhfb,
  articleno =    "29",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Belson:2014:AMP,
  author =       "Brandt A. Belson and Jonathan H. Tu and Clarence W.
                 Rowley",
  title =        "Algorithm 945: {{\tt modred}} --- A Parallelized Model
                 Reduction Library",
  journal =      j-TOMS,
  volume =       "40",
  number =       "4",
  pages =        "30:1--30:23",
  month =        jun,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2616912",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 2 18:28:58 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We describe a new parallelized Python library for
                 model reduction, modal analysis, and system
                 identification of large systems and datasets. Our
                 library, called modred, handles a wide range of
                 problems and any data format. The modred library
                 contains implementations of the Proper Orthogonal
                 Decomposition (POD), balanced POD (BPOD)
                 Petrov--Galerkin projection, and a more efficient
                 variant of the Dynamic Mode Decomposition (DMD). The
                 library contains two implementations of these
                 algorithms, each with its own advantages. One is for
                 smaller and simpler datasets, requires minimal
                 knowledge to use, and follows a common matrix-based
                 formulation. The second, for larger and more
                 complicated datasets, preserves the abstraction of
                 vectors as elements of a vector space and, as a result,
                 allows the library to work with arbitrary data formats
                 and eases distributed memory parallelization. We also
                 include implementations of the Eigensystem Realization
                 Algorithm (ERA), and Observer/Kalman Filter
                 Identification (OKID). These methods are typically not
                 computationally demanding and are not parallelized. The
                 library is designed to be easy to use, with an
                 object-oriented design, and includes comprehensive
                 automated tests. In almost all cases, parallelization
                 is done internally so that scripts that use the
                 parallelized classes can be run in serial or in
                 parallel without any modifications.",
  acknowledgement = ack-nhfb,
  articleno =    "30",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{DAmore:2014:ARC,
  author =       "Luisa D'Amore and Rosanna Campagna and Valeria Mele
                 and Almerico Murli",
  title =        "Algorithm 946: {ReLIADiff} ---A {C++} Software Package
                 for Real {Laplace} Transform Inversion based on
                 Algorithmic Differentiation",
  journal =      j-TOMS,
  volume =       "40",
  number =       "4",
  pages =        "31:1--31:20",
  month =        jun,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2616971",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 2 18:28:58 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Algorithm 662 of the ACM TOMS library is a software
                 package, based on the Weeks method, which is used for
                 calculating function values of the inverse Laplace
                 transform. The software requires transform values at
                 arbitrary points in the complex plane. We developed a
                 software package, called ReLIADiff, which is a
                 modification of Algorithm 662 using transform values at
                 arbitrary points on real axis. ReLIADiff, implemented
                 in C++, relies on TADIFF software package designed for
                 Algorithmic Differentiation. In this article, we
                 present ReLIADiff focusing on its design principles,
                 performance, and use.",
  acknowledgement = ack-nhfb,
  articleno =    "31",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Patterson:2014:GIM,
  author =       "Michael A. Patterson and Anil V. Rao",
  title =        "{GPOPS-II}: a {MATLAB} Software for Solving
                 Multiple-Phase Optimal Control Problems Using $ h
                 p$-Adaptive {Gaussian} Quadrature Collocation Methods
                 and Sparse Nonlinear Programming",
  journal =      j-TOMS,
  volume =       "41",
  number =       "1",
  pages =        "1:1--1:37",
  month =        oct,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2558904",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 27 16:37:25 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A general-purpose MATLAB software program called
                 GPOPS--II is described for solving multiple-phase
                 optimal control problems using variable-order Gaussian
                 quadrature collocation methods. The software employs a
                 Legendre--Gauss--Radau quadrature orthogonal
                 collocation method where the continuous-time optimal
                 control problem is transcribed to a large sparse
                 nonlinear programming problem (NLP). An adaptive mesh
                 refinement method is implemented that determines the
                 number of mesh intervals and the degree of the
                 approximating polynomial within each mesh interval to
                 achieve a specified accuracy. The software can be
                 interfaced with either quasi-Newton (first derivative)
                 or Newton (second derivative) NLP solvers, and all
                 derivatives required by the NLP solver are approximated
                 using sparse finite-differencing of the optimal control
                 problem functions. The key components of the software
                 are described in detail and the utility of the software
                 is demonstrated on five optimal control problems of
                 varying complexity. The software described in this
                 article provides researchers a useful platform upon
                 which to solve a wide variety of complex constrained
                 optimal control problems.",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Mitchell:2014:CAS,
  author =       "William F. Mitchell and Marjorie A. McClain",
  title =        "A Comparison of $ h p$-Adaptive Strategies for
                 Elliptic Partial Differential Equations",
  journal =      j-TOMS,
  volume =       "41",
  number =       "1",
  pages =        "2:1--2:39",
  month =        oct,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2629459",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 27 16:37:25 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The $ h p $ version of the finite element method ($ h
                 p $ -FEM) combined with adaptive mesh refinement is a
                 particularly efficient method for solving PDEs because
                 it can achieve an exponential convergence rate in the
                 number of degrees of freedom. $ h p$-FEM allows for
                 refinement in both the element size, $h$, and the
                 polynomial degree, $p$. Like adaptive refinement for
                 the $h$ version of the finite element method, a
                 posteriori error estimates can be used to determine
                 where the mesh needs to be refined, but a single error
                 estimate cannot simultaneously determine whether it is
                 better to do the refinement by $h$ or $p$. Several
                 strategies for making this determination have been
                 proposed over the years. These strategies are
                 summarized, and the results of a numerical experiment
                 to study the performance of these strategies is
                 presented. It was found that the
                 reference-solution-based methods are very effective,
                 but also considerably more expensive, in terms of
                 computation time, than other approaches. The method
                 based on a priori knowledge is very effective when
                 there are known point singularities. The method based
                 on the decay rate of the expansion coefficients appears
                 to be the best choice as a general strategy across all
                 categories of problems, whereas many of the other
                 strategies perform well in particular situations and
                 are reasonable in general.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kim:2014:PSD,
  author =       "Kyungjoo Kim and Victor Eijkhout",
  title =        "A Parallel Sparse Direct Solver via Hierarchical {DAG}
                 Scheduling",
  journal =      j-TOMS,
  volume =       "41",
  number =       "1",
  pages =        "3:1--3:27",
  month =        oct,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2629641",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 27 16:37:25 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a parallel sparse direct solver for
                 multicore architectures based on Directed Acyclic Graph
                 (DAG) scheduling. Recently, DAG scheduling has become
                 popular in advanced Dense Linear Algebra libraries due
                 to its efficient asynchronous parallel execution of
                 tasks. However, its application to sparse matrix
                 problems is more challenging as it has to deal with an
                 enormous number of highly irregular tasks. This
                 typically results in substantial scheduling overhead
                 both in time and space, which causes overall parallel
                 performance to be suboptimal. We describe a parallel
                 solver based on two-level task parallelism: tasks are
                 first generated from a parallel tree traversal on the
                 assembly tree; next, those tasks are further refined by
                 using algorithms-by-blocks to gain fine-grained
                 parallelism. The resulting fine-grained tasks are
                 asynchronously executed after their dependencies are
                 analyzed. Our approach is distinct from others in that
                 we adopt two-level task scheduling to mirror the
                 two-level parallelism. As a result, we reduce
                 scheduling overhead, and increase efficiency and
                 flexibility. The proposed parallel sparse direct solver
                 is evaluated for the particular problems arising from
                 the $ h p$-Finite Element Method where conventional
                 sparse direct solvers do not scale well.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Seibold:2014:SSO,
  author =       "Benjamin Seibold and Martin Frank",
  title =        "{StaRMAP} --- a Second Order Staggered {Grid} Method
                 for Spherical Harmonics Moment Equations of Radiative
                 Transfer",
  journal =      j-TOMS,
  volume =       "41",
  number =       "1",
  pages =        "4:1--4:28",
  month =        oct,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2590808",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 27 16:37:25 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a simple method to solve spherical
                 harmonics moment systems, such as the time-dependent PN
                 and SPN equations, of radiative transfer. The method,
                 which works for arbitrary moment order $N$, makes use
                 of the specific coupling between the moments in the PN
                 equations. This coupling naturally induces staggered
                 grids in space and time, which in turn give rise to a
                 canonical, second-order accurate finite difference
                 scheme. While the scheme does not possess TVD or
                 realizability limiters, its simplicity allows for a
                 very efficient implementation in Matlab. We present
                 several test cases, some of which demonstrate that the
                 code solves problems with ten million degrees of
                 freedom in space, angle, and time within a few seconds.
                 The code for the numerical scheme, called StaRMAP
                 (Staggered grid Radiation Moment Approximation), along
                 with files for all presented test cases, can be
                 downloaded so that all results can be reproduced by the
                 reader.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Langr:2014:APP,
  author =       "Daniel Langr and Pavel Tvrd{\'\i}k and Tom{\'a}s
                 Dytrych and Jerry P. Draayer",
  title =        "{Algorithm 947}: {Paraperm} --- Parallel Generation of
                 Random Permutations with {MPI}",
  journal =      j-TOMS,
  volume =       "41",
  number =       "1",
  pages =        "5:1--5:26",
  month =        oct,
  year =         "2014",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2669372",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 27 16:37:25 MDT 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "An algorithm for parallel generation of a random
                 permutation of a large set of distinct integers is
                 presented. This algorithm is designed for massively
                 parallel systems with distributed memory architectures
                 and the MPI-based runtime environments. Scalability of
                 the algorithm is analyzed according to the memory and
                 communication requirements. An implementation of the
                 algorithm in a form of a software library based on the
                 C++ programming language and the MPI application
                 programming interface is further provided. Finally,
                 performed experiments are described and their results
                 discussed. The biggest of these experiments resulted in
                 a generation of a random permutation of $ 2^{41} $
                 integers in slightly more than four minutes using
                 131072 CPU cores.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Smigaj:2015:SBI,
  author =       "Wojciech {\'S}migaj and Timo Betcke and Simon Arridge
                 and Joel Phillips and Martin Schweiger",
  title =        "Solving Boundary Integral Problems with {BEM++}",
  journal =      j-TOMS,
  volume =       "41",
  number =       "2",
  pages =        "6:1--6:40",
  month =        jan,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2590830",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 4 17:49:11 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Many important partial differential equation problems
                 in homogeneous media, such as those of acoustic or
                 electromagnetic wave propagation, can be represented in
                 the form of integral equations on the boundary of the
                 domain of interest. In order to solve such problems,
                 the boundary element method (BEM) can be applied. The
                 advantage compared to domain-discretisation-based
                 methods such as finite element methods is that only a
                 discretisation of the boundary is necessary, which
                 significantly reduces the number of unknowns. Yet, BEM
                 formulations are much more difficult to implement than
                 finite element methods. In this article, we present
                 BEM++, a novel open-source library for the solution of
                 boundary integral equations for Laplace, Helmholtz and
                 Maxwell problems in three space dimensions. BEM++ is a
                 C++ library with Python bindings for all important
                 features, making it possible to integrate the library
                 into other C++ projects or to use it directly via
                 Python scripts. The internal structure and design
                 decisions for BEM++ are discussed. Several examples are
                 presented to demonstrate the performance of the library
                 for larger problems.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Muller:2015:ECC,
  author =       "Jean-Michel Muller",
  title =        "On the Error of Computing $ a b + c d $ using
                 {Cornea}, {Harrison} and {Tang}'s Method",
  journal =      j-TOMS,
  volume =       "41",
  number =       "2",
  pages =        "7:1--7:8",
  month =        jan,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2629615",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 4 17:49:11 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In their book, \booktitle{Scientific Computing on the
                 Itanium}, Cornea et al. [2002] introduce an accurate
                 algorithm for evaluating expressions of the form $ a b
                 + c d $ in binary floating-point arithmetic, assuming
                 an FMA instruction is available. They show that if $p$
                 is the precision of the floating-point format and if $
                 u = 2^{-p} $, the relative error of the result is of
                 order $u$. We improve their proof to show that the
                 relative error is bounded by $ 2 u + 7 u^2 + 6 u^3 $.
                 Furthermore, by building an example for which the
                 relative error is asymptotically (as $ p \to \infty $
                 or, equivalently, as $ u \to 0 $) equivalent to $ 2 u
                 $, we show that our error bound is asymptotically
                 optimal.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "This article compares two algorithms (Kahan's and
                 Cornea / Harrison / Tang's) for computing $ a b + c d
                 $. It shows that the worst-case error with FMA and
                 round-to-nearest arithmetic is $ 2 u $ for the first,
                 and $ 2 u + 7 u^2 + 6 u^3 $ for the second, suggesting
                 that Kahan's is preferred. However, the second
                 guarantees that $ a b + c d = = c d + a b $, whereas
                 the first does not, so it may be preferred for
                 applications like complex multiplication and division,
                 in order to guarantee commutative arithmetic",
}

@Article{Lorenz:2015:SBP,
  author =       "Dirk A. Lorenz and Marc E. Pfetsch and Andreas M.
                 Tillmann",
  title =        "Solving Basis Pursuit: Heuristic Optimality Check and
                 Solver Comparison",
  journal =      j-TOMS,
  volume =       "41",
  number =       "2",
  pages =        "8:1--8:29",
  month =        jan,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2689662",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 4 17:49:11 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The problem of finding a minimum $ l_1 $ -norm
                 solution to an underdetermined linear system is an
                 important problem in compressed sensing, where it is
                 also known as basis pursuit. We propose a heuristic
                 optimality check as a general tool for $ l_1 $
                 -minimization, which often allows for early termination
                 by ``guessing'' a primal-dual optimal pair based on an
                 approximate support. Moreover, we provide an extensive
                 numerical comparison of various state-of-the-art $ l_1
                 $ -solvers that have been proposed during the last
                 decade, on a large test set with a variety of
                 explicitly given matrices and several right-hand sides
                 per matrix reflecting different levels of solution
                 difficulty. The results, as well as improvements by the
                 proposed heuristic optimality check, are analyzed in
                 detail to provide an answer to the question which
                 algorithm is the best.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pryce:2015:DMT,
  author =       "John D. Pryce and Nedialko S. Nedialkov and Guangning
                 Tan",
  title =        "{DAESA} --- a {Matlab} Tool for Structural Analysis of
                 Differential-Algebraic Equations: Theory",
  journal =      j-TOMS,
  volume =       "41",
  number =       "2",
  pages =        "9:1--9:20",
  month =        jan,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2689664",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 4 17:49:11 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "DAESA, \underline{D}ifferential-\underline{A}lgebraic
                 \underline{E}quations \underline{S}tructural
                 \underline{A}nalyzer, is a Matlab tool for structural
                 analysis of differential-algebraic equations (DAEs). It
                 allows convenient translation of a DAE system into
                 Matlab and provides a small set of easy-to-use
                 functions. daesa can analyze systems that are fully
                 nonlinear, high-index, and of any order. It determines
                 structural index, number of degrees of freedom,
                 constraints, variables to be initialized, and suggests
                 a solution scheme. The structure of a DAE can be
                 readily visualized by this tool. It also can construct
                 a block-triangular form of the DAE, which can be
                 exploited to solve it efficiently in a block-wise
                 manner. This article describes the theory and
                 algorithms underlying the code.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Janna:2015:FSP,
  author =       "Carlo Janna and Massimiliano Ferronato and Flavio
                 Sartoretto and Giuseppe Gambolati",
  title =        "{FSAIPACK}: a Software Package for High-Performance
                 Factored Sparse Approximate Inverse Preconditioning",
  journal =      j-TOMS,
  volume =       "41",
  number =       "2",
  pages =        "10:1--10:26",
  month =        jan,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2629475",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 4 17:49:11 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The Factorized Sparse Approximate Inverse (FSAI) is an
                 efficient technique for preconditioning parallel
                 solvers of symmetric positive definite sparse linear
                 systems. The key factor controlling FSAI efficiency is
                 the identification of an appropriate nonzero pattern.
                 Currently, several strategies have been proposed for
                 building such a nonzero pattern, using both static and
                 dynamic techniques. This article describes a fresh
                 software package, called FSAIPACK, which we developed
                 for shared memory parallel machines. It collects all
                 available algorithms for computing FSAI
                 preconditioners. FSAIPACK allows for combining
                 different techniques according to any specified
                 strategy, hence enabling the user to thoroughly exploit
                 the potential of each preconditioner, in solving any
                 peculiar problem. FSAIPACK is freely available as a
                 compiled library at
                 http://www.dmsa.unipd.it/~janna/software.html, together
                 with an open-source command language interpreter. By
                 writing a command ASCII file, one can easily perform
                 and test any given strategy for building an FSAI
                 preconditioner. Numerical experiments are discussed in
                 order to highlight the FSAIPACK features and evaluate
                 its computational performance.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Si:2015:TDB,
  author =       "Hang Si",
  title =        "{TetGen}, a {Delaunay}-Based Quality Tetrahedral Mesh
                 Generator",
  journal =      j-TOMS,
  volume =       "41",
  number =       "2",
  pages =        "11:1--11:36",
  month =        jan,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2629697",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 4 17:49:11 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "TetGen is a C++ program for generating good quality
                 tetrahedral meshes aimed to support numerical methods
                 and scientific computing. The problem of quality
                 tetrahedral mesh generation is challenged by many
                 theoretical and practical issues. TetGen uses
                 Delaunay-based algorithms which have theoretical
                 guarantee of correctness. It can robustly handle
                 arbitrary complex 3D geometries and is fast in
                 practice. The source code of TetGen is freely
                 available. This article presents the essential
                 algorithms and techniques used to develop TetGen. The
                 intended audience are researchers or developers in mesh
                 generation or other related areas. It describes the key
                 software components of TetGen, including an efficient
                 tetrahedral mesh data structure, a set of enhanced
                 local mesh operations (combination of flips and edge
                 removal), and filtered exact geometric predicates. The
                 essential algorithms include incremental Delaunay
                 algorithms for inserting vertices, constrained Delaunay
                 algorithms for inserting constraints (edges and
                 triangles), a new edge recovery algorithm for
                 recovering constraints, and a new constrained Delaunay
                 refinement algorithm for adaptive quality tetrahedral
                 mesh generation. Experimental examples as well as
                 comparisons with other software are presented.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Nedialkov:2015:ADM,
  author =       "Nedialko S. Nedialkov and John D. Pryce and Guangning
                 Tan",
  title =        "Algorithm 948: {DAESA} --- a {Matlab} Tool for
                 Structural Analysis of Differential-Algebraic
                 Equations: Software",
  journal =      j-TOMS,
  volume =       "41",
  number =       "2",
  pages =        "12:1--12:14",
  month =        jan,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2700586",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 4 17:49:11 MST 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "daesa, \underline{D}ifferential-\underline{A}lgebraic
                 \underline{E}quations \underline{S}tructural
                 \underline{A}nalyzer, is a Matlab tool for structural
                 analysis of differential-algebraic equations (DAEs). It
                 allows convenient translation of a DAE system into
                 Matlab and provides a small set of easy-to-use
                 functions. daesa can analyze systems that are fully
                 nonlinear, high-index, and of any order. It determines
                 structural index, number of degrees of freedom,
                 constraints, variables to be initialized, and suggests
                 a solution scheme. The structure of a DAE can be
                 readily visualized by this tool. It can also construct
                 a block-triangular form of the DAE, which can be
                 exploited to solve it efficiently in a block-wise
                 manner.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Heroux:2015:EAT,
  author =       "Michael A. Heroux",
  title =        "Editorial: {ACM TOMS Replicated Computational Results
                 Initiative}",
  journal =      j-TOMS,
  volume =       "41",
  number =       "3",
  pages =        "13:1--13:5",
  month =        jun,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2743015",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jun 3 17:59:32 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The scientific community relies on the peer review
                 process for assuring the quality of published material,
                 the goal of which is to build a body of work we can
                 trust. Computational journals such as the ACM
                 Transactions on Mathematical Software (TOMS) use this
                 process for rigorously promoting the clarity and
                 completeness of content, and citation of prior work. At
                 the same time, it is unusual to independently confirm
                 computational results. ACM TOMS has established a
                 Replicated Computational Results (RCR) review process
                 as part of the manuscript peer review process. The
                 purpose is to provide independent confirmation that
                 results contained in a manuscript are replicable.
                 Successful completion of the RCR process awards a
                 manuscript with the Replicated Computational Results
                 Designation. This issue of ACM TOMS contains the first
                 [Van Zee and van de Geijn 2015] of what we anticipate
                 to be a growing number of articles to receive the RCR
                 designation, and the related RCR reviewer report
                 [Willenbring 2015]. We hope that the TOMS RCR process
                 will serve as a model for other publications and
                 increase the confidence in and value of computational
                 results in TOMS articles.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{VanZee:2015:RCR,
  author =       "Field G. {Van Zee} and Robert A. van de Geijn",
  title =        "Replicated Computational Results Certified {BLIS}: a
                 Framework for Rapidly Instantiating {BLAS}
                 Functionality",
  journal =      j-TOMS,
  volume =       "41",
  number =       "3",
  pages =        "14:1--14:33",
  month =        jun,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2764454",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jun 3 17:59:32 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See result replication \cite{Willenbring:2015:RCR}.",
  abstract =     "The BLAS-like Library Instantiation Software (BLIS)
                 framework is a new infrastructure for rapidly
                 instantiating Basic Linear Algebra Subprograms (BLAS)
                 functionality. Its fundamental innovation is that
                 virtually all computation within level-2
                 (matrix--vector) and level-3 (matrix--matrix) BLAS
                 operations can be expressed and optimized in terms of
                 very simple kernels. While others have had similar
                 insights, BLIS reduces the necessary kernels to what we
                 believe is the simplest set that still supports the
                 high performance that the computational science
                 community demands. Higher-level framework code is
                 generalized and implemented in ISO C99 so that it can
                 be reused and/or reparameterized for different
                 operations (and different architectures) with little to
                 no modification. Inserting high-performance kernels
                 into the framework facilitates the immediate
                 optimization of any BLAS-like operations which are cast
                 in terms of these kernels, and thus the framework acts
                 as a productivity multiplier. Users of BLAS-dependent
                 applications are given a choice of using the
                 traditional Fortran-77 BLAS interface, a generalized C
                 interface, or any other higher level interface that
                 builds upon this latter API. Preliminary performance of
                 level-2 and level-3 operations is observed to be
                 competitive with two mature open source libraries
                 (OpenBLAS and ATLAS) as well as an established
                 commercial product (Intel MKL).",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Willenbring:2015:RCR,
  author =       "James M. Willenbring",
  title =        "Replicated Computational Results {(RCR)} Report for
                 {``BLIS: a Framework for Rapidly Instantiating BLAS
                 Functionality''}",
  journal =      j-TOMS,
  volume =       "41",
  number =       "3",
  pages =        "15:1--15:4",
  month =        jun,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2738033",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jun 3 17:59:32 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{VanZee:2015:RCR}.",
  abstract =     "``BLIS: A Framework for Rapidly Instantiating BLAS
                 Functionality'' includes single-platform BLIS
                 performance results for both level-2 and level-3
                 operations that is competitive with OpenBLAS, ATLAS,
                 and Intel MKL. A detailed description of the
                 configuration used to generate the performance results
                 was provided to the reviewer by the authors. All the
                 software components used in the comparison were
                 reinstalled and new performance results were generated
                 and compared to the original results. After completing
                 this process, the published results are deemed
                 replicable by the reviewer.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pandis:2015:NID,
  author =       "Vassilis Pandis",
  title =        "Numerical Integration of Discontinuous Functions in
                 Many Dimensions",
  journal =      j-TOMS,
  volume =       "41",
  number =       "3",
  pages =        "16:1--16:7",
  month =        jun,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2629476",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jun 3 17:59:32 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We consider the problem of numerically integrating
                 functions with hyperplane discontinuities over the
                 entire Euclidean space in many dimensions. We describe
                 a simple process through which the Euclidean space is
                 partitioned into simplices on which the integrand is
                 smooth, generalising the standard practice of dividing
                 the interval used in one-dimensional problems. Our
                 procedure is combined with existing adaptive cubature
                 algorithms to significantly reduce the necessary number
                 of function evaluations and memory requirements of the
                 integrator. The method is embarrassingly parallel and
                 can be trivially scaled across many cores with
                 virtually no overhead. Our method is particularly
                 pertinent to the integration of Green's functions, a
                 problem directly related to the perturbation theory of
                 impurity models. In three spatial dimensions, we
                 observe a speed-up of order 100 which increases with
                 increasing dimensionality.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kroshko:2015:OPN,
  author =       "Andrew Kroshko and Raymond J. Spiteri",
  title =        "{odeToJava}: a {PSE} for the Numerical Solution of
                 {IVPs}",
  journal =      j-TOMS,
  volume =       "41",
  number =       "3",
  pages =        "17:1--17:33",
  month =        jun,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2641563",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jun 3 17:59:32 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/java2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Problem-solving environments (PSEs) offer a powerful
                 yet flexible and convenient means for general
                 experimentation with computational methods, algorithm
                 prototyping, and visualization and manipulation of
                 data. Consequently, PSEs have become the modus operandi
                 of many computational scientists and engineers.
                 However, despite these positive aspects, PSEs typically
                 do not offer the level of granularity required by the
                 specialist or algorithm designer to conveniently modify
                 the details. In other words, the level at which PSEs
                 are black boxes is often still too high for someone
                 interested in modifying an algorithm as opposed to
                 trying an alternative. In this article, we describe
                 odeToJava, a Java-based PSE for initial-value problems
                 in ordinary differential equations. odeToJava
                 implements explicit and linearly implicit
                 implicit-explicit Runge--Kutta methods with error and
                 stepsize control and intra-step interpolation (dense
                 output), giving the user control and flexibility over
                 the implementational aspects of these methods. We
                 illustrate the usage and functionality of odeToJava by
                 means of computational case studies of initial-value
                 problems (IVPs).",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Nelson:2015:RGH,
  author =       "Thomas Nelson and Geoffrey Belter and Jeremy G. Siek
                 and Elizabeth Jessup and Boyana Norris",
  title =        "Reliable Generation of High-Performance Matrix
                 Algebra",
  journal =      j-TOMS,
  volume =       "41",
  number =       "3",
  pages =        "18:1--18:27",
  month =        jun,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2629698",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jun 3 17:59:32 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/multithreading.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Scientific programmers often turn to vendor-tuned
                 Basic Linear Algebra Subprograms (BLAS) to obtain
                 portable high performance. However, many numerical
                 algorithms require several BLAS calls in sequence, and
                 those successive calls do not achieve optimal
                 performance. The entire sequence needs to be optimized
                 in concert. Instead of vendor-tuned BLAS, a programmer
                 could start with source code in Fortran or C (e.g.,
                 based on the Netlib BLAS) and use a state-of-the-art
                 optimizing compiler. However, our experiments show that
                 optimizing compilers often attain only one-quarter of
                 the performance of hand-optimized code. In this
                 article, we present a domain-specific compiler for
                 matrix kernels, the Build to Order BLAS (BTO), that
                 reliably achieves high performance using a scalable
                 search algorithm for choosing the best combination of
                 loop fusion, array contraction, and multithreading for
                 data parallelism. The BTO compiler generates code that
                 is between 16\% slower and 39\% faster than
                 hand-optimized code.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kowalczyk:2015:CRF,
  author =       "Piotr Kowalczyk",
  title =        "Complex Root Finding Algorithm Based on {Delaunay}
                 Triangulation",
  journal =      j-TOMS,
  volume =       "41",
  number =       "3",
  pages =        "19:1--19:13",
  month =        jun,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699457",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jun 3 17:59:32 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A simple and flexible algorithm for finding zeros of a
                 complex function is presented. An arbitrary-shaped
                 search region can be considered and a very wide class
                 of functions can be analyzed, including those
                 containing singular points or even branch cuts. The
                 proposed technique is based on sampling the function at
                 nodes of a regular or a self-adaptive mesh and on the
                 analysis of the function sign changes. As a result, a
                 set of candidate points is created, where the signs of
                 the real and imaginary parts of the function change
                 simultaneously. To verify and refine the results, an
                 iterative algorithm is applied. The validity of the
                 presented technique is supported by the results
                 obtained in numerical tests involving three different
                 types of functions.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fu:2015:AMT,
  author =       "Zhixing Fu and Luis F. Gatica and Francisco-javier
                 Sayas",
  title =        "Algorithm 949: {MATLAB} Tools for {HDG} in Three
                 Dimensions",
  journal =      j-TOMS,
  volume =       "41",
  number =       "3",
  pages =        "20:1--20:21",
  month =        jun,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2658992",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jun 3 17:59:32 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this article, we provide some MATLAB tools for
                 efficient vectorized implementation of the Hybridizable
                 Discontinuous Galerkin for linear variable coefficient
                 reaction-diffusion problems in polyhedral domains. The
                 resulting tools are modular and include enhanced
                 structures to deal with convection-diffusion problems,
                 plus several projection operators and the
                 postprocessing implementation that is necessary to
                 realize the superconvergence property of the method.
                 Loops over the elements are exclusively local and, as
                 such, have been parallelized.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Wittek:2015:ANS,
  author =       "Peter Wittek",
  title =        "Algorithm 950: {Ncpol2sdpa} --- Sparse Semidefinite
                 Programming Relaxations for Polynomial Optimization
                 Problems of Noncommuting Variables",
  journal =      j-TOMS,
  volume =       "41",
  number =       "3",
  pages =        "21:1--21:12",
  month =        jun,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699464",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jun 3 17:59:32 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A hierarchy of semidefinite programming (SDP)
                 relaxations approximates the global optimum of
                 polynomial optimization problems of noncommuting
                 variables. Generating the relaxation, however, is a
                 computationally demanding task, and only problems of
                 commuting variables have efficient generators. We
                 develop an implementation for problems of noncommuting
                 variables that creates the relaxation to be solved by
                 SDPA --- a high-performance solver that runs in a
                 distributed environment. We further exploit the
                 inherent sparsity of optimization problems in quantum
                 physics to reduce the complexity of the resulting
                 relaxations. Constrained problems with a relaxation of
                 order two may contain up to a hundred variables. The
                 implementation is available in Python. The tool helps
                 solve such as finding the ground state energy or
                 testing quantum correlations.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sosonkina:2015:RAV,
  author =       "Masha Sosonkina and Layne T. Watson and Jian He",
  title =        "Remark on Algorithm 897: {VTDIRECT95}: Serial and
                 Parallel Codes for the Global Optimization Algorithm
                 {DIRECT}",
  journal =      j-TOMS,
  volume =       "41",
  number =       "3",
  pages =        "22:1--22:2",
  month =        jun,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699459",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jun 3 17:59:32 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{He:2009:AVS}.",
  abstract =     "The Fortran95 code VTDIRECT95, based on the original
                 MPI, has been modified to use MPI-2. An option for
                 VTDIRECT95 is to divide the feasible box into
                 subdomains, and concurrently apply the global direct
                 search algorithm DIRECT within each subdomain. When the
                 number of subdomains is greater than one, a bug causes
                 VTDIRECT95 to occasionally sample outside the given
                 feasible box, which is serious if the objective
                 function is not defined outside the given box. This bug
                 has been fixed, and the sample output files have been
                 updated to reflect the correction. For completeness,
                 the package VTDIRECT95 now contains both the MPI-1
                 (with the multiple subdomain bug fixed) and the MPI-2
                 versions of the code.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Jamin:2015:CGF,
  author =       "Cl{\'e}ment Jamin and Pierre Alliez and Mariette
                 Yvinec and Jean-Daniel Boissonnat",
  title =        "{CGALmesh}: a Generic Framework for {Delaunay} Mesh
                 Generation",
  journal =      j-TOMS,
  volume =       "41",
  number =       "4",
  pages =        "23:1--23:24",
  month =        oct,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699463",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 26 17:31:15 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "CGALmesh is the mesh generation software package of
                 the Computational Geometry Algorithm Library (CGAL). It
                 generates isotropic simplicial meshes---surface
                 triangular meshes or volume tetrahedral meshes---from
                 input surfaces, 3D domains, and 3D multidomains, with
                 or without sharp features. The underlying meshing
                 algorithm relies on restricted Delaunay triangulations
                 to approximate domains and surfaces and on Delaunay
                 refinement to ensure both approximation accuracy and
                 mesh quality. CGALmesh provides guarantees on
                 approximation quality and on the size and shape of the
                 mesh elements. It provides four optional mesh
                 optimization algorithms to further improve the mesh
                 quality. A distinctive property of CGALmesh is its high
                 flexibility with respect to the input domain
                 representation. Such a flexibility is achieved through
                 a careful software design, gathering into a single
                 abstract concept, denoted by the oracle, all required
                 interface features between the meshing engine and the
                 input domain. We already provide oracles for domains
                 defined by polyhedral and implicit surfaces.",
  acknowledgement = ack-nhfb,
  articleno =    "23",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Graillat:2015:ECF,
  author =       "Stef Graillat and Christoph Lauter and Ping Tak Peter
                 Tang and Naoya Yamanaka and Shin'ichi Oishi",
  title =        "Efficient Calculations of Faithfully Rounded $
                 l_2$-Norms of $n$-Vectors",
  journal =      j-TOMS,
  volume =       "41",
  number =       "4",
  pages =        "24:1--24:20",
  month =        oct,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699469",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 26 17:31:15 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In this article, we present an efficient algorithm to
                 compute the faithful rounding of the $ l_2 $-norm of a
                 floating-point vector. This means that the result is
                 accurate to within 1 bit of the underlying
                 floating-point type. This algorithm does not generate
                 overflows or underflows spuriously, but does so when
                 the final result calls for such a numerical exception
                 to be raised. Moreover, the algorithm is well suited
                 for parallel implementation and vectorization. The
                 implementation runs up to 3 times faster than the
                 netlib version on current processors.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Dalton:2015:OSM,
  author =       "Steven Dalton and Luke Olson and Nathan Bell",
  title =        "Optimizing Sparse Matrix--Matrix Multiplication for
                 the {GPU}",
  journal =      j-TOMS,
  volume =       "41",
  number =       "4",
  pages =        "25:1--25:20",
  month =        oct,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699470",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 26 17:31:15 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Sparse matrix--matrix multiplication (SpGEMM) is a key
                 operation in numerous areas from information to the
                 physical sciences. Implementing SpGEMM efficiently on
                 throughput-oriented processors, such as the graphics
                 processing unit (GPU), requires the programmer to
                 expose substantial fine-grained parallelism while
                 conserving the limited off-chip memory bandwidth.
                 Balancing these concerns, we decompose the SpGEMM
                 operation into three highly parallel phases: expansion,
                 sorting, and contraction, and introduce a set of
                 complementary bandwidth-saving performance
                 optimizations. Our implementation is fully general and
                 our optimization strategy adaptively processes the
                 SpGEMM workload row-wise to substantially improve
                 performance by decreasing the work complexity and
                 utilizing the memory hierarchy more effectively.",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Naumann:2015:ADN,
  author =       "Uwe Naumann and Johannes Lotz and Klaus Leppkes and
                 Markus Towara",
  title =        "Algorithmic Differentiation of Numerical Methods:
                 Tangent and Adjoint Solvers for Parameterized Systems
                 of Nonlinear Equations",
  journal =      j-TOMS,
  volume =       "41",
  number =       "4",
  pages =        "26:1--26:21",
  month =        oct,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2700820",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 26 17:31:15 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We discuss software tool support for the algorithmic
                 differentiation (AD), also known as automatic
                 differentiation, of numerical simulation programs that
                 contain calls to solvers for parameterized systems of n
                 nonlinear equations. The local computational overhead
                 and the additional memory requirement for the
                 computation of directional derivatives or adjoints of
                 the solution of the nonlinear system with respect to
                 the parameters can quickly become prohibitive for large
                 values of n. Both are reduced drastically by analytical
                 (and symbolic) approaches to differentiation of the
                 underlying numerical methods. Following the discussion
                 of the proposed terminology, we develop the algorithmic
                 formalism building on prior work by other colleagues
                 and present an implementation based on the AD software
                 dco/c++. A representative case study supports the
                 theoretically obtained computational complexity results
                 with practical runtime measurements.",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Wang:2015:ACA,
  author =       "Menghan Wang and Meera Sitharam",
  title =        "Algorithm 951: {Cayley} Analysis of Mechanism
                 Configuration Spaces using {CayMos}: Software
                 Functionalities and Architecture",
  journal =      j-TOMS,
  volume =       "41",
  number =       "4",
  pages =        "27:1--27:8",
  month =        oct,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699462",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 26 17:31:15 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "For a common class of two-dimensional (2D) mechanisms
                 called 1-dof tree-decomposable linkages, we present a
                 software package, CayMos, which uses new theoretical
                 results from Sitharam and Wang [2014] and Sitharam et
                 al. [2011a, 2011b] to implement efficient algorithmic
                 solutions for (a) meaningfully representing and
                 visualizing the connected components in the Euclidean
                 realization space; (b) finding a path of continuous
                 motion between two realizations in the same connected
                 component, with or without restricting the realization
                 type (sometimes called orientation type); and (c)
                 finding two ``closest'' realizations in different
                 connected components.",
  acknowledgement = ack-nhfb,
  articleno =    "27",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Dong:2015:APL,
  author =       "Bohan Dong and Rida T. Farouki",
  title =        "Algorithm 952: {PHquintic}: a Library of Basic
                 Functions for the Construction and Analysis of Planar
                 Quintic {Pythagorean}-Hodograph Curves",
  journal =      j-TOMS,
  volume =       "41",
  number =       "4",
  pages =        "28:1--28:20",
  month =        oct,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699467",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 26 17:31:15 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The implementation of a library of basic functions for
                 the construction and analysis of planar quintic
                 Pythagorean-hodograph (PH) curves is presented using
                 the complex representation. The special algebraic
                 structure of PH curves permits exact algorithms for the
                 computation of key properties, such as arc length,
                 elastic bending energy, and offset (parallel) curves.
                 Single planar PH quintic segments are constructed as
                 interpolants to first-order Hermite data (end points
                 and derivatives), and this construction is then
                 extended to open or closed C$^2$ PH quintic spline
                 curves interpolating a sequence of points in the plane.
                 The nonlinear nature of PH curves incurs a multiplicity
                 of formal solutions to such interpolation problems, and
                 a key aspect of the algorithms is to efficiently single
                 out the unique ``good'' interpolant among them.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Granat:2015:APL,
  author =       "Robert Granat and Bo K{\aa}gstr{\"o}m and Daniel
                 Kressner and Meiyue Shao",
  title =        "Algorithm 953: Parallel Library Software for the
                 Multishift {$ Q R $} Algorithm with Aggressive Early
                 Deflation",
  journal =      j-TOMS,
  volume =       "41",
  number =       "4",
  pages =        "29:1--29:23",
  month =        oct,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699471",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 26 17:31:15 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Library software implementing a parallel small-bulge
                 multishift QR algorithm with Aggressive Early Deflation
                 (AED) targeting distributed memory high-performance
                 computing systems is presented. Starting from recent
                 developments of the parallel multishift QR algorithm
                 [Granat et al., SIAM J. Sci. Comput. 32(4), 2010], we
                 describe a number of algorithmic and implementation
                 improvements. These include communication avoiding
                 algorithms via data redistribution and a refined
                 strategy for balancing between multishift QR sweeps and
                 AED. Guidelines concerning several important tunable
                 algorithmic parameters are provided. As a result of
                 these improvements, a computational bottleneck within
                 AED has been removed in the parallel multishift QR
                 algorithm. A performance model is established to
                 explain the scalability behavior of the new parallel
                 multishift QR algorithm. Numerous computational
                 experiments confirm that our new implementation
                 significantly outperforms previous parallel
                 implementations of the QR algorithm.",
  acknowledgement = ack-nhfb,
  articleno =    "29",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Flocke:2015:AAE,
  author =       "N. Flocke",
  title =        "{Algorithm 954}: an Accurate and Efficient Cubic and
                 Quartic Equation Solver for Physical Applications",
  journal =      j-TOMS,
  volume =       "41",
  number =       "4",
  pages =        "30:1--30:24",
  month =        oct,
  year =         "2015",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699468",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 26 17:31:15 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We report on an accurate and efficient algorithm for
                 obtaining all roots of general real cubic and quartic
                 polynomials. Both the cubic and quartic solvers give
                 highly accurate roots and place no restrictions on the
                 magnitude of the polynomial coefficients. The key to
                 the algorithm is a proper rescaling of both
                 polynomials. This puts upper bounds on the magnitude of
                 the roots and is very useful in stabilizing the root
                 finding process. The cubic solver is based on dividing
                 the cubic polynomial into six classes. By analyzing the
                 root surface for each class, a fast convergent
                 Newton--Raphson starting point for a real root is
                 obtained at a cost no higher than three additions and
                 four multiplications. The quartic solver uses the cubic
                 solver in getting information about stationary points
                 and, when the quartic has real roots, stable
                 Newton--Raphson iterations give one of the extreme real
                 roots. The remaining roots follow by composite
                 deflation to a cubic. If the quartic has only complex
                 roots, the present article shows that a stable
                 Newton--Raphson iteration on a derived symmetric sixth
                 degree polynomial can be formulated for the real parts
                 of the complex roots. The imaginary parts follow by
                 solving suitable quadratics.",
  acknowledgement = ack-nhfb,
  articleno =    "30",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hogg:2016:SSI,
  author =       "Jonathan D. Hogg and Evgueni Ovtchinnikov and Jennifer
                 A. Scott",
  title =        "A Sparse Symmetric Indefinite Direct Solver for {GPU}
                 Architectures",
  journal =      j-TOMS,
  volume =       "42",
  number =       "1",
  pages =        "1:1--1:25",
  month =        feb,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2756548",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 17:07:56 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In recent years, there has been considerable interest
                 in the potential for graphics processing units (GPUs)
                 to speed up the performance of sparse direct linear
                 solvers. Efforts have focused on symmetric
                 positive-definite systems for which no pivoting is
                 required, while little progress has been reported for
                 the much harder indefinite case. We address this
                 challenge by designing and developing a sparse
                 symmetric indefinite solver SSIDS. This new
                 library-quality LDL$^T$ factorization is designed for
                 use on GPU architectures and incorporates threshold
                 partial pivoting within a multifrontal approach. Both
                 the factorize and the solve phases are performed using
                 the GPU. Another important feature is that the solver
                 produces bit-compatible results. Numerical results for
                 indefinite problems arising from a range of practical
                 applications demonstrate that, for large problems,
                 SSIDS achieves performance improvements of up to a
                 factor of 4.6 $ \times $ compared with a
                 state-of-the-art multifrontal solver on a multicore
                 CPU.",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bavier:2016:RCR,
  author =       "Eric T. Bavier",
  title =        "{Replicated Computational Results (RCR)} Report for A
                 Sparse Symmetric Indefinite Direct Solver for {GPU}
                 Architectures",
  journal =      j-TOMS,
  volume =       "42",
  number =       "1",
  pages =        "2:1--2:10",
  month =        feb,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2851489",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 17:07:56 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A Sparse Symmetric Indefinite Direct Solver for GPU
                 Architectures includes performance results and
                 comparisons of the developed GPU direct solver against
                 a CPU direct solver. New performance data were gathered
                 using software provided by the manuscript authors on
                 two new platforms and compared against the performance
                 of the MUMPS direct solver. After completing this
                 process, the published results have been deemed
                 replicable by the reviewer.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Karney:2016:SEN,
  author =       "Charles F. F. Karney",
  title =        "Sampling Exactly from the Normal Distribution",
  journal =      j-TOMS,
  volume =       "42",
  number =       "1",
  pages =        "3:1--3:14",
  month =        feb,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2710016",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 17:07:56 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compstat.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See improvement in \cite{Du:2021:IES}.",
  abstract =     "An algorithm for sampling exactly from the normal
                 distribution is given. The algorithm reads some number
                 of uniformly distributed random digits in a given base
                 and generates an initial portion of the representation
                 of a normal deviate in the same base. Thereafter,
                 uniform random digits are copied directly into the
                 representation of the normal deviate. Thus, in contrast
                 to existing methods, it is possible to generate normal
                 deviates exactly rounded to any precision with a mean
                 cost that scales linearly in the precision. The method
                 performs no extended precision arithmetic, calls no
                 transcendental functions, and uses no floating point
                 arithmetic whatsoever; it uses only simple integer
                 operations. It can easily be adapted to sample exactly
                 from the discrete normal distribution whose parameters
                 are rational numbers.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Deadman:2016:TMF,
  author =       "Edvin Deadman and Nicholas J. Higham",
  title =        "Testing Matrix Function Algorithms Using Identities",
  journal =      j-TOMS,
  volume =       "42",
  number =       "1",
  pages =        "4:1--4:15",
  month =        feb,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2723157",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65F60",
  MRnumber =     "3472420",
  bibdate =      "Tue Mar 1 17:07:56 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Algorithms for computing matrix functions are
                 typically tested by comparing the forward error with
                 the product of the condition number and the unit
                 roundoff. The forward error is computed with the aid of
                 a reference solution, typically computed at high
                 precision. An alternative approach is to use functional
                 identities such as the ``round-trip tests'' $ e^{\log
                 A} = A $ and $ (A^{1 / p})^p = A $, as are currently
                 employed in a SciPy test module. We show how a
                 linearized perturbation analysis for a functional
                 identity allows the determination of a maximum residual
                 consistent with backward stability of the constituent
                 matrix function evaluations. Comparison of this maximum
                 residual with a computed residual provides a necessary
                 test for backward stability. We also show how the
                 actual linearized backward error for these relations
                 can be computed. Our approach makes use of Fr{\'e}chet
                 derivatives and estimates of their norms. Numerical
                 experiments show that the proposed approaches are able
                 both to detect instability and to confirm stability.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kutyniok:2016:SFD,
  author =       "Gitta Kutyniok and Wang-Q Lim and Rafael Reisenhofer",
  title =        "{ShearLab $3$D}: Faithful Digital Shearlet Transforms
                 Based on Compactly Supported Shearlets",
  journal =      j-TOMS,
  volume =       "42",
  number =       "1",
  pages =        "5:1--5:42",
  month =        feb,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2740960",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 17:07:56 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Wavelets and their associated transforms are highly
                 efficient when approximating and analyzing
                 one-dimensional signals. However, multivariate signals
                 such as images or videos typically exhibit curvilinear
                 singularities, which wavelets are provably deficient in
                 sparsely approximating and also in analyzing in the
                 sense of, for instance, detecting their direction.
                 Shearlets are a directional representation system
                 extending the wavelet framework, which overcomes those
                 deficiencies. Similar to wavelets, shearlets allow a
                 faithful implementation and fast associated transforms.
                 In this article, we will introduce a comprehensive
                 carefully documented software package coined ShearLab
                 3D (www.ShearLab.org) and discuss its algorithmic
                 details. This package provides MATLAB code for a novel
                 faithful algorithmic realization of the 2D and 3D
                 shearlet transform (and their inverses) associated with
                 compactly supported universal shearlet systems
                 incorporating the option of using CUDA. We will present
                 extensive numerical experiments in 2D and 3D concerning
                 denoising, inpainting, and feature extraction,
                 comparing the performance of ShearLab 3D with similar
                 transform-based algorithms such as curvelets,
                 contourlets, or surfacelets. In the spirit of
                 reproducible research, all scripts are accessible on
                 www.ShearLab.org.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Burton:2016:PCD,
  author =       "Benjamin A. Burton and Thomas Lewiner and Jo{\~a}o
                 Paix{\~a}o and Jonathan Spreer",
  title =        "Parameterized Complexity of Discrete {Morse} Theory",
  journal =      j-TOMS,
  volume =       "42",
  number =       "1",
  pages =        "6:1--6:24",
  month =        feb,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2738034",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 17:07:56 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Optimal Morse matchings reveal essential structures of
                 cell complexes that lead to powerful tools to study
                 discrete geometrical objects, in particular, discrete
                 3-manifolds. However, such matchings are known to be
                 NP-hard to compute on 3-manifolds through a reduction
                 to the erasability problem. Here, we refine the study
                 of the complexity of problems related to discrete Morse
                 theory in terms of parameterized complexity. On the one
                 hand, we prove that the erasability problem is W [ P
                 ]-complete on the natural parameter. On the other hand,
                 we propose an algorithm for computing optimal Morse
                 matchings on triangulations of 3-manifolds, which is
                 fixed-parameter tractable in the treewidth of the
                 bipartite graph representing the adjacency of the 1-
                 and 2-simplices. This algorithm also shows
                 fixed-parameter tractability for problems such as
                 erasability and maximum alternating cycle-free
                 matching. We further show that these results are also
                 true when the treewidth of the dual graph of the
                 triangulated 3-manifold is bounded. Finally, we discuss
                 the topological significance of the chosen parameters
                 and investigate the respective treewidths of simplicial
                 and generalized triangulations of 3-manifolds.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Giles:2016:AAI,
  author =       "Michael B. Giles",
  title =        "Algorithm 955: Approximation of the Inverse {Poisson}
                 Cumulative Distribution Function",
  journal =      j-TOMS,
  volume =       "42",
  number =       "1",
  pages =        "7:1--7:22",
  month =        feb,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699466",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 17:07:56 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "New approximations for the inverse of the incomplete
                 gamma function are derived, which are used to develop
                 efficient evaluations of the inverse Poisson cumulative
                 distribution function. An asymptotic approximation
                 based on the standard Normal approximation is
                 particularly good for CPUs with MIMD cores, while for
                 GPUs and other hardware with vector units, a second
                 asymptotic approximation based on Temme's approximation
                 of the incomplete gamma function is more efficient due
                 to conditional branching within each vector. The
                 accuracy and efficiency of the software implementations
                 is assessed on both CPUs and GPUs.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Aruliah:2016:APP,
  author =       "D. A. Aruliah and Lennaert {Van Veen} and Alex
                 Dubitski",
  title =        "Algorithm 956: {PAMPAC}, A Parallel Adaptive Method
                 for Pseudo-Arclength Continuation",
  journal =      j-TOMS,
  volume =       "42",
  number =       "1",
  pages =        "8:1--8:18",
  month =        feb,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2714570",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 17:07:56 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Pseudo-arclength continuation is a well-established
                 method for generating a numerical curve approximating
                 the solution of an underdetermined system of nonlinear
                 equations. It is an inherently sequential
                 predictor-corrector method in which new approximate
                 solutions are extrapolated from previously converged
                 results and then iteratively refined. Convergence of
                 the iterative corrections is guaranteed only for
                 sufficiently small prediction steps. In
                 high-dimensional systems, corrector steps are extremely
                 costly to compute and the prediction step length must
                 be adapted carefully to avoid failed steps or
                 unnecessarily slow progress. We describe a parallel
                 method for adapting the step length employing several
                 predictor-corrector sequences of different step lengths
                 computed concurrently. In addition, the algorithm
                 permits intermediate results of correction sequences
                 that have not converged to seed new predictions. This
                 strategy results in an aggressive optimization of the
                 step length at the cost of redundancy in the concurrent
                 computation. We present two examples of convoluted
                 solution curves of high-dimensional systems showing
                 that speed-up by a factor of two can be attained on a
                 multicore CPU while a factor of three is attainable on
                 a small cluster.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gautschi:2016:AER,
  author =       "Walter Gautschi",
  title =        "Algorithm 957: Evaluation of the Repeated Integral of
                 the Coerror Function by Half-Range {Gauss--Hermite}
                 Quadrature",
  journal =      j-TOMS,
  volume =       "42",
  number =       "1",
  pages =        "9:1--9:10",
  month =        feb,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2735626",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 17:07:56 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Nonstandard Gaussian quadrature is applied to evaluate
                 the repeated integral $ i^n \erfc x $ of the coerror
                 function for $ n \in N_0 $, $ x \in R $ in an
                 appropriate domain of the $ (n, x)$-plane. Relevant
                 software in MATLAB is provided: in particular, two
                 routines evaluating the function to an accuracy of 12
                 respective 30-decimal digits.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Novoselsky:2016:RAD,
  author =       "Alexander Novoselsky and Eugene Kagan",
  title =        "Remark on {``Algorithm 673: Dynamic Huffman
                 Coding''}",
  journal =      j-TOMS,
  volume =       "42",
  number =       "1",
  pages =        "10:1--10:1",
  month =        feb,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2740959",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 1 17:07:56 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Vitter:1989:ADH}.",
  abstract =     "This remark presents a correction to Algorithm 673
                 (dynamic Huffman coding) [Vitter 1989] and its
                 translation to MATLAB.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Weinstein:2016:STO,
  author =       "Matthew J. Weinstein and Anil V. Rao",
  title =        "A Source Transformation via Operator Overloading
                 Method for the Automatic Differentiation of
                 Mathematical Functions in {MATLAB}",
  journal =      j-TOMS,
  volume =       "42",
  number =       "2",
  pages =        "11:1--11:42",
  month =        jun,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2699456",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 3 18:52:21 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A source transformation via operator overloading
                 method is presented for computing derivatives of
                 mathematical functions defined by MATLAB computer
                 programs. The transformed derivative code that results
                 from the method of this article computes a sparse
                 representation of the derivative of the function
                 defined in the original code. As in all source
                 transformation automatic differentiation techniques, an
                 important feature of the method is that any flow
                 control in the original function code is preserved in
                 the derivative code. Furthermore, the resulting
                 derivative code relies solely upon the native MATLAB
                 library. The method is useful in applications where it
                 is required to repeatedly evaluate the derivative of
                 the original function. The approach is demonstrated on
                 several examples and is found to be highly efficient
                 when compared to well-known MATLAB automatic
                 differentiation programs.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{VanZee:2016:BFE,
  author =       "Field G. {Van Zee} and Tyler M. Smith and Bryan Marker
                 and Tze Meng Low and Robert A. {Van De Geijn} and
                 Francisco D. Igual and Mikhail Smelyanskiy and Xianyi
                 Zhang and Michael Kistler and Vernon Austel and John
                 A. Gunnels and Lee Killough",
  title =        "The {BLIS} Framework: Experiments in Portability",
  journal =      j-TOMS,
  volume =       "42",
  number =       "2",
  pages =        "12:1--12:19",
  month =        jun,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2755561",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 3 18:52:21 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/multithreading.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "BLIS is a new software framework for instantiating
                 high-performance BLAS-like dense linear algebra
                 libraries. We demonstrate how BLIS acts as a
                 productivity multiplier by using it to implement the
                 level-3 BLAS on a variety of current architectures. The
                 systems for which we demonstrate the framework include
                 state-of-the-art general-purpose, low-power, and
                 many-core architectures. We show, with very little
                 effort, how the BLIS framework yields sequential and
                 parallel implementations that are competitive with the
                 performance of ATLAS, OpenBLAS (an effort to maintain
                 and extend the GotoBLAS), and commercial vendor
                 implementations such as AMD's ACML, IBM's ESSL, and
                 Intel's MKL libraries. Although most of this article
                 focuses on single-core implementation, we also provide
                 compelling results that suggest the framework's
                 leverage extends to the multithreaded domain.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Mei:2016:CDC,
  author =       "Yi Mei and Mohammad Nabi Omidvar and Xiaodong Li and
                 Xin Yao",
  title =        "A Competitive Divide-and-Conquer Algorithm for
                 Unconstrained Large-Scale Black-Box Optimization",
  journal =      j-TOMS,
  volume =       "42",
  number =       "2",
  pages =        "13:1--13:24",
  month =        jun,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2791291",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 3 18:52:21 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article proposes a competitive divide-and-conquer
                 algorithm for solving large-scale black-box
                 optimization problems for which there are thousands of
                 decision variables and the algebraic models of the
                 problems are unavailable. We focus on problems that are
                 partially additively separable, since this type of
                 problem can be further decomposed into a number of
                 smaller independent subproblems. The proposed algorithm
                 addresses two important issues in solving large-scale
                 black-box optimization: (1) the identification of the
                 independent subproblems without explicitly knowing the
                 formula of the objective function and (2) the
                 optimization of the identified black-box subproblems.
                 First, a Global Differential Grouping (GDG) method is
                 proposed to identify the independent subproblems. Then,
                 a variant of the Covariance Matrix Adaptation Evolution
                 Strategy (CMA-ES) is adopted to solve the subproblems
                 resulting from its rotation invariance property. GDG
                 and CMA-ES work together under the cooperative
                 co-evolution framework. The resultant algorithm, named
                 CC-GDG-CMAES, is then evaluated on the CEC'2010
                 large-scale global optimization (LSGO) benchmark
                 functions, which have a thousand decision variables and
                 black-box objective functions. The experimental results
                 show that, on most test functions evaluated in this
                 study, GDG manages to obtain an ideal partition of the
                 index set of the decision variables, and CC-GDG-CMAES
                 outperforms the state-of-the-art results. Moreover, the
                 competitive performance of the well-known CMA-ES is
                 extended from low-dimensional to high-dimensional
                 black-box problems.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sayed:2016:WCR,
  author =       "Wafaa S. Sayed and Hossam A. H. Fahmy",
  title =        "What are the Correct Results for the Special Values of
                 the Operands of the Power Operation?",
  journal =      j-TOMS,
  volume =       "42",
  number =       "2",
  pages =        "14:1--14:17",
  month =        jun,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2809783",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 3 18:52:21 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Language standards such as C99 and C11, as well as the
                 IEEE Standard for Floating-Point Arithmetic 754 (IEEE
                 Std 754-2008) specify the expected behavior of binary
                 and decimal floating-point arithmetic in
                 computer-programming environments and the handling of
                 special values and exception conditions. Many
                 researchers focus on verifying the compliance of
                 implementations for binary and decimal floating-point
                 operations with these standards. In this article, we
                 are concerned with the special values of the operands
                 of the power function Z = X$^Y$. We study how the
                 standards define the correct results for this
                 operation, propose a mathematically justified
                 definition for the correct results of the power
                 function on the occurrence of these special values as
                 its operands, test how different software
                 implementations for the power function deal with these
                 special values, and classify the behavior of different
                 programming languages from the viewpoint of how much
                 they conform to the standards and our proposed
                 mathematical definition. We present inconsistencies
                 between the implementations and the standards, and
                 discuss incompatibilities between different versions of
                 the same software.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lecuyer:2016:ALB,
  author =       "Pierre L'Ecuyer and David Munger",
  title =        "{Algorithm 958}: {Lattice Builder}: a General Software
                 Tool for Constructing Rank-1 Lattice Rules",
  journal =      j-TOMS,
  volume =       "42",
  number =       "2",
  pages =        "15:1--15:30",
  month =        jun,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2754929",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 3 18:52:21 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We introduce a new software tool and library named
                 Lattice Builder, written in C++, that implements a
                 variety of construction algorithms for good rank-1
                 lattice rules. It supports exhaustive and random
                 searches, as well as component-by-component (CBC) and
                 random CBC constructions, for any number of points, and
                 for various measures of (non)uniformity of the points.
                 The measures currently implemented are all
                 shift-invariant and represent the worst-case
                 integration error for certain classes of integrands.
                 They include, for example, the weighted P $ \alpha $
                 square discrepancy, the R $ \alpha $ criterion, and
                 figures of merit based on the spectral test, with
                 projection-dependent weights. Each of these measures
                 can be computed as a finite sum. For the P $ \alpha $
                 and R $ \alpha $ criteria, efficient specializations of
                 the CBC algorithm are provided for
                 projection-dependent, order-dependent, and product
                 weights. For numbers of points that are integer powers
                 of a prime base, the construction of embedded rank-1
                 lattice rules is supported through any of these
                 algorithms, and through a fast CBC algorithm, with a
                 variety of possibilities for the normalization of the
                 merit values of individual embedded levels and for
                 their combination into a single merit value. The
                 library is extensible, thanks to the decomposition of
                 the algorithms into decoupled components, which makes
                 it easy to implement new types of weights, new search
                 domains, new figures of merit, and so on.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Alvarez-Cubero:2016:AVL,
  author =       "Jos{\'e} Antonio {\'A}lvarez-Cubero and Pedro J.
                 Zufiria",
  title =        "{Algorithm 959}: {VBF}: a Library of {C++} Classes for
                 Vector {Boolean} Functions in Cryptography",
  journal =      j-TOMS,
  volume =       "42",
  number =       "2",
  pages =        "16:1--16:22",
  month =        may,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2794077",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 23 16:40:02 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/hash.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "VBF is a collection of C++ classes designed for
                 analyzing vector Boolean functions (functions that map
                 a Boolean vector to another Boolean vector) from a
                 cryptographic perspective. This implementation uses the
                 NTL library from Victor Shoup, adding new modules that
                 call NTL functions and complement the existing ones,
                 making it better suited to cryptography. The class
                 representing a vector Boolean function can be
                 initialized by several alternative types of data
                 structures such as Truth Table, Trace Representation,
                 and Algebraic Normal Form (ANF), among others. The most
                 relevant cryptographic criteria for both block and
                 stream ciphers as well as for hash functions can be
                 evaluated with VBF: it obtains the nonlinearity,
                 linearity distance, algebraic degree, linear
                 structures, and frequency distribution of the absolute
                 values of the Walsh Spectrum or the Autocorrelation
                 Spectrum, among others. In addition, operations such as
                 equality testing, composition, inversion, sum, direct
                 sum, bricklayering (parallel application of vector
                 Boolean functions as employed in Rijndael cipher), and
                 adding coordinate functions of two vector Boolean
                 functions are presented. Finally, three real
                 applications of the library are described: the first
                 one analyzes the KASUMI block cipher, the second one
                 analyzes the Mini-AES cipher, and the third one finds
                 Boolean functions with very high nonlinearity, a key
                 property for robustness against linear attacks.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ibanez:2016:PPU,
  author =       "Daniel A. Ibanez and E. Seegyoung Seol and Cameron W.
                 Smith and Mark S. Shephard",
  title =        "{PUMI}: Parallel Unstructured Mesh Infrastructure",
  journal =      j-TOMS,
  volume =       "42",
  number =       "3",
  pages =        "17:1--17:28",
  month =        may,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2814935",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 23 16:40:02 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The Parallel Unstructured Mesh Infrastructure (PUMI)
                 is designed to support the representation of, and
                 operations on, unstructured meshes as needed for the
                 execution of mesh-based simulations on massively
                 parallel computers. In PUMI, the mesh representation is
                 complete in the sense of being able to provide any
                 adjacency of mesh entities of multiple topologies in
                 O(1) time, and fully distributed to support
                 relationships of mesh entities across multiple memory
                 spaces in a manner consistent with supporting massively
                 parallel simulation workflows. PUMI's mesh maintains
                 links to the high-level model definition in terms of a
                 model topology as produced by CAD systems, and is
                 specifically designed to efficiently support evolving
                 meshes as required for mesh generation and adaptation.
                 To support the needs of parallel unstructured mesh
                 simulations, PUMI also supports a specific set of
                 services such as the migration of mesh entities between
                 parts while maintaining the mesh adjacencies,
                 maintaining read-only mesh entity copies from
                 neighboring parts (ghosting), repartitioning parts as
                 the mesh evolves, and dynamic mesh load balancing. Here
                 we present the overall design, software structures,
                 example programs, and performance results. The
                 effectiveness of PUMI is demonstrated by its
                 applications to massively parallel adaptive simulation
                 workflows.",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Abdelfattah:2016:KOL,
  author =       "Ahmad Abdelfattah and David Keyes and Hatem Ltaief",
  title =        "{KBLAS}: an Optimized Library for Dense Matrix-Vector
                 Multiplication on {GPU} Accelerators",
  journal =      j-TOMS,
  volume =       "42",
  number =       "3",
  pages =        "18:1--18:31",
  month =        may,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2818311",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 23 16:40:02 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "KBLAS is an open-source, high-performance library that
                 provides optimized kernels for a subset of Level 2 BLAS
                 functionalities on CUDA-enabled GPUs. Since performance
                 of dense matrix-vector multiplication is hindered by
                 the overhead of memory accesses, a double-buffering
                 optimization technique is employed to overlap data
                 motion with computation. After identifying a proper set
                 of tuning parameters, KBLAS efficiently runs on various
                 GPU architectures while avoiding code rewriting and
                 retaining compliance with the standard BLAS API.
                 Another optimization technique allows ensuring
                 coalesced memory access when dealing with submatrices,
                 especially for high-level dense linear algebra
                 algorithms. All KBLAS kernels have been leveraged to a
                 multi-GPU environment, which requires the introduction
                 of new APIs. Considering general matrices, KBLAS is
                 very competitive with existing state-of-the-art kernels
                 and provides a smoother performance across a wide range
                 of matrix dimensions. Considering symmetric and
                 Hermitian matrices, the KBLAS performance outperforms
                 existing state-of-the-art implementations on all matrix
                 sizes and achieves asymptotically up to 50\% and 60\%
                 speedup against the best competitor on single GPU and
                 multi-GPUs systems, respectively. Performance results
                 also validate our performance model. A subset of KBLAS
                 high-performance kernels have been integrated into
                 NVIDIA's standard BLAS implementation (cuBLAS) for
                 larger dissemination, starting from version 6.0.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Jeannerod:2016:RIE,
  author =       "Claude-Pierre Jeannerod",
  title =        "A Radix-Independent Error Analysis of the
                 {Cornea--Harrison--Tang} Method",
  journal =      j-TOMS,
  volume =       "42",
  number =       "3",
  pages =        "19:1--19:20",
  month =        may,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2824252",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 23 16:40:02 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Assuming floating-point arithmetic with a fused
                 multiply-add operation and rounding to nearest, the
                 Cornea--Harrison--Tang method aims to evaluate
                 expressions of the form $ a b + c d $ with high
                 relative accuracy. In this article, we provide a
                 rounding error analysis of this method, which unlike
                 previous studies is not restricted to binary
                 floating-point arithmetic but holds for any radix $
                 \beta $. We show first that an asymptotically optimal
                 bound on the relative error of this method is $ 2 \beta
                 u + 2 u^2 / \beta - 2 u^2 = 2 u + 2 / \beta u^2 + O
                 (u^3) $, where $ u = 1 / 2 \beta^{1 - p} $ is the unit
                 roundoff in radix $ \beta $ and precision $p$. Then we
                 show that the possibility of removing the $ O (u^2)$
                 term from this bound is governed by the radix parity
                 and the tie-breaking strategy used for rounding: if $
                 \beta $ is odd or rounding is to nearest even, then the
                 simpler bound $ 2 u$ is obtained, while if $ \beta $ is
                 even and rounding is to nearest away, then there exist
                 floating-point inputs $a$, $b$, $c$, $d$ that lead to a
                 relative error larger than $ 2 u + 2 / \beta u^2 - 4
                 u^3$. All these results hold provided underflows and
                 overflows do not occur and under some mild assumptions
                 on $p$ satisfied by IEEE 754-2008 formats.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Boyer:2016:MMW,
  author =       "Brice Boyer and Jean-Guillaume Dumas",
  title =        "Matrix Multiplication Over Word-Size Modular Rings
                 Using Approximate Formulas",
  journal =      j-TOMS,
  volume =       "42",
  number =       "3",
  pages =        "20:1--20:12",
  month =        jun,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2829947",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 4 10:55:03 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=2829947",
  abstract =     "Bini--Capovani--Lotti--Romani approximate formula (or
                 border rank) for matrix multiplication achieves a
                 better complexity than Strassen's matrix multiplication
                 formula. In this article, we show a novel way to use
                 the approximate formula in the special case where the
                 ring is $ \mathbb {Z} / p \mathbb {Z} $. In addition,
                 we show an implementation {\`a} la FFLAS--FFPACK, where
                 $p$ is a word-size modulo, that improves on
                 state-of-the-art $ \mathbb {Z} / p \mathbb {Z}$ matrix
                 multiplication implementations.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Wang:2016:PGM,
  author =       "Shen Wang and Xiaoye S. Li and Fran{\c{c}}ois-Henry
                 Rouet and Jianlin Xia and Maarten V. {De Hoop}",
  title =        "A Parallel Geometric Multifrontal Solver Using
                 Hierarchically Semiseparable Structure",
  journal =      j-TOMS,
  volume =       "42",
  number =       "3",
  pages =        "21:1--21:21",
  month =        may,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2830569",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 23 16:40:02 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a structured parallel geometry-based
                 multifrontal sparse solver using hierarchically
                 semiseparable (HSS) representations and exploiting the
                 inherent low-rank structures. Parallel strategies for
                 nested dissection ordering (taking low rankness into
                 account), symbolic factorization, and structured
                 numerical factorization are shown. In particular, we
                 demonstrate how to manage two layers of tree
                 parallelism to integrate parallel HSS operations within
                 the parallel multifrontal sparse factorization. Such a
                 structured multifrontal factorization algorithm can be
                 shown to have asymptotically lower complexities in both
                 operation counts and memory than the conventional
                 factorization algorithms for certain partial
                 differential equations. We present numerical results
                 from the solution of the anisotropic Helmholtz
                 equations for seismic imaging, and demonstrate that our
                 new solver was able to solve 3D problems up to 600$^3$
                 mesh size, with 216M degrees of freedom in the linear
                 system. For this specific model problem, our solver is
                 both faster and more memory efficient than a
                 geometry-based multifrontal solver (which is further
                 faster than general-purpose algebraic solvers such as
                 MUMPS and SuperLU_DIST). For the 600$^3$ mesh size, the
                 structured factors from our solver need about 5.9 times
                 less memory.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Davis:2016:EHA,
  author =       "Timothy A. Davis and William W. Hager and James T.
                 Hungerford",
  title =        "An Efficient Hybrid Algorithm for the Separable Convex
                 Quadratic Knapsack Problem",
  journal =      j-TOMS,
  volume =       "42",
  number =       "3",
  pages =        "22:1--22:25",
  month =        may,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2828635",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 23 16:40:02 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article considers the problem of minimizing a
                 convex, separable quadratic function subject to a
                 knapsack constraint and a box constraint. An algorithm
                 called NAPHEAP has been developed to solve this
                 problem. The algorithm solves the Karush--Kuhn--Tucker
                 system using a starting guess to the optimal Lagrange
                 multiplier and updating the guess monotonically in the
                 direction of the solution. The starting guess is
                 computed using the variable fixing method or is
                 supplied by the user. A key innovation in our algorithm
                 is the implementation of a heap data structure for
                 storing the break points of the dual function and
                 computing the solution of the dual problem. Also, a new
                 version of the variable fixing algorithm is developed
                 that is convergent even when the objective Hessian is
                 not strictly positive definite. The hybrid algorithm
                 NAPHEAP that uses a Newton-type method (variable fixing
                 method, secant method, or Newton's method) to bracket a
                 root, followed by a heap-based monotone break point
                 search, can be faster than a Newton-type method by
                 itself, as demonstrated in the numerical experiments.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Delgado:2016:APO,
  author =       "Jorge Delgado and Juan Manuel Pe{\~n}a",
  title =        "{Algorithm 960}: {POLYNOMIAL}: an Object-Oriented
                 {Matlab} Library of Fast and Efficient Algorithms for
                 Polynomials",
  journal =      j-TOMS,
  volume =       "42",
  number =       "3",
  pages =        "23:1--23:19",
  month =        may,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2814567",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 23 16:40:02 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The design and implementation of a Matlab
                 object-oriented software library for working with
                 polynomials is presented. The construction and
                 evaluation of polynomials in Bernstein form are
                 motivated and justified. Efficient constructions for
                 the coefficients of a polynomial in Bernstein form when
                 the polynomial is not given with this representation
                 are provided. The presented adaptive evaluation
                 algorithm uses the VS (Volk and Schumaker) algorithm,
                 the de Casteljau algorithm, and a compensated VS
                 algorithm. In addition, we have completed the library
                 with other algorithms to perform other usual operations
                 with polynomials in Bernstein form.",
  acknowledgement = ack-nhfb,
  articleno =    "23",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Benner:2016:AFS,
  author =       "Peter Benner and Vasile Sima and Matthias Voigt",
  title =        "{Algorithm 961}: {Fortran 77} Subroutines for the
                 Solution of Skew-{Hamiltonian\slash Hamiltonian}
                 Eigenproblems",
  journal =      j-TOMS,
  volume =       "42",
  number =       "3",
  pages =        "24:1--24:26",
  month =        may,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2818313",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 23 16:40:02 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Skew-Hamiltonian/Hamiltonian matrix pencils $ \lambda
                 S - H $ appear in many applications, including
                 linear-quadratic optimal control problems, $ H_\infty
                 $-optimization, certain multibody systems, and many
                 other areas in applied mathematics, physics, and
                 chemistry. In these applications it is necessary to
                 compute certain eigenvalues and/or corresponding
                 deflating subspaces of these matrix pencils. Recently
                 developed methods exploit and preserve the
                 skew-Hamiltonian/Hamiltonian structure and hence
                 increase the reliability, accuracy, and performance of
                 the computations. In this article, we describe the
                 corresponding algorithms which have been implemented in
                 the style of subroutines of the Subroutine Library in
                 Control Theory (SLICOT). Furthermore, we address some
                 of their applications. We describe variants for real
                 and complex problems, as well as implementation details
                 and perform numerical tests using real-world examples
                 to demonstrate the superiority of the new algorithms
                 compared to standard methods.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pew:2016:ABB,
  author =       "Jack Pew and Zhi Li and Paul Muir",
  title =        "{Algorithm 962}: {BACOLI}: {B}-spline Adaptive
                 Collocation Software for {PDEs} with
                 Interpolation-Based Spatial Error Control",
  journal =      j-TOMS,
  volume =       "42",
  number =       "3",
  pages =        "25:1--25:17",
  month =        may,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2818312",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 23 16:40:02 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "BACOL and BACOLR are (Fortran 77) B-spline adaptive
                 collocation packages for the numerical solution of 1D
                 parabolic Partial Differential Equations (PDEs). The
                 packages have been shown to be superior to other
                 similar packages, especially for problems exhibiting
                 sharp, moving spatial layer regions, where a stringent
                 tolerance is imposed. In addition to providing temporal
                 error control through the timestepping software, BACOL
                 and BACOLR feature control of a high-order estimate of
                 the spatial error of the approximate solution, obtained
                 by computing a second approximate solution of one
                 higher order of accuracy; the cost is
                 substantial-execution time and memory usage are almost
                 doubled. In this article, we discuss BACOLI, a new
                 version of BACOL that computes only one approximate
                 solution and uses efficient interpolation-based schemes
                 to obtain a spatial error estimate. In previous studies
                 these schemes have been shown to provide spatial error
                 estimates of comparable quality to those of BACOL. We
                 describe the substantial modification of BACOL needed
                 to obtain BACOLI, and provide numerical results showing
                 that BACOLI is significantly more efficient than BACOL,
                 in some cases by as much as a factor of 2. We also
                 introduce a Fortran 95 wrapper for BACOLI (called
                 BACOLI95) and discuss its simplified user interface.",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Zaghloul:2016:RAC,
  author =       "Mofreh R. Zaghloul",
  title =        "Remark on {``Algorithm 916: Computing the Faddeyeva
                 and Voigt Functions''}: Efficiency Improvements and
                 {Fortran} Translation",
  journal =      j-TOMS,
  volume =       "42",
  number =       "3",
  pages =        "26:1--26:9",
  month =        may,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2806884",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 23 16:40:02 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Zaghloul:2011:ACF}.",
  abstract =     "This remark describes efficiency improvements to
                 Algorithm 916 [Zaghloul and Ali 2011]. It is shown that
                 the execution time required by the algorithm, when run
                 at its highest accuracy, may be improved by more than a
                 factor of 2. A better accuracy vs efficiency tradeoff
                 scheme is also implemented; this requires the user to
                 supply the number of significant figures desired in the
                 computed values as an extra input argument to the
                 function. Using this tradeoff, it is shown that the
                 efficiency of the algorithm may be further improved
                 significantly while maintaining reasonably accurate and
                 safe results that are free of the pitfalls and complete
                 loss of accuracy seen in other competitive techniques.
                 The current version of the code is provided in Matlab
                 and Scilab in addition to a Fortran translation
                 prepared to meet the needs of real-world problems where
                 very large numbers of function evaluations would
                 require the use of a compiled language. To fulfill this
                 last requirement, a recently proposed reformed version
                 of Huml{\'\i}cek's w4 routine, shown to maintain the
                 claimed accuracy of the algorithm over a wide and fine
                 grid, is implemented in the present Fortran translation
                 for the case of four significant figures. This latter
                 modification assures the reliability of the code in the
                 solution of practical problems requiring numerous
                 evaluation of the function for applications requiring
                 low-accuracy computations ($ < 10^{-4}$).",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rouet:2016:DMP,
  author =       "Fran{\c{c}}ois-Henry Rouet and Xiaoye S. Li and Pieter
                 Ghysels and Artem Napov",
  title =        "A Distributed-Memory Package for Dense Hierarchically
                 Semi-Separable Matrix Computations Using
                 Randomization",
  journal =      j-TOMS,
  volume =       "42",
  number =       "4",
  pages =        "27:1--27:35",
  month =        jul,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2930660",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:24 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2930660",
  acknowledgement = ack-nhfb,
  articleno =    "27",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Meiser:2016:RCR,
  author =       "Dominic Meiser",
  title =        "{Replicated Computational Results (RCR)} Report for
                 {``A Distributed-Memory Package for Dense
                 Hierarchically Semi-Separable Matrix Computations Using
                 Randomization''}",
  journal =      j-TOMS,
  volume =       "42",
  number =       "4",
  pages =        "28:1--28:5",
  month =        jul,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2929907",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:24 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2929907",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ledoux:2016:MMT,
  author =       "Veerle Ledoux and Marnix {Van Daele}",
  title =        "{Matslise 2.0}: A {Matlab} Toolbox for
                 {Sturm--Liouville} Computations",
  journal =      j-TOMS,
  volume =       "42",
  number =       "4",
  pages =        "29:1--29:18",
  month =        jul,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2839299",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:24 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2839299",
  acknowledgement = ack-nhfb,
  articleno =    "29",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Vigna:2016:EEM,
  author =       "Sebastiano Vigna",
  title =        "An Experimental Exploration of {Marsaglia}'s {\tt
                 xorshift} Generators, Scrambled",
  journal =      j-TOMS,
  volume =       "42",
  number =       "4",
  pages =        "30:1--30:23",
  month =        jul,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2845077",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:24 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/m/marsaglia-george.bib;
                 https://www.math.utah.edu/pub/tex/bib/jstatsoft.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/tomacs.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2845077",
  abstract =     "Marsaglia proposed xorshift generators are a class of
                 very fast, good-quality pseudorandom number generators.
                 Subsequent analysis by Panneton and L'Ecuyer has
                 lowered the expectations raised by Marsaglia's article,
                 showing several weaknesses of such generators.
                 Nonetheless, many of the weaknesses of xorshift
                 generators fade away if their result is scrambled by a
                 nonlinear operation (as originally suggested by
                 Marsaglia). In this article we explore the space of
                 possible generators obtained by multiplying the result
                 of a xorshift generator by a suitable constant. We
                 sample generators at 100 points of their state space
                 and obtain detailed statistics that lead us to choices
                 of parameters that improve on the current ones. We then
                 explore for the first time the space of
                 high-dimensional xorshift generators, following another
                 suggestion in Marsaglia's article, finding choices of
                 parameters providing periods of length $ 2^{1024} 1 $
                 and $ 2^{4096} 1 $. The resulting generators are of
                 extremely high quality, faster than current similar
                 alternatives, and generate long-period sequences
                 passing strong statistical tests using only eight
                 logical operations, one addition, and one
                 multiplication by a constant.",
  acknowledgement = ack-nhfb,
  articleno =    "30",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Laszlo:2016:MAB,
  author =       "Endre L{\'a}szl{\'o} and Mike Giles and Jeremy
                 Appleyard",
  title =        "Manycore Algorithms for Batch Scalar and Block
                 Tridiagonal Solvers",
  journal =      j-TOMS,
  volume =       "42",
  number =       "4",
  pages =        "31:1--31:36",
  month =        jul,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2830568",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:24 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2830568",
  acknowledgement = ack-nhfb,
  articleno =    "31",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Prusa:2016:DWT,
  author =       "Zden{\v{e}}k Pr{\ocirc{u}}sa and Peter L.
                 S{\o}ndergaard and Pavel Rajmic",
  title =        "Discrete Wavelet Transforms in the Large
                 Time-Frequency Analysis Toolbox for {MATLAB\slash GNU
                 Octave}",
  journal =      j-TOMS,
  volume =       "42",
  number =       "4",
  pages =        "32:1--32:23",
  month =        jul,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2839298",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:24 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2839298",
  acknowledgement = ack-nhfb,
  articleno =    "32",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Escobar:2016:AES,
  author =       "Marcos Escobar and Benedikt Rudolph and Rudi Zagst",
  title =        "Algorithm 963: Estimation of Stochastic Covariance
                 Models using a Continuum of Moment Conditions",
  journal =      j-TOMS,
  volume =       "42",
  number =       "4",
  pages =        "33:1--33:26",
  month =        jul,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2834115",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:24 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2834115",
  acknowledgement = ack-nhfb,
  articleno =    "33",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lozano-Duran:2016:AEA,
  author =       "Adri{\'a}n Lozano-Dur{\'a}n and Guillem Borrell",
  title =        "Algorithm 964: An Efficient Algorithm to Compute the
                 Genus of Discrete Surfaces and Applications to
                 Turbulent Flows",
  journal =      j-TOMS,
  volume =       "42",
  number =       "4",
  pages =        "34:1--34:19",
  month =        jul,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2845076",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:24 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2845076",
  acknowledgement = ack-nhfb,
  articleno =    "34",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{delaCruz:2016:GTU,
  author =       "Luis M. de la Cruz and Eduardo Ramos",
  title =        "General Template Units for the Finite Volume Method in
                 Box-Shaped Domains",
  journal =      j-TOMS,
  volume =       "43",
  number =       "1",
  pages =        "1:1--1:32",
  month =        aug,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2835175",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2835175",
  abstract =     "In this work, we develop an extension of the Curiously
                 Recurring Template Pattern (CRTP), which allows us to
                 organize three related concepts in a class hierarchy.
                 Generalizations, specializations and special procedures
                 are the concepts that we use to define and implement
                 several tools. We call these tools general template
                 units because they are well-defined building blocks
                 (units) for numerically solving partial differential
                 equations (PDEs), are based on the use of templates of
                 the C++ language, and can be applied in the solution of
                 different kinds of problems. We focus on the solution
                 of PDEs using the Finite Volume Method (FVM) in
                 box-shaped domains. The three concepts just mentioned
                 are intensively used to generate optimized codes for
                 each case study. The convenience of our approach is
                 highlighted in the numerical solutions of the examples
                 of application, including laminar thermal convection,
                 turbulent thermal convection, as well as a two-phase
                 flow model in porous media, all of them in one, two,
                 and three dimensions. The mathematical models of these
                 examples were obtained using the axiomatic formulation,
                 which provides generality, simplicity, and clarity to
                 tackle any continuum mechanics application. The ideas
                 explained in this work are quite simple but powerful in
                 solving fluid dynamics problems, in which the
                 conservativeness of the FVM is an important feature.
                 The techniques developed in this work allow us to swap
                 easily between numerical schemes for computing the
                 coefficients obtained by applying the FVM.",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Turcksin:2016:WDP,
  author =       "Bruno Turcksin and Martin Kronbichler and Wolfgang
                 Bangerth",
  title =        "{WorkStream} -- A Design Pattern for Multicore-Enabled
                 Finite Element Computations",
  journal =      j-TOMS,
  volume =       "43",
  number =       "1",
  pages =        "2:1--2:29",
  month =        aug,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2851488",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2851488",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kohler:2016:BLI,
  author =       "Martin K{\"o}hler and Jens Saak",
  title =        "On {BLAS} Level-3 Implementations of Common Solvers
                 for (Quasi-) Triangular Generalized {Lyapunov}
                 Equations",
  journal =      j-TOMS,
  volume =       "43",
  number =       "1",
  pages =        "3:1--3:23",
  month =        aug,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2850415",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2850415",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Garrett:2016:NAB,
  author =       "C. Kristopher Garrett and Zhaojun Bai and Ren-Cang
                 Li",
  title =        "A Nonlinear {$ Q R $} Algorithm for Banded Nonlinear
                 Eigenvalue Problems",
  journal =      j-TOMS,
  volume =       "43",
  number =       "1",
  pages =        "4:1--4:19",
  month =        aug,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2870628",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2870628",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  journal-URL =  "https://dl.acm.org/loi/toms",
  abstract =     "A variation of Kublanovskaya's nonlinear QR method for
                 solving banded nonlinear eigenvalue problems is
                 presented in this article. The new method is iterative
                 and specifically designed for problems too large to use
                 dense linear algebra techniques. For the unstructurally
                 banded nonlinear eigenvalue problem, a new data
                 structure is used for storing the matrices to keep
                 memory and computational costs low. In addition, an
                 algorithm is presented for computing several nearby
                 nonlinear eigenvalues to already-computed ones.
                 Finally, numerical examples are given to show the
                 efficacy of the new methods, and the source code has
                 been made publicly available.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{vanderHoeven:2016:MSA,
  author =       "Joris van der Hoeven and Gr{\'e}goire Lecerf and
                 Guillaume Quintin",
  title =        "Modular {SIMD} arithmetic in {Mathemagix}",
  journal =      j-TOMS,
  volume =       "43",
  number =       "1",
  pages =        "5:1--5:37",
  month =        aug,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2876503",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2876503",
  abstract =     "Modular integer arithmetic occurs in many algorithms
                 for computer algebra, cryptography, and error
                 correcting codes. Although recent microprocessors
                 typically offer a wide range of highly optimized
                 arithmetic functions, modular integer operations still
                 require dedicated implementations. In this article, we
                 survey existing algorithms for modular integer
                 arithmetic and present detailed vectorized
                 counterparts. We also describe several applications,
                 such as fast modular Fourier transforms and
                 multiplication of integer polynomials and matrices. The
                 vectorized algorithms have been implemented in C++
                 inside the free computer algebra and analysis system
                 Mathemagix. The performance of our implementation is
                 illustrated by various benchmarks.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sukkari:2016:HPQ,
  author =       "Dalal Sukkari and Hatem Ltaief and David Keyes",
  title =        "A High Performance {QDWH-SVD} Solver Using Hardware
                 Accelerators",
  journal =      j-TOMS,
  volume =       "43",
  number =       "1",
  pages =        "6:1--6:25",
  month =        aug,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2894747",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2894747",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Filip:2016:RSI,
  author =       "Silviu-Ioan Filip",
  title =        "A Robust and Scalable Implementation of the
                 {Parks--McClellan} Algorithm for Designing {FIR}
                 Filters",
  journal =      j-TOMS,
  volume =       "43",
  number =       "1",
  pages =        "7:1--7:24",
  month =        aug,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2904902",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2904902",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ong:2016:ARM,
  author =       "Benjamin W. Ong and Ronald D. Haynes and Kyle Ladd",
  title =        "Algorithm 965: {RIDC} Methods: A Family of Parallel
                 Time Integrators",
  journal =      j-TOMS,
  volume =       "43",
  number =       "1",
  pages =        "8:1--8:13",
  month =        aug,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2964377",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2964377",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sluanschi:2016:AAD,
  author =       "Emil I. Slu{\c{s}}anschi and Vlad Dumitrel",
  title =        "{ADiJaC} --- Automatic Differentiation of {Java}
                 Classfiles",
  journal =      j-TOMS,
  volume =       "43",
  number =       "2",
  pages =        "9:1--9:33",
  month =        sep,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2904901",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/java2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2904901",
  abstract =     "This work presents the current design and
                 implementation of ADiJaC, an automatic differentiation
                 tool for Java classfiles. ADiJaC uses source
                 transformation to generate derivative codes in both the
                 forward and the reverse modes of automatic
                 differentiation. We describe the overall architecture
                 of the tool and present various details and examples
                 for each of the two modes of differentiation. We
                 emphasize the enhancements that have been made over
                 previous versions of ADiJaC and illustrate their
                 influence on the generality of the tool and on the
                 performance of the generated derivative codes. The
                 ADiJaC tool has been used to generate derivatives for a
                 variety of problems, including real-world applications.
                 We evaluate the performance of such codes and compare
                 it to derivatives generated by Tapenade, a
                 well-established automatic differentiation tool for
                 Fortran and C/C++. Additionally, we present a more
                 detailed performance analysis of a real-world
                 application. Apart from being the only general-purpose
                 automatic differentiation tool for Java bytecode, we
                 argue that ADiJaC's features and performance are
                 comparable to those of similar mature tools for other
                 programming languages such as C/C++ or Fortran.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Yamazaki:2016:SPV,
  author =       "Ichitaro Yamazaki and Stanimire Tomov and Jack
                 Dongarra",
  title =        "Stability and Performance of Various Singular Value {$
                 Q R $} Implementations on Multicore {CPU} with a
                 {GPU}",
  journal =      j-TOMS,
  volume =       "43",
  number =       "2",
  pages =        "10:1--10:18",
  month =        sep,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2898347",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2898347",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rupp:2016:PIS,
  author =       "Karl Rupp and Josef Weinbub and Ansgar J{\"u}ngel and
                 Tibor Grasser",
  title =        "Pipelined Iterative Solvers with Kernel Fusion for
                 Graphics Processing Units",
  journal =      j-TOMS,
  volume =       "43",
  number =       "2",
  pages =        "11:1--11:27",
  month =        sep,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2907944",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2907944",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Low:2016:AME,
  author =       "Tze Meng Low and Francisco D. Igual and Tyler M. Smith
                 and Enrique S. Quintana-Orti",
  title =        "Analytical Modeling Is Enough for High-Performance
                 {BLIS}",
  journal =      j-TOMS,
  volume =       "43",
  number =       "2",
  pages =        "12:1--12:18",
  month =        sep,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2925987",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2925987",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Agullo:2016:IMS,
  author =       "Emmanuel Agullo and Alfredo Buttari and Abdou
                 Guermouche and Florent Lopez",
  title =        "Implementing Multifrontal Sparse Solvers for Multicore
                 Architectures with Sequential Task Flow Runtime
                 Systems",
  journal =      j-TOMS,
  volume =       "43",
  number =       "2",
  pages =        "13:1--13:22",
  month =        sep,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2898348",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2898348",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lee:2016:TOI,
  author =       "Mokwon Lee and Kokichi Sugihara and Deok-Soo Kim",
  title =        "Topology-Oriented Incremental Algorithm for the Robust
                 Construction of the {Voronoi} Diagrams of Disks",
  journal =      j-TOMS,
  volume =       "43",
  number =       "2",
  pages =        "14:1--14:23",
  month =        sep,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2939366",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2939366",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gould:2016:NPP,
  author =       "Nicholas Gould and Jennifer Scott",
  title =        "A Note on Performance Profiles for Benchmarking
                 Software",
  journal =      j-TOMS,
  volume =       "43",
  number =       "2",
  pages =        "15:1--15:5",
  month =        sep,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2950048",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2950048",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Tozoni:2016:API,
  author =       "Davi C. Tozoni and Pedro J. De Rezende and Cid C. {De
                 Souza}",
  title =        "{Algorithm 966}: A Practical Iterative Algorithm for
                 the Art Gallery Problem Using Integer Linear
                 Programming",
  journal =      j-TOMS,
  volume =       "43",
  number =       "2",
  pages =        "16:1--16:27",
  month =        sep,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2890491",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2890491",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Malhotra:2016:ADM,
  author =       "Dhairya Malhotra and George Biros",
  title =        "{Algorithm 967}: A Distributed-Memory Fast Multipole
                 Method for Volume Potentials",
  journal =      j-TOMS,
  volume =       "43",
  number =       "2",
  pages =        "17:1--17:27",
  month =        sep,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2898349",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/fastmultipole.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2898349",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Vallivaara:2016:SAS,
  author =       "Ilari Vallivaara and Katja Poikselk{\"a} and Pauli
                 Rikula and Juha R{\"o}ning",
  title =        "Systematic Alias Sampling: An Efficient and
                 Low-Variance Way to Sample from a Discrete
                 Distribution",
  journal =      j-TOMS,
  volume =       "43",
  number =       "3",
  pages =        "18:1--18:17",
  month =        nov,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2935745",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2935745",
  abstract =     "In this article, we combine the Alias method with the
                 concept of systematic sampling, a method commonly used
                 in particle filters for efficient low-variance
                 resampling. The proposed method allows very fast
                 sampling from a discrete distribution: drawing $k$
                 samples is up to an order of magnitude faster than
                 binary search from the cumulative distribution function
                 (cdf) or inversion methods used in many libraries. The
                 produced empirical distribution function is evaluated
                 using a modified Cram{\'e}r--von Mises goodness-of-fit
                 statistic, showing that the method compares very
                 favorably to multinomial sampling. As continuous
                 distributions can often be approximated with discrete
                 ones, the proposed method can be used as a very general
                 way to efficiently produce random samples for particle
                 filter proposal distributions, for example, for motion
                 models in robotics.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Meister:2016:PME,
  author =       "Oliver Meister and Kaveh Rahnema and Michael Bader",
  title =        "Parallel Memory-Efficient Adaptive Mesh Refinement on
                 Structured Triangular Meshes with Billions of Grid
                 Cells",
  journal =      j-TOMS,
  volume =       "43",
  number =       "3",
  pages =        "19:1--19:27",
  month =        sep,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2947668",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2947668",
  abstract =     "We present sam(oa) 2, a software package for a
                 dynamically adaptive, parallel solution of 2D partial
                 differential equations on triangular grids created via
                 newest vertex bisection. An element order imposed by
                 the Sierpinski space-filling curve provides an
                 algorithm for grid generation, refinement, and
                 traversal that is inherently memory efficient. Based
                 purely on stack and stream data structures, it
                 completely avoids random memory access. Using an
                 element-oriented data view suitable for local
                 operators, concrete simulation scenarios are
                 implemented based on control loops and event hooks,
                 which hide the complexity of the underlying traversal
                 scheme. Two case studies are presented: two-phase flow
                 in heterogeneous porous media and tsunami wave
                 propagation, demonstrated on the Tohoku tsunami 2011 in
                 Japan. sam(oa) 2 features hybrid MPI+OpenMP
                 parallelization based on the Sierpinski order induced
                 on the elements. Sections defined by contiguous grid
                 cells define atomic tasks for OpenMP work sharing and
                 stealing, as well as for migration of grid cells
                 between MPI processes. Using optimized communication
                 and load balancing algorithms, sam(oa) 2 achieves 88\%
                 strong scaling efficiency from 16 to 512 cores and 92\%
                 efficiency in a weak scaling test on 8,192 cores with
                 10 billion elements-all tests including adaptive mesh
                 refinement and load balancing in each time step.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rump:2017:IPK,
  author =       "Siegfried M. Rump",
  title =        "{IEEE754} Precision-$k$ base-$ \beta $ Arithmetic
                 Inherited by Precision-$m$ Base-$ \beta $ Arithmetic
                 for $ k < m$",
  journal =      j-TOMS,
  volume =       "43",
  number =       "3",
  pages =        "20:1--20:15",
  month =        jan,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2785965",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 4 10:55:07 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=2785965",
  abstract =     "Suppose an $m$-digit floating-point arithmetic in base
                 $ \beta \geq 2$ following the IEEE754 arithmetic
                 standard is available. We show how a $k$-digit
                 arithmetic with $ k < m$ can be inherited solely using
                 $m$-digit operations. This includes the rounding into
                 $k$ digits, the four basic operations and the square
                 root, all for even or odd base $ \beta $. In
                 particular, we characterize the relation between $k$
                 and $m$ so that no double rounding occurs when
                 computing in $m$ digits and rounding the result into
                 $k$ digits. We discuss rounding to nearest as well as
                 directed rounding, and our approach covers exceptional
                 values including signed zero. For binary arithmetic, a
                 Matlab toolbox based on binary64 including $k$-bit
                 scalar, vector and matrix operations as well as $k$-bit
                 interval arithmetic is part of Version 8 of INTLAB, the
                 Matlab toolbox for reliable computing.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Jacquelin:2017:PDM,
  author =       "Mathias Jacquelin and Lin Lin and Chao Yang",
  title =        "{PSelInv} --- a Distributed Memory Parallel Algorithm
                 for Selected Inversion: The Symmetric Case",
  journal =      j-TOMS,
  volume =       "43",
  number =       "3",
  pages =        "21:1--21:28",
  month =        jan,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2786977",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 4 10:55:07 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=2786977",
  abstract =     "We describe an efficient parallel implementation of
                 the selected inversion algorithm for distributed memory
                 computer systems, which we call PSelInv. The PSelInv
                 method computes selected elements of a general sparse
                 matrix A that can be decomposed as A = LU, where L is
                 lower triangular and U is upper triangular. The
                 implementation described in this article focuses on the
                 case of sparse symmetric matrices. It contains an
                 interface that is compatible with the distributed
                 memory parallel sparse direct factorization
                 SuperLU_DIST. However, the underlying data structure
                 and design of PSelInv allows it to be easily combined
                 with other factorization routines, such as PARDISO. We
                 discuss general parallelization strategies such as data
                 and task distribution schemes. In particular, we
                 describe how to exploit the concurrency exposed by the
                 elimination tree associated with the LU factorization
                 of A. We demonstrate the efficiency and accuracy of
                 PSelInv by presenting several numerical experiments. In
                 particular, we show that PSelInv can run efficiently on
                 more than 4,000 cores for a modestly sized matrix. We
                 also demonstrate how PSelInv can be used to accelerate
                 large-scale electronic structure calculations.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fortin:2017:GAG,
  author =       "Pierre Fortin and Mourad Gouicem and Stef Graillat",
  title =        "{GPU}-Accelerated Generation of Correctly Rounded
                 Elementary Functions",
  journal =      j-TOMS,
  volume =       "43",
  number =       "3",
  pages =        "22:1--22:26",
  month =        jan,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2935746",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 4 10:55:07 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=2935746",
  abstract =     "The IEEE 754-2008 standard recommends the correct
                 rounding of some elementary functions. This requires
                 solving the Table Maker's Dilemma (TMD), which implies
                 a huge amount of CPU computation time. In this article,
                 we consider accelerating such computations, namely the
                 Lef{\`e}vre algorithm on graphics processing units
                 (GPUs), which are massively parallel architectures with
                 a partial single instruction, multiple data execution.
                 We first propose an analysis of the Lef{\`e}vre
                 hard-to-round argument search using the concept of
                 continued fractions. We then propose a new parallel
                 search algorithm that is much more efficient on GPUs
                 thanks to its more regular control flow. We also
                 present an efficient hybrid CPU-GPU deployment of the
                 generation of the polynomial approximations required in
                 the Lef{\`e}vre algorithm. In the end, we manage to
                 obtain overall speedups up to 53.4 $ \times $ on one
                 GPU over a sequential CPU execution and up to 7.1 $
                 \times $ over a hex-core CPU, which enable a much
                 faster solution of the TMD for the double-precision
                 format.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Marin:2017:ERF,
  author =       "Manuel Marin and David Defour and Federico Milano",
  title =        "An Efficient Representation Format for Fuzzy Intervals
                 Based on Symmetric Membership Functions",
  journal =      j-TOMS,
  volume =       "43",
  number =       "3",
  pages =        "23:1--23:22",
  month =        jan,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2939364",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 4 10:55:07 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=2939364",
  abstract =     "This article addresses the execution cost of
                 arithmetic operations with a focus on fuzzy arithmetic.
                 Thanks to an appropriate representation format for
                 fuzzy intervals, we show that it is possible to halve
                 the number of operations and divide by 2 to 8 the
                 memory requirements compared to conventional solutions.
                 In addition, we demonstrate the benefit of some
                 hardware features encountered in today's accelerators
                 (GPU) such as static rounding, memory usage,
                 instruction-level parallelism (ILP), and thread-level
                 parallelism (TLP). We then describe a library of fuzzy
                 arithmetic operations written in CUDA and C++. The
                 library is evaluated against traditional approaches
                 using compute-bound and memory-bound benchmarks on
                 Nvidia GPUs, with an observed performance gain of 2 to
                 20.",
  acknowledgement = ack-nhfb,
  articleno =    "23",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rathgeber:2017:FAF,
  author =       "Florian Rathgeber and David A. Ham and Lawrence
                 Mitchell and Michael Lange and Fabio Luporini and
                 Andrew T. T. Mcrae and Gheorghe-Teodor Bercea and
                 Graham R. Markall and Paul H. J. Kelly",
  title =        "{Firedrake}: Automating the Finite Element Method by
                 Composing Abstractions",
  journal =      j-TOMS,
  volume =       "43",
  number =       "3",
  pages =        "24:1--24:27",
  month =        jan,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2998441",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 4 10:55:07 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=2998441",
  abstract =     "Firedrake is a new tool for automating the numerical
                 solution of partial differential equations. Firedrake
                 adopts the domain-specific language for the finite
                 element method of the FEniCS project, but with a pure
                 Python runtime-only implementation centered on the
                 composition of several existing and new abstractions
                 for particular aspects of scientific computing. The
                 result is a more complete separation of concerns that
                 eases the incorporation of separate contributions from
                 computer scientists, numerical analysts, and
                 application specialists. These contributions may add
                 functionality or improve performance. Firedrake
                 benefits from automatically applying new optimizations.
                 This includes factorizing mixed function spaces,
                 transforming and vectorizing inner loops, and
                 intrinsically supporting block matrix operations.
                 Importantly, Firedrake presents a simple public API for
                 escaping the UFL abstraction. This allows users to
                 implement common operations that fall outside of pure
                 variational formulations, such as flux limiters.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Calvo:2017:ADM,
  author =       "Manuel Calvo and Juan I. Montijano and Luis
                 R{\'a}ndez",
  title =        "Algorithm 968: {DISODE45}: A {Matlab} {Runge--Kutta}
                 Solver for Piecewise Smooth {IVPs} of {Filippov} Type",
  journal =      j-TOMS,
  volume =       "43",
  number =       "3",
  pages =        "25:1--25:14",
  month =        jan,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2907054",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 4 10:55:07 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=2907054",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gil:2016:ACI,
  author =       "Amparo Gil and Diego Ruiz-Antol{\'\i}n and Javier
                 Segura and Nico M. Temme",
  title =        "{Algorithm 969}: Computation of the Incomplete Gamma
                 Function for Negative Values of the Argument",
  journal =      j-TOMS,
  volume =       "43",
  number =       "3",
  pages =        "26:1--26:9",
  month =        nov,
  year =         "2016",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2972951",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Nov 22 17:45:25 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=2972951",
  abstract =     "An algorithm for computing the incomplete gamma
                 function $ \gamma^(a, z) $ for real values of the
                 parameter $a$ and negative real values of the argument
                 $z$ is presented. The algorithm combines the use of
                 series expansions, Poincar{\'e}-type expansions,
                 uniform asymptotic expansions, and recurrence
                 relations, depending on the parameter region. A
                 relative accuracy $ \approx 10^{-13}$ in the parameter
                 region $ (a, z) \in [500, 500] \times [500, 0)$ can be
                 obtained when computing the function $ \gamma^\ast (a,
                 z)$ with the Fortran 90 module IncgamNEG implementing
                 the algorithm.",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sys:2017:AON,
  author =       "Marek S{\'y}s and Zden{\k{e}}k {\v{R}}{\'\i}ha and
                 Vashek Maty{\'a}{\v{s}}",
  title =        "{Algorithm 970}: Optimizing the {NIST Statistical Test
                 Suite} and the {Berlekamp--Massey} Algorithm",
  journal =      j-TOMS,
  volume =       "43",
  number =       "3",
  pages =        "27:1--27:11",
  month =        jan,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2988228",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 24 08:52:28 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The NIST Statistical Test Suite (NIST STS) is one of
                 the most popular tools for the analysis of randomness.
                 This test battery is widely used, but its
                 implementation is quite inefficient. A complete
                 randomness analysis using the NIST STS can take hours
                 on a standard computer when the tested data volume is
                 on the order of GB. We improved the most time-consuming
                 test (Linear Complexity) from the previous most
                 efficient implementation of the NIST STS. We also
                 optimized other tests and achieved an overall speedup
                 of $ 50.6 \times $ compared with the reference
                 implementation. This means that 20MB of data can be
                 tested within a minute using our new optimized version
                 of the NIST STS. To speed up the Linear Complexity
                 test, we proposed a new version of the
                 Berlekamp--Massey algorithm that computes only the
                 linear complexity of a sequence. This new variant does
                 not construct a linear feedback shift register and is
                 approximately $ 187 \times $ faster than the original
                 NIST implementation of the Berlekamp--Massey
                 algorithm.",
  acknowledgement = ack-nhfb,
  articleno =    "27",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Li:2017:AIR,
  author =       "Huamin Li and George C. Linderman and Arthur Szlam and
                 Kelly P. Stanton and Yuval Kluger and Mark Tygert",
  title =        "{Algorithm 971}: an Implementation of a Randomized
                 Algorithm for Principal Component Analysis",
  journal =      j-TOMS,
  volume =       "43",
  number =       "3",
  pages =        "28:1--28:14",
  month =        jan,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3004053",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 24 08:52:28 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Recent years have witnessed intense development of
                 randomized methods for low-rank approximation. These
                 methods target principal component analysis and the
                 calculation of truncated singular value decompositions.
                 The present article presents an essentially black-box,
                 foolproof implementation for Mathworks MATLAB, a
                 popular software platform for numerical computation. As
                 illustrated via several tests, the randomized
                 algorithms for low-rank approximation outperform or at
                 least match the classical deterministic techniques
                 (such as Lanczos iterations run to convergence) in
                 basically all respects: accuracy, computational
                 efficiency (both speed and memory usage), ease-of-use,
                 parallelizability, and reliability. However, the
                 classical procedures remain the methods of choice for
                 estimating spectral norms and are far superior for
                 calculating the least singular values and corresponding
                 singular vectors (or singular subspaces).",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Perez:2017:AJI,
  author =       "Juan F. P{\'e}rez and Daniel F. Silva and Julio C.
                 G{\'o}ez and Andr{\'e}s Sarmiento and Andr{\'e}s
                 Sarmiento-Romero and Raha Akhavan-Tabatabaei and
                 Germ{\'a}n Ria{\~n}o",
  title =        "{Algorithm 972}: {jMarkov}: an Integrated Framework
                 for {Markov} Chain Modeling",
  journal =      j-TOMS,
  volume =       "43",
  number =       "3",
  pages =        "29:1--29:22",
  month =        jan,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3009968",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 24 08:52:28 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Markov chains (MC) are a powerful tool for modeling
                 complex stochastic systems. Whereas a number of tools
                 exist for solving different types of MC models, the
                 first step in MC modeling is to define the model
                 parameters. This step is, however, error prone and far
                 from trivial when modeling complex systems. In this
                 article, we introduce jMarkov, a framework for MC
                 modeling that provides the user with the ability to
                 define MC models from the basic rules underlying the
                 system dynamics. From these rules, jMarkov
                 automatically obtains the MC parameters and solves the
                 model to determine steady-state and transient
                 performance measures. The jMarkov framework is composed
                 of four modules: (i) the main module supports MC models
                 with a finite state space; (ii) the jQBD module enables
                 the modeling of Quasi-Birth-and-Death processes, a
                 class of MCs with infinite state space; (iii) the jMDP
                 module offers the capabilities to determine optimal
                 decision rules based on Markov Decision Processes; and
                 (iv) the jPhase module supports the manipulation and
                 inclusion of phase-type variables to represent more
                 general behaviors than that of the standard exponential
                 distribution. In addition, jMarkov is highly
                 extensible, allowing the users to introduce new
                 modeling abstractions and solvers.",
  acknowledgement = ack-nhfb,
  articleno =    "29",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Filippone:2017:SMV,
  author =       "Salvatore Filippone and Valeria Cardellini and Davide
                 Barbieri and Alessandro Fanfarillo",
  title =        "Sparse Matrix-Vector Multiplication on {GPGPUs}",
  journal =      j-TOMS,
  volume =       "43",
  number =       "4",
  pages =        "30:1--30:49",
  month =        mar,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3017994",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 24 08:51:05 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The multiplication of a sparse matrix by a dense
                 vector (SpMV) is a centerpiece of scientific computing
                 applications: it is the essential kernel for the
                 solution of sparse linear systems and sparse eigenvalue
                 problems by iterative methods. The efficient
                 implementation of the sparse matrix-vector
                 multiplication is therefore crucial and has been the
                 subject of an immense amount of research, with interest
                 renewed with every major new trend in high-performance
                 computing architectures. The introduction of
                 General-Purpose Graphics Processing Units (GPGPUs) is
                 no exception, and many articles have been devoted to
                 this problem. With this article, we provide a review of
                 the techniques for implementing the SpMV kernel on
                 GPGPUs that have appeared in the literature of the last
                 few years. We discuss the issues and tradeoffs that
                 have been encountered by the various researchers, and a
                 list of solutions, organized in categories according to
                 common features. We also provide a performance
                 comparison across different GPGPU models and on a set
                 of test matrices coming from various application
                 domains.",
  acknowledgement = ack-nhfb,
  articleno =    "30",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Torun:2017:PMN,
  author =       "F. Sukru Torun and Murat Manguoglu and Cevdet
                 Aykanat",
  title =        "Parallel Minimum Norm Solution of Sparse Block
                 Diagonal Column Overlapped Underdetermined Systems",
  journal =      j-TOMS,
  volume =       "43",
  number =       "4",
  pages =        "31:1--31:21",
  month =        mar,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3004280",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 24 08:51:05 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Underdetermined systems of equations in which the
                 minimum norm solution needs to be computed arise in
                 many applications, such as geophysics, signal
                 processing, and biomedical engineering. In this
                 article, we introduce a new parallel algorithm for
                 obtaining the minimum 2-norm solution of an
                 underdetermined system of equations. The proposed
                 algorithm is based on the Balance scheme, which was
                 originally developed for the parallel solution of
                 banded linear systems. The proposed scheme assumes a
                 generalized banded form where the coefficient matrix
                 has column overlapped block structure in which the
                 blocks could be dense or sparse. In this article, we
                 implement the more general sparse case. The blocks can
                 be handled independently by any existing sequential or
                 parallel QR factorization library. A smaller reduced
                 system is formed and solved before obtaining the
                 minimum norm solution of the original system in
                 parallel. We experimentally compare and confirm the
                 error bound of the proposed method against the QR
                 factorization based techniques by using true
                 single-precision arithmetic. We implement the proposed
                 algorithm by using the message passing paradigm. We
                 demonstrate numerical effectiveness as well as parallel
                 scalability of the proposed algorithm on both shared
                 and distributed memory architectures for solving
                 various types of problems.",
  acknowledgement = ack-nhfb,
  articleno =    "31",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Krislock:2017:BSB,
  author =       "Nathan Krislock and J{\'e}r{\^o}me Malick and
                 Fr{\'e}d{\'e}ric Roupin",
  title =        "{BiqCrunch}: a Semidefinite Branch-and-Bound Method
                 for Solving Binary Quadratic Problems",
  journal =      j-TOMS,
  volume =       "43",
  number =       "4",
  pages =        "32:1--32:23",
  month =        mar,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3005345",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 24 08:51:05 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "This article presents BiqCrunch, an exact solver for
                 binary quadratic optimization problems. BiqCrunch is a
                 branch-and-bound method that uses an original,
                 efficient semidefinite-optimization-based bounding
                 procedure. It has been successfully tested on a variety
                 of well-known combinatorial optimization problems, such
                 as Max-Cut, Max- k -Cluster, and Max-Independent-Set.
                 The code is publicly available online; a web interface
                 and many conversion tools are also provided.",
  acknowledgement = ack-nhfb,
  articleno =    "32",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Aurentz:2017:CCS,
  author =       "Jared L. Aurentz and Lloyd N. Trefethen",
  title =        "Chopping a {Chebyshev} Series",
  journal =      j-TOMS,
  volume =       "43",
  number =       "4",
  pages =        "33:1--33:21",
  month =        mar,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/2998442",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 24 08:51:05 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Chebfun and related software projects for numerical
                 computing with functions are based on the idea that at
                 each step of a computation, a function $ f(x) $ defined
                 on an interval $ [a, b] $ is ``rounded'' to a
                 prescribed precision by constructing a Chebyshev series
                 and chopping it at an appropriate point. Designing a
                 chopping algorithm with the right properties proves to
                 be a surprisingly complex and interesting problem. We
                 describe the chopping algorithm introduced in Chebfun
                 Version 5.3 in 2015 after many years of discussion and
                 the considerations that led to this design.",
  acknowledgement = ack-nhfb,
  articleno =    "33",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Magron:2017:CRE,
  author =       "Victor Magron and George Constantinides and Alastair
                 Donaldson",
  title =        "Certified Roundoff Error Bounds Using Semidefinite
                 Programming",
  journal =      j-TOMS,
  volume =       "43",
  number =       "4",
  pages =        "34:1--34:31",
  month =        mar,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3015465",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 24 08:51:05 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Roundoff errors cannot be avoided when implementing
                 numerical programs with finite precision. The ability
                 to reason about rounding is especially important if one
                 wants to explore a range of potential representations,
                 for instance, for FPGAs or custom hardware
                 implementations. This problem becomes challenging when
                 the program does not employ solely linear operations as
                 non-linearities are inherent to many interesting
                 computational problems in real-world applications.
                 Existing solutions to reasoning possibly lead to either
                 inaccurate bounds or high analysis time in the presence
                 of nonlinear correlations between variables.
                 Furthermore, while it is easy to implement a
                 straightforward method such as interval arithmetic,
                 sophisticated techniques are less straightforward to
                 implement in a formal setting. Thus there is a need for
                 methods that output certificates that can be formally
                 validated inside a proof assistant. We present a
                 framework to provide upper bounds on absolute roundoff
                 errors of floating-point nonlinear programs. This
                 framework is based on optimization techniques employing
                 semidefinite programming and sums of squares
                 certificates, which can be checked inside the Coq
                 theorem prover to provide formal roundoff error bounds
                 for polynomial programs. Our tool covers a wide range
                 of nonlinear programs, including polynomials and
                 transcendental operations as well as conditional
                 statements. We illustrate the efficiency and precision
                 of this tool on non-trivial programs coming from
                 biology, optimization, and space control. Our tool
                 produces more accurate error bounds for 23\% of all
                 programs and yields better performance in 66\% of all
                 programs.",
  acknowledgement = ack-nhfb,
  articleno =    "34",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Huckelheim:2017:ADC,
  author =       "Jan Christian H{\"u}ckelheim and Laurent Hasco{\"e}t
                 and Jens-Dominik M{\"u}ller",
  title =        "Algorithmic Differentiation of Code with Multiple
                 Context-Specific Activities",
  journal =      j-TOMS,
  volume =       "43",
  number =       "4",
  pages =        "35:1--35:21",
  month =        mar,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3015464",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 24 08:51:05 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Algorithmic differentiation (AD) by
                 source-transformation is an established method for
                 computing derivatives of computational algorithms.
                 Static dataflow analysis is commonly used by AD tools
                 to determine the set of active variables, that is,
                 variables that are influenced by the program input in a
                 differentiable way and have a differentiable influence
                 on the program output. In this work, a
                 context-sensitive static analysis combined with
                 procedure cloning is used to generate specialised
                 versions of differentiated procedures for each call
                 site. This enables better detection and elimination of
                 unused computations and memory storage, resulting in
                 performance improvements of the generated code, in both
                 forward- and reverse-mode AD. The implications of this
                 multi-activity AD approach on the static analysis of an
                 AD tool is shown using dataflow equations. The
                 worst-case cost of multi-activity AD on the
                 differentiation process is analysed and practical
                 remedies to avoid running into this worst case are
                 presented. The method was implemented in the AD tool
                 Tapenade, and we present its application to a 3D
                 unstructured compressible flow solver, for which we
                 generate an adjoint solver that performs significantly
                 faster when multi-activity AD is used.",
  acknowledgement = ack-nhfb,
  articleno =    "35",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gould:2017:SAP,
  author =       "Nicholas Gould and Jennifer Scott",
  title =        "The State-of-the-Art of Preconditioners for Sparse
                 Linear Least-Squares Problems",
  journal =      j-TOMS,
  volume =       "43",
  number =       "4",
  pages =        "36:1--36:35",
  month =        mar,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3014057",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 24 08:51:05 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "In recent years, a variety of preconditioners have
                 been proposed for use in solving large sparse linear
                 least-squares problems. These include simple diagonal
                 preconditioning, preconditioners based on incomplete
                 factorizations, and stationary inner iterations used
                 with Krylov subspace methods. In this study, we briefly
                 review preconditioners for which software has been made
                 available, then present a numerical evaluation of them
                 using performance profiles and a large set of problems
                 arising from practical applications. Comparisons are
                 made with state-of-the-art sparse direct methods.",
  acknowledgement = ack-nhfb,
  articleno =    "36",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Deckers:2017:AER,
  author =       "Karl Deckers and Ahlem Mougaida and H{\'e}di
                 Belhadjsalah",
  title =        "{Algorithm 973}: Extended Rational {Fej{\'e}r}
                 Quadrature Rules Based on {Chebyshev} Orthogonal
                 Rational Functions",
  journal =      j-TOMS,
  volume =       "43",
  number =       "4",
  pages =        "37:1--37:29",
  month =        mar,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3054077",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 24 08:51:05 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present a numerical procedure to approximate
                 integrals of the form $ \int^b_a f(x) \, d x $, where
                 $f$ is a function with singularities close to, but
                 outside the interval $ [a, b]$, with $ - \infty \leq a
                 < b \leq + \infty $ . The algorithm is based on
                 rational interpolatory Fej{\'e}r quadrature rules,
                 together with a sequence of real and/or complex
                 conjugate poles that are given in advance. Since for n
                 fixed in advance, the accuracy of the computed nodes
                 and weights in the n point rational quadrature formula
                 strongly depends on the given sequence of poles, we
                 propose a small number of iterations over the number of
                 points in the rational quadrature rule, limited by the
                 value $n$ (instead of fixing the number of points in
                 advance) in order to obtain the best approximation
                 among the first $n$. The proposed algorithm is
                 implemented as a Matlab program.",
  acknowledgement = ack-nhfb,
  articleno =    "37",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Novoselsky:2017:AOM,
  author =       "Alexander Novoselsky and Eugene Kagan",
  title =        "{Algorithm 974}: The {OutlierLib} --- a {MATLAB}
                 Library for Outliers' Detection",
  journal =      j-TOMS,
  volume =       "43",
  number =       "4",
  pages =        "38:1--38:3",
  month =        mar,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3054078",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 24 08:51:05 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The article presents a library of MATLAB functions
                 that implement the widely used algorithms of outlier
                 detection. The library includes the outlier tests for
                 univariate and multivariate data sets with an
                 approximately normal distribution. The software library
                 is accompanied by a brief review of the methods for
                 detecting and treating outliers.",
  acknowledgement = ack-nhfb,
  articleno =    "38",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Krogh:2017:RAF,
  author =       "Fred T. Krogh and Richard J. Hanson and Philip W.
                 Sharp",
  title =        "Remark on {Algorithm 936: a Fortran Message
                 Processor}",
  journal =      j-TOMS,
  volume =       "43",
  number =       "4",
  pages =        "39:1--39:1",
  month =        mar,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3004279",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 24 08:51:05 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Krogh:2014:AFM}.",
  abstract =     "The Fortran output routine messy enables debugging and
                 error message processing strategies in the design of
                 numerical and mathematical software. It supports
                 separate output from different processes in a parallel
                 computing environment.",
  acknowledgement = ack-nhfb,
  articleno =    "39",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Greif:2017:SII,
  author =       "Chen Greif and Shiwen He and Paul Liu",
  title =        "{SYM-ILDL}: Incomplete {$ L D L^T $} Factorization of
                 Symmetric Indefinite and Skew-Symmetric Matrices",
  journal =      j-TOMS,
  volume =       "44",
  number =       "1",
  pages =        "1:1--1:21",
  month =        jul,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3054948",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 14 16:39:28 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "SYM-ILDL is a numerical software package that computes
                 incomplete LDL$^T$ (ILDL) factorizations of symmetric
                 indefinite and real skew-symmetric matrices. The core
                 of the algorithm is a Crout variant of incomplete LU
                 (ILU), originally introduced and implemented for
                 symmetric matrices by Li and Saad [2005]. Our code is
                 economical in terms of storage, and it deals with real
                 skew-symmetric matrices as well as symmetric ones. The
                 package is written in C++ and is templated, is open
                 source, and includes a Matlab interface. The code
                 includes built-in RCM and AMD reordering, two
                 equilibration strategies, threshold Bunch-Kaufman
                 pivoting, and rook pivoting, as well as a wrapper to
                 MC64, a popular matching-based equilibration and
                 reordering algorithm. We also include two built-in
                 iterative solvers: SQMR, preconditioned with ILDL, and
                 MINRES, preconditioned with a symmetric positive
                 definite preconditioner based on the ILDL
                 factorization.",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Reps:2017:CAG,
  author =       "Bram Reps and Tobias Weinzierl",
  title =        "Complex Additive Geometric Multilevel Solvers for
                 {Helmholtz} Equations on Spacetrees",
  journal =      j-TOMS,
  volume =       "44",
  number =       "1",
  pages =        "2:1--2:36",
  month =        jul,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3054946",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 14 16:39:28 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We introduce a family of implementations of low-order,
                 additive, geometric multilevel solvers for systems of
                 Helmholtz equations arising from Schr{\o}dinger
                 equations. Both grid spacing and arithmetics may
                 comprise complex numbers, and we thus can apply complex
                 scaling to the indefinite Helmholtz operator. Our
                 implementations are based on the notion of a spacetree
                 and work exclusively with a finite number of
                 precomputed local element matrices. They are globally
                 matrix-free. Combining various relaxation factors with
                 two grid transfer operators allows us to switch from
                 additive multigrid over a hierarchical basis method
                 into a Bramble-Pasciak-Xu (BPX)-type solver, with
                 several multiscale smoothing variants within one code
                 base. Pipelining allows us to realize full
                 approximation storage (FAS) within the additive
                 environment where, amortized, each grid vertex carrying
                 degrees of freedom is read/written only once per
                 iteration. The codes realize a single-touch policy.
                 Among the features facilitated by matrix-free FAS is
                 arbitrary dynamic mesh refinement (AMR) for all solver
                 variants. AMR as an enabler for full multigrid (FMG)
                 cycling the grid unfolds throughout the computation
                 allows us to reduce the cost per unknown. The present
                 work primary contributes toward software realization
                 and design questions. Our experiments show that the
                 consolidation of single-touch FAS, dynamic AMR, and
                 vectorization-friendly, complex scaled, matrix-free FMG
                 cycles delivers a mature implementation blueprint for
                 solvers of Helmholtz equations in general. For this
                 blueprint, we put particular emphasis on a strict
                 implementation formalism as well as some implementation
                 correctness proofs.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Luporini:2017:AOF,
  author =       "Fabio Luporini and David A. Ham and Paul H. J. Kelly",
  title =        "An Algorithm for the Optimization of Finite Element
                 Integration Loops",
  journal =      j-TOMS,
  volume =       "44",
  number =       "1",
  pages =        "3:1--3:26",
  month =        jul,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3054944",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 14 16:39:28 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "We present an algorithm for the optimization of a
                 class of finite-element integration loop nests. This
                 algorithm, which exploits fundamental mathematical
                 properties of finite-element operators, is proven to
                 achieve a locally optimal operation count. In specified
                 circumstances the optimum achieved is global. Extensive
                 numerical experiments demonstrate significant
                 performance improvements over the state of the art in
                 finite-element code generation in almost all cases.
                 This validates the effectiveness of the algorithm
                 presented here and illustrates its limitations.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Boldo:2017:RFA,
  author =       "Sylvie Boldo and Stef Graillat and Jean-Michel
                 Muller",
  title =        "On the Robustness of the {2Sum} and {Fast2Sum}
                 Algorithms",
  journal =      j-TOMS,
  volume =       "44",
  number =       "1",
  pages =        "4:1--4:14",
  month =        jul,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3054947",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 14 16:39:28 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The 2Sum and Fast2Sum algorithms are important
                 building blocks in numerical computing. They are used
                 (implicitly or explicitly) in many compensated
                 algorithms (such as compensated summation or
                 compensated polynomial evaluation). They are also used
                 for manipulating floating-point expansions. We show
                 that these algorithms are much more robust than it is
                 usually believed: The returned result makes sense even
                 when the rounding function is not round-to-nearest, and
                 they are almost immune to overflow.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Agelek:2017:OEU,
  author =       "Rainer Agelek and Michael Anderson and Wolfgang
                 Bangerth and William L. Barth",
  title =        "On Orienting Edges of Unstructured Two- and
                 Three-Dimensional Meshes",
  journal =      j-TOMS,
  volume =       "44",
  number =       "1",
  pages =        "5:1--5:22",
  month =        jul,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3061708",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 4 10:55:07 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3061708",
  abstract =     "Finite element codes typically use data structures
                 that represent unstructured meshes as collections of
                 cells, faces, and edges, each of which require
                 associated coordinate systems. One then needs to store
                 how the coordinate system of each edge relates to that
                 of neighboring cells. However, we can simplify data
                 structures and algorithms if we can a priori orient
                 coordinate systems in such a way that the coordinate
                 systems on the edges follow uniquely from those on the
                 cells by rule. Such rules require that every
                 unstructured mesh allow the assignment of directions to
                 edges that satisfy the convention in adjacent cells. We
                 show that the convention chosen for unstructured
                 quadrilateral meshes in the deal.II library always
                 allows to orient meshes. It can therefore be used to
                 make codes simpler, faster, and less bug prone. We
                 present an algorithm that orients meshes in $ O(N) $
                 operations. We then show that consistent orientations
                 are not always possible for 3D hexahedral meshes. Thus,
                 cells generally need to store the direction of adjacent
                 edges, but our approach also allows the
                 characterization of cases where this is not necessary.
                 The 3D extension of our algorithm either orients edges
                 consistently, or aborts, both within $ O(N) $ steps.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Porcelli:2017:BTD,
  author =       "Margherita Porcelli and Philippe L. Toint",
  title =        "{BFO}, A Trainable Derivative-free Brute Force
                 Optimizer for Nonlinear Bound-constrained Optimization
                 and Equilibrium Computations with Continuous and
                 Discrete Variables",
  journal =      j-TOMS,
  volume =       "44",
  number =       "1",
  pages =        "6:1--6:25",
  month =        jul,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3085592",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 14 16:39:28 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A direct-search derivative-free Matlab optimizer for
                 bound-constrained problems is described, whose
                 remarkable features are its ability to handle a mix of
                 continuous and discrete variables, a versatile
                 interface as well as a novel self-training option. Its
                 performance compares favorably with that of NOMAD
                 (Nonsmooth Optimization by Mesh Adaptive Direct
                 Search), a well-known derivative-free optimization
                 package. It is also applicable to multilevel
                 equilibrium- or constrained-type problems. Its
                 easy-to-use interface provides a number of
                 user-oriented features, such as checkpointing and
                 restart, variable scaling, and early termination
                 tools.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{VanZee:2017:IHP,
  author =       "Field G. {Van Zee} and Tyler M. Smith",
  title =        "Implementing High-performance Complex Matrix
                 Multiplication via the 3m and 4m Methods",
  journal =      j-TOMS,
  volume =       "44",
  number =       "1",
  pages =        "7:1--7:36",
  month =        jul,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3086466",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Oct 4 10:55:07 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3086466",
  abstract =     "In this article, we explore the implementation of
                 complex matrix multiplication. We begin by briefly
                 identifying various challenges associated with the
                 conventional approach, which calls for a carefully
                 written kernel that implements complex arithmetic at
                 the lowest possible level (i.e., assembly language). We
                 then set out to develop a method of complex matrix
                 multiplication that avoids the need for complex kernels
                 altogether. This constraint promotes code reuse and
                 portability within libraries such as Basic Linear
                 Algebra Subprograms and BLAS-Like Library Instantiation
                 Software (BLIS) and allows kernel developers to focus
                 their efforts on fewer and simpler kernels. We develop
                 two alternative approaches --- one based on the 3m
                 method and one that reflects the classic 4m formulation
                 --- each with multiple variants, all of which rely only
                 on real matrix multiplication kernels. We discuss the
                 performance characteristics of these ``induced''
                 methods and observe that the assembly-level method
                 actually resides along the 4m spectrum of algorithmic
                 variants. Implementations are developed within the BLIS
                 framework, and testing on modern hardware confirms that
                 while the less numerically stable 3m method yields the
                 fastest runtimes, the more stable (and thus widely
                 applicable) 4m method's performance is somewhat limited
                 due to implementation challenges that appear inherent
                 in nature.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Szo:2017:PET,
  author =       "M{\'a}t{\'e} Sz{\H{o}}ke and Tam{\'a}s Istv{\'a}n
                 J{\'o}zsa and {\'A}d{\'a}m Kolesz{\'a}r and Irene
                 Moulitsas and L{\'a}szl{\'o} K{\"o}n{\"o}zsy",
  title =        "Performance Evaluation of a Two-Dimensional Lattice
                 {Boltzmann} Solver Using {CUDA} and {PGAS UPC} Based
                 Parallelisation",
  journal =      j-TOMS,
  volume =       "44",
  number =       "1",
  pages =        "8:1--8:22",
  month =        jul,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3085590",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 14 16:39:28 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3085590",
  abstract =     "The Unified Parallel C (UPC) language from the
                 Partitioned Global Address Space (PGAS) family unifies
                 the advantages of shared and local memory spaces and
                 offers a relatively straightforward code
                 parallelisation with the Central Processing Unit
                 (CPU). In contrast, the Computer Unified Device
                 Architecture (CUDA) development kit gives a tool to
                 make use of the Graphics Processing Unit (GPU). We
                 provide a detailed comparison between these novel
                 techniques through the parallelisation of a
                 two-dimensional lattice Boltzmann method based fluid
                 flow solver. Our comparison between the CUDA and UPC
                 parallelisation takes into account the required
                 conceptual effort, the performance gain, and the
                 limitations of the approaches from the application
                 oriented developers' point of view. We demonstrated
                 that UPC led to competitive efficiency with the local
                 memory implementation. However, the performance of the
                 shared memory code fell behind our expectations, and we
                 concluded that the investigated UPC compilers could not
                 efficiently treat the shared memory space. The CUDA
                 implementation proved to be more complex compared to
                 the UPC approach mainly because of the complicated
                 memory structure of the graphics card which also makes
                 GPUs suitable for the parallelisation of the lattice
                 Boltzmann method.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ganesh:2017:ATM,
  author =       "M. Ganesh and S. C. Hawkins",
  title =        "Algorithm 975: {TMATROM} -- A {$T$}-Matrix Reduced
                 Order Model Software",
  journal =      j-TOMS,
  volume =       "44",
  number =       "1",
  pages =        "9:1--9:18",
  month =        jul,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3054945",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 14 16:39:28 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "The T-matrix (TMAT) of a scatterer fully describes the
                 way the scatterer interacts with incident fields and
                 scatters waves, and is therefore used extensively in
                 several science and engineering applications. The
                 T-matrix is independent of several input parameters in
                 a wave propagation model and hence the offline
                 computation of the T-matrix provides an efficient
                 reduced order model (ROM) framework for performing
                 online scattering simulations for various choices of
                 the input parameters. The authors developed and
                 mathematically analyzed a numerically stable
                 formulation for computing the T-matrix (J. Comput.
                 Appl. Math. 234 (2010), 1702--1709). The TMATROM
                 software package provides an object-oriented
                 implementation of the numerically stable formulation
                 and can be used in conjunction with the user's
                 preferred forward solver for the two-dimensional
                 Helmholtz model. We compare TMATROM with standard
                 methods to compute the T-matrix for a range of
                 two-dimensional test scatterers with large aspect
                 ratios and acoustic sizes. Our numerical results
                 demonstrate the robust numerical stability of the
                 TMATROM implementation, even with scatterers for which
                 the standard methods are numerically unstable. The
                 efficiency and flexibility of the TMATROM software
                 package to handle a wide range of two-dimensional
                 scatterers with various shapes and material properties
                 are also demonstrated.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Brake:2017:ABN,
  author =       "Daniel A. Brake and Daniel J. Bates and Wenrui Hao and
                 Jonathan D. Hauenstein and Andrew J. Sommese and
                 Charles W. Wampler",
  title =        "Algorithm 976: {Bertini\_real}: Numerical
                 Decomposition of Real Algebraic Curves and Surfaces",
  journal =      j-TOMS,
  volume =       "44",
  number =       "1",
  pages =        "10:1--10:30",
  month =        jul,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3056528",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 14 16:39:28 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Bertini_real is a compiled command line program for
                 numerically decomposing the real portion of a
                 positive-dimensional complex component of an algebraic
                 set. The software uses homotopy continuation to solve a
                 series of systems via regeneration from a witness set
                 to compute a cell decomposition. The implemented
                 decomposition algorithms are similar to the well-known
                 cylindrical algebraic decomposition (CAD) first
                 established by Collins in that they produce a set of
                 connected cells. In contrast to the CAD, Bertini_real
                 produces cells with midpoints connected to boundary
                 points by homotopies, which can easily be numerically
                 tracked. Furthermore, the implemented decomposition for
                 surfaces naturally yields a triangulation. This
                 CAD-like decomposition captures the topological
                 information and permits further computation on the real
                 sets, such as sampling, visualization, and
                 three-dimensional printing.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Drmac:2017:AQP,
  author =       "Zlatko Drma{\v{c}}",
  title =        "Algorithm 977: a {$ Q R $}-Preconditioned {$ Q R $
                 SVD} Method for Computing the {SVD} with High
                 Accuracy",
  journal =      j-TOMS,
  volume =       "44",
  number =       "1",
  pages =        "11:1--11:30",
  month =        jul,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3061709",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jul 14 16:39:28 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "A new software for computing the singular value
                 decomposition (SVD) of real or complex matrices is
                 proposed. The method implemented in the code xGESVDQ is
                 essentially the $ Q R $ SVD algorithm available as
                 xGESVD in LAPACK. The novelty is an extra step, the $ Q
                 R $ factorization with column (or complete row and
                 column) pivoting, also already available in LAPACK as
                 xGEQP3. For experts in matrix computations, the
                 combination of the $ Q R $ factorization and an SVD
                 computation routine is not new. However, what seems to
                 be new and important for applications is that the
                 resulting procedure is numerically superior to xGESVD
                 and that it is capable of reaching the accuracy of the
                 Jacobi SVD. Further, when combined with pivoted
                 Cholesky factorization, xGESVDQ provides numerically
                 accurate and fast solvers (designated as xPHEVC,
                 xPSEVC) for the Hermitian positive definite eigenvalue
                 problem. For instance, using accurately computed
                 Cholesky factor, xPSEVC computes all eigenvalues of the
                 $ 200 \times 200 $ Hilbert matrix (whose spectral
                 condition number is greater that $ 10^{300}$) to nearly
                 full machine precision. Furthermore, xGESVDQ can be
                 used for accurate spectral decomposition of general
                 (indefinite) Hermitian matrices.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Anderson:2017:ASS,
  author =       "Edward Anderson",
  title =        "{Algorithm 978}: Safe Scaling in the {Level 1 BLAS}",
  journal =      j-TOMS,
  volume =       "44",
  number =       "1",
  pages =        "12:1--12:28",
  month =        jul,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3061665",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 17:21:07 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=3061665",
  abstract =     "The square root of a sum of squares is well known to
                 be prone to overflow and underflow. Ad hoc scaling of
                 intermediate results, as has been done in numerical
                 software such as the BLAS and LAPACK, mostly avoids the
                 problem, but it can still occur at extreme values in
                 the range of representable numbers. More careful
                 scaling, as has been implemented in recent versions of
                 the standard algorithms, may come at the expense of
                 performance or clarity. This work reimplements the
                 vector 2-norm and the generation of Givens rotations
                 from the Level 1 BLAS to improve their performance and
                 design. In addition, support for negative increments is
                 extended to the Level 1 BLAS operations on a single
                 vector, and a comprehensive test suite for all the
                 Level 1 BLAS is included.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hogg:2017:NAO,
  author =       "Jonathan Hogg and Jennifer Scott and Sue Thorne",
  title =        "Numerically Aware Orderings for Sparse Symmetric
                 Indefinite Linear Systems",
  journal =      j-TOMS,
  volume =       "44",
  number =       "2",
  pages =        "13:1--13:22",
  month =        sep,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3104991",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 17:19:59 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=3104991",
  abstract =     "Sparse symmetric indefinite problems arise in a large
                 number of important application areas; they are often
                 solved through the use of an LDL T factorization via a
                 sparse direct solver. While for many problems
                 prescaling the system matrix A is sufficient to
                 maintain stability of the factorization, for a small
                 but important fraction of problems numerical pivoting
                 is required. Pivoting often incurs a significant
                 overhead, and consequently, a number of techniques have
                 been proposed to try and limit the need for pivoting.
                 In particular, numerically aware ordering algorithms
                 may be used, that is, orderings that depend not only on
                 the sparsity pattern of A but also on the values of its
                 (scaled) entries. Current approaches identify large
                 entries of A and symmetrically permute them onto the
                 subdiagonal, where they can be used as part of a 2 $
                 \times $ 2 pivot. This is numerically effective, but
                 the fill in the factor L and hence the runtime of the
                 factorization and subsequent triangular solves may be
                 significantly increased over a standard ordering if no
                 pivoting is required. We present a new algorithm that
                 combines a matching-based approach with a numerically
                 aware nested dissection ordering. Numerical comparisons
                 with current approaches for some tough symmetric
                 indefinite problems are given.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Engwer:2017:GRI,
  author =       "Christian Engwer and Andreas N{\"u}{\ss}ing",
  title =        "Geometric Reconstruction of Implicitly Defined
                 Surfaces and Domains with Topological Guarantees",
  journal =      j-TOMS,
  volume =       "44",
  number =       "2",
  pages =        "14:1--14:20",
  month =        sep,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3104989",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 17:19:59 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=3104989",
  abstract =     "Implicitly described domains are a well-established
                 tool in the simulation of time-dependent problems, for
                 example, using level-set methods. To solve partial
                 differential equations on such domains, a range of
                 numerical methods was developed, for example, the
                 Immersed Boundary method, the Unfitted Finite Element
                 or Unfitted Discontinuous Galerkin methods, and the
                 eXtended or Generalised Finite Element methods, just to
                 name a few. Many of these methods involve integration
                 over cut-cells or their boundaries, as they are
                 described by sub-domains of the original level-set
                 mesh. We present a new algorithm to geometrically
                 evaluate the integrals over domains described by a
                 first-order, conforming level-set function. The
                 integration is based on a polyhedral reconstruction of
                 the implicit geometry, following the concepts of the
                 marching cubes algorithm. The algorithm preserves
                 various topological properties of the implicit geometry
                 in its polyhedral reconstruction, making it suitable
                 for Finite Element computations. Numerical experiments
                 show second-order accuracy of the integration. An
                 implementation of the algorithm is available as free
                 software, which allows for an easy incorporation into
                 other projects. The software is in productive use
                 within the DUNE framework (Bastian et al. 2008a).",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Springer:2017:THP,
  author =       "Paul Springer and Jeff R. Hammond and Paolo
                 Bientinesi",
  title =        "{TTC}: A High-Performance Compiler for Tensor
                 Transpositions",
  journal =      j-TOMS,
  volume =       "44",
  number =       "2",
  pages =        "15:1--15:21",
  month =        sep,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3104988",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 17:19:59 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=3104988",
  abstract =     "We present Tensor Transpose Compiler (TTC), an
                 open-source parallel compiler for multidimensional
                 tensor transpositions. To generate high-performance C++
                 code, TTC explores a number of optimizations, including
                 software prefetching, blocking, loop-reordering, and
                 explicit vectorization. To evaluate the performance of
                 multidimensional transpositions across a range of
                 possible use-cases, we also release a benchmark
                 covering arbitrary transpositions of up to six
                 dimensions. Performance results show that the routines
                 generated by TTC achieve close to peak memory bandwidth
                 on both the Intel Haswell and the AMD Steamroller
                 architectures and yield significant performance gains
                 over modern compilers. By implementing a set of pruning
                 heuristics, TTC allows users to limit the number of
                 potential solutions; this option is especially useful
                 when dealing with high-dimensional tensors, as the
                 search space might become prohibitively large.
                 Experiments indicate that when only 100 potential
                 solutions are considered, the resulting performance is
                 about 99\% of that achieved with exhaustive search.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Joldes:2017:TRE,
  author =       "Mioara Joldes and Jean-Michel Muller and Valentina
                 Popescu",
  title =        "Tight and Rigorous Error Bounds for Basic Building
                 Blocks of Double-Word Arithmetic",
  journal =      j-TOMS,
  volume =       "44",
  number =       "2",
  pages =        "15res:1--15res:27",
  month =        oct,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3121432",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Oct 10 17:52:02 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3121432",
  abstract =     "We analyze several classical basic building blocks of
                 double-word arithmetic (frequently called
                 ``double-double arithmetic'' in the literature): the
                 addition of a double-word number and a floating-point
                 number, the addition of two double-word numbers, the
                 multiplication of a double-word number by a
                 floating-point number, the multiplication of two
                 double-word numbers, the division of a double-word
                 number by a floating-point number, and the division of
                 two double-word numbers. For multiplication and
                 division we get better relative error bounds than the
                 ones previously published. For addition of two
                 double-word numbers, we show that the previously
                 published bound was incorrect, and we provide a new
                 relative error bound. We introduce new algorithms for
                 division. We also give examples that illustrate the
                 tightness of our bounds.",
  acknowledgement = ack-nhfb,
  articleno =    "15res",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "This article is erroneously assigned the same article
                 number as the preceding one!",
}

@Article{Peise:2017:ARA,
  author =       "Elmar Peise and Paolo Bientinesi",
  title =        "{Algorithm 979}: Recursive Algorithms for Dense Linear
                 Algebra --- The {ReLAPACK} Collection",
  journal =      j-TOMS,
  volume =       "44",
  number =       "2",
  pages =        "16:1--16:19",
  month =        sep,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3061664",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 17:19:59 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=3061664",
  abstract =     "To exploit both memory locality and the full
                 performance potential of highly tuned kernels, dense
                 linear algebra libraries, such as linear algebra
                 package (LAPACK), commonly implement operations as
                 blocked algorithms. However, to achieve near-optimal
                 performance with such algorithms, significant tuning is
                 required. In contrast, recursive algorithms are
                 virtually tuning free and attain similar performance.
                 In this article, we first analyze and compare blocked
                 and recursive algorithms in terms of performance and
                 then introduce recursive LAPACK (ReLAPACK), an
                 open-source library of recursive algorithms to
                 seamlessly replace many of LAPACK's blocked algorithms.
                 In most scenarios, ReLAPACK outperforms reference
                 LAPACK and in many situations improves upon the
                 performance of optimized libraries.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Yeralan:2017:ASQ,
  author =       "Sencer Nuri Yeralan and Timothy A. Davis and Wissam M.
                 Sid-Lakhdar and Sanjay Ranka",
  title =        "{Algorithm 980}: Sparse {$ Q R $} Factorization on the
                 {GPU}",
  journal =      j-TOMS,
  volume =       "44",
  number =       "2",
  pages =        "17:1--17:29",
  month =        sep,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3065870",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 17:19:59 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=3065870",
  abstract =     "Sparse matrix factorization involves a mix of regular
                 and irregular computation, which is a particular
                 challenge when trying to obtain high-performance on the
                 highly parallel general-purpose computing cores
                 available on graphics processing units (GPUs). We
                 present a sparse multifrontal $ Q R $ factorization
                 method that meets this challenge and is significantly
                 faster than a highly optimized method on a multicore
                 CPU. Our method factorizes many frontal matrices in
                 parallel and keeps all the data transmitted between
                 frontal matrices on the GPU. A novel bucket scheduler
                 algorithm extends the communication-avoiding $ Q R $
                 factorization for dense matrices by exploiting more
                 parallelism and by exploiting the staircase form
                 present in the frontal matrices of a sparse
                 multifrontal method.",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rizzardi:2017:ATS,
  author =       "Mariarosaria Rizzardi",
  title =        "{Algorithm 981}: {Talbot Suite DE}: Application of
                 Modified {Talbot}'s Method to Solve Differential
                 Problems",
  journal =      j-TOMS,
  volume =       "44",
  number =       "2",
  pages =        "18:1--18:23",
  month =        sep,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3089248",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 17:19:59 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=3089248",
  abstract =     "In order to solve a differential problem, the Laplace
                 Transform method, when applicable, replaces the problem
                 with a simpler one; the solution is obtained by solving
                 the new problem and then by computing the inverse
                 Laplace Transform of this function. In a numerical
                 context, since the solution of the transformed problem
                 consists of a sequence of Laplace Transform samples,
                 most of the software for the numerical inversion cannot
                 be used since the transform, among parameters, must be
                 passed as a function. To fill this gap, we present
                 Talbot Suite DE, a C software collection for Laplace
                 Transform inversions, specifically designed for these
                 problems and based on Talbot's method. It contains both
                 sequential and parallel implementations; the latter is
                 accomplished by means of OpenMP. We also report some
                 performance results. Aimed at non-expert users, the
                 software is equipped with several examples and a User
                 Guide that includes the external documentation,
                 explains how to use all the sample code, and reports
                 its results about accuracy and efficiency. Some
                 examples are entirely in C and others combine different
                 programming languages (C/MATLAB, C/FORTRAN). The User
                 Guide also contains useful hints to avoid possible
                 errors issued during the compilation or execution of
                 mixed-language code.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Snyder:2017:AES,
  author =       "W. Van Snyder",
  title =        "{Algorithm 982}: Explicit Solutions of Triangular
                 Systems of First-Order Linear Initial-Value Ordinary
                 Differential Equations with Constant Coefficients",
  journal =      j-TOMS,
  volume =       "44",
  number =       "2",
  pages =        "19:1--19:4",
  month =        sep,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3092892",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 17:19:59 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=3092892",
  abstract =     "A method to compute explicit solutions of homogeneous
                 triangular systems of first-order linear initial-value
                 ordinary differential equations with constant
                 coefficients is described. It is suitable for the
                 limited case of well separated eigenvalues, or for
                 multiple zero eigenvalues provided the entire column
                 corresponding to a zero eigenvalue is zero. The
                 solution for the case of constant inhomogeneity is
                 described. The method requires only the computation of
                 a constant matrix using a simple recurrence. Computing
                 the solutions of the system from that matrix, for
                 values of the independent variable, requires one to
                 exponentiate only the diagonal of a matrix. It is not
                 necessary to compute the exponential of a general
                 triangular matrix. Although this work was motivated by
                 a study of nuclear decay without fission or neutron
                 absorption, which is used throughout as an example, it
                 has wider applicability.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fahmy:2017:AFC,
  author =       "Thierry Fahmy and Arnaud Bell{\'e}toile",
  title =        "{Algorithm 983}: Fast Computation of the
                 Non-Asymptotic {Cochran}'s {$Q$} Statistic for
                 Heterogeneity Detection",
  journal =      j-TOMS,
  volume =       "44",
  number =       "2",
  pages =        "20:1--20:12",
  month =        sep,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3095076",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 17:19:59 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=3095076",
  abstract =     "The detection of heterogeneity among objects
                 (products, treatments, medical studies) assessed on a
                 series of blocks (consumers, patients, methods,
                 pathologists) is critical in numerous areas such as
                 clinical research, cosmetic studies, or survey
                 analysis. The Cochran's $Q$ test is the most widely
                 used test for identifying heterogeneity on binary data
                 (success vs. failure, cure vs. not cure, 1 vs. 0,
                 etc.). For a large number of blocks, the $Q$
                 distribution can be approximated by a $ \chi^2$
                 distribution. Unfortunately, this does not hold for
                 limited sample sizes or sparse tables. In such
                 situations, one has to either run Monte Carlo
                 simulations or compute the exact $Q$ distribution to
                 obtain an accurate and reliable result. However, the
                 latter method is often disregarded in favor of the
                 former due to computational expense considerations. The
                 purpose of this article is to propose an extremely fast
                 implementation of the exact Cochran's $Q$ test so one
                 can benefit from its accuracy at virtually no cost
                 regarding computation time. It is implemented as a part
                 of the XLSTAT statistical software (Addinsoft 2015).
                 After a short presentation of the Cochran's $Q$ test
                 and the motivation for its exact version, we detail our
                 approach and present its actual implementation. We then
                 demonstrate the gain of this algorithm with performance
                 evaluations and measurements. Comparisons against a
                 well-established implementation have shown an increase
                 of the computational velocity by a factor ranging from
                 100 up to $ 1 \times 10^6$ in the most favorable
                 cases.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Weinstein:2017:AAT,
  author =       "Matthew J. Weinstein and Anil V. Rao",
  title =        "Algorithm 984: {ADiGator}, a Toolbox for the
                 Algorithmic Differentiation of Mathematical Functions
                 in {MATLAB} Using Source Transformation via Operator
                 Overloading",
  journal =      j-TOMS,
  volume =       "44",
  number =       "2",
  pages =        "21:1--21:25",
  month =        sep,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3104990",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 17:19:59 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=3104990",
  abstract =     "A toolbox called ADiGator is described for
                 algorithmically differentiating mathematical functions
                 in MATLAB. ADiGator performs source transformation via
                 operator overloading using forward mode algorithmic
                 differentiation and produces a file that can be
                 evaluated to obtain the derivative of the original
                 function at a numeric value of the input. A convenient
                 by-product of the file generation is the sparsity
                 pattern of the derivative function. Moreover, because
                 both the input and output to the algorithm are source
                 codes, the algorithm may be applied recursively to
                 generate derivatives of any order. A key component of
                 the algorithm is its ability to statically exploit
                 derivative sparsity at the MATLAB operation level to
                 improve runtime performance. The algorithm is applied
                 to four different classes of example problems and is
                 shown to produce runtime efficient derivative code. Due
                 to the static nature of the approach, the algorithm is
                 well suited and intended for use with problems
                 requiring many repeated derivative computations.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Zaghloul:2017:ASE,
  author =       "Mofreh R. Zaghloul",
  title =        "Algorithm 985: Simple, Efficient, and Relatively
                 Accurate Approximation for the Evaluation of the
                 {Faddeyeva} Function",
  journal =      j-TOMS,
  volume =       "44",
  number =       "2",
  pages =        "22:1--22:9",
  month =        sep,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3119904",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 19 17:19:59 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://dl.acm.org/citation.cfm?id=3119904",
  abstract =     "We present a new simple algorithm for efficient, and
                 relatively accurate computation of the Faddeyeva
                 function $ w(z) $. The algorithm carefully exploits
                 previous approximations by Hui et al. (1978) and
                 Huml{\'\i}cek (1982) along with asymptotic expressions
                 from Laplace continued fractions. Over a wide and fine
                 grid of the complex argument, $ z = x + i y $,
                 numerical results from the present approximation show a
                 maximum relative error less than $ 4.0 \times 10^{-5} $
                 for both real and imaginary parts of $w$ while running
                 in a relatively shorter execution time than other
                 competitive techniques. In addition to the calculation
                 of the Faddeyeva function, $w$, partial derivatives of
                 the real and imaginary parts of the function can easily
                 be calculated and returned as optional output.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Mehra:2017:ASC,
  author =       "Mani Mehra and Kuldip Singh Patel",
  title =        "{Algorithm 986}: A Suite of Compact Finite Difference
                 Schemes",
  journal =      j-TOMS,
  volume =       "44",
  number =       "2",
  pages =        "23:1--23:31",
  month =        oct,
  year =         "2017",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3119905",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Oct 5 18:31:10 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3119905",
  abstract =     "A collection of Matlab routines that compute
                 derivative approximations of arbitrary functions using
                 high-order compact finite difference schemes is
                 presented. Tenth-order accurate compact finite
                 difference schemes for first and second derivative
                 approximations and sixth-order accurate compact finite
                 difference schemes for third and fourth derivative
                 approximations are discussed for the functions with
                 periodic boundary conditions. Fourier analysis of
                 compact finite difference schemes is explained, and it
                 is observed that compact finite difference schemes have
                 better resolution characteristics when compared to
                 classical finite difference schemes. Compact finite
                 difference schemes for the functions with Dirichlet and
                 Neumann boundary conditions are also discussed.
                 Moreover, compact finite difference schemes for partial
                 derivative approximations of functions in two variables
                 are also given. For each case a Matlab routine is
                 provided to compute the differentiation matrix and
                 results are validated using the test functions.",
  acknowledgement = ack-nhfb,
  articleno =    "23",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hanson:2018:RAM,
  author =       "Richard J. Hanson and Tim Hopkins",
  title =        "Remark on {Algorithm 539: A Modern Fortran Reference
                 Implementation for Carefully Computing the {Euclidean}
                 Norm}",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "24:1--24:23",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3134441",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 22 17:49:32 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Lawson:1979:ABL}.",
  URL =          "https://dl.acm.org/citation.cfm?id=3134441",
  abstract =     "We propose a set of new Fortran reference
                 implementations, based on an algorithm proposed by
                 Kahan, for the Level 1 BLAS routines *NRM2 that compute
                 the Euclidean norm of a real or complex input vector.
                 The principal advantage of these routines over the
                 current offerings is that, rather than losing accuracy
                 as the length of the vector increases, they generate
                 results that are accurate to almost machine precision
                 for vectors of length $ N < N_{\rm max} $ where $
                 N_{\rm max} $ depends upon the precision of the
                 floating point arithmetic being used. In addition, we
                 make use of intrinsic modules, introduced in the latest
                 Fortran standards, to detect occurrences of non-finite
                 numbers in the input data and return suitable values as
                 well as setting IEEE floating point status flags as
                 appropriate. A set of C interface routines is also
                 provided to allow simple, portable access to the new
                 routines. To improve execution speed, we advocate a
                 hybrid algorithm; a simple loop is used first and, only
                 if IEEE floating point exception flags signal, do we
                 fall back on Kahan's algorithm. Since most input
                 vectors are ``easy,'' i.e., they do not require the
                 sophistication of Kahan's algorithm, the simple loop
                 improves performance while the use of compensated
                 summation ensures high accuracy. We also report on a
                 comprehensive suite of test problems that has been
                 developed to test both our new implementation and
                 existing codes for both accuracy and the appropriate
                 settings of the IEEE arithmetic status flags.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Neirynck:2018:NBA,
  author =       "Niels Neirynck and Willy Govaerts and Yuri A.
                 Kuznetsov and Hil G. E. Meijer",
  title =        "Numerical Bifurcation Analysis of Homoclinic Orbits
                 Embedded in One-Dimensional Manifolds of Maps",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "25:1--25:19",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3134443",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 22 17:49:32 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3134443",
  abstract =     "We describe new methods for initializing the
                 computation of homoclinic orbits for maps in a state
                 space with arbitrary dimension and for detecting their
                 bifurcations. The initialization methods build on known
                 and improved methods for computing one-dimensional
                 stable and unstable manifolds. The methods are
                 implemented in MatContM, a freely available toolbox in
                 Matlab for numerical analysis of bifurcations of fixed
                 points, periodic orbits, and connecting orbits of
                 smooth nonlinear maps. The bifurcation analysis of
                 homoclinic connections under variation of one parameter
                 is based on continuation methods and allows us to
                 detect all known codimension 1 and 2 bifurcations in
                 three-dimensional (3D) maps, including tangencies and
                 generalized tangencies. MatContM provides a graphical
                 user interface, enabling interactive control for all
                 computations. As the prime new feature, we discuss an
                 algorithm for initializing connecting orbits in the
                 important special case where either the stable or
                 unstable manifold is one-dimensional, allowing us to
                 compute all homoclinic orbits to saddle points in 3D
                 maps. We illustrate this algorithm in the study of the
                 adaptive control map, a 3D map introduced in 1991 by
                 Frouzakis, Adomaitis, and Kevrekidis, to obtain a
                 rather complete bifurcation diagram of the resonance
                 horn in a 1:5 Neimark--Sacker bifurcation point,
                 revealing new features.",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Elafrou:2018:SLH,
  author =       "Athena Elafrou and Vasileios Karakasis and Theodoros
                 Gkountouvas and Kornilios Kourtis and Georgios Goumas
                 and Nectarios Koziris",
  title =        "{SparseX}: A Library for High-Performance Sparse
                 Matrix--Vector Multiplication on Multicore Platforms",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "26:1--26:32",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3134442",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 22 17:49:32 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3134442",
  abstract =     "The Sparse Matrix-Vector Multiplication (SpMV) kernel
                 ranks among the most important and thoroughly studied
                 linear algebra operations, as it lies at the heart of
                 many iterative methods for the solution of sparse
                 linear systems, and often constitutes a severe
                 performance bottleneck. Its optimization, which is
                 intimately associated with the data structures used to
                 store the sparse matrix, has always been of particular
                 interest to the applied mathematics and computer
                 science communities and has attracted further attention
                 since the advent of multicore architectures. In this
                 article, we present SparseX, an open source software
                 package for SpMV targeting multicore platforms, that
                 employs the state-of-the-art Compressed Sparse eXtended
                 (CSX) sparse matrix storage format to deliver high
                 efficiency through a highly usable ``BLAS-like''
                 interface that requires limited or no tuning.
                 Performance results indicate that our library achieves
                 superior performance over competitive libraries on
                 large-scale problems.",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Doliskani:2018:SCR,
  author =       "Javad Doliskani and Pascal Giorgi and Romain Lebreton
                 and Eric Schost",
  title =        "Simultaneous Conversions with the Residue Number
                 System Using Linear Algebra",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "27:1--27:21",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3145573",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 22 17:49:32 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3145573",
  abstract =     "We present an algorithm for simultaneous conversions
                 between a given set of integers and their Residue
                 Number System representations based on linear algebra.
                 We provide a highly optimized implementation of the
                 algorithm that exploits the computational features of
                 modern processors. The main application of our
                 algorithm is matrix multiplication over integers. Our
                 speed-up of the conversions to and from the Residue
                 Number System significantly improves the overall
                 running time of matrix multiplication.",
  acknowledgement = ack-nhfb,
  articleno =    "27",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Springer:2018:DHP,
  author =       "Paul Springer and Paolo Bientinesi",
  title =        "Design of a High-Performance {GEMM}-like
                 Tensor--Tensor Multiplication",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "28:1--28:29",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3157733",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 22 17:49:32 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3157733",
  abstract =     "We present ``GEMM-like Tensor--Tensor multiplication''
                 (GETT), a novel approach for dense tensor contractions
                 that mirrors the design of a high-performance general
                 matrix--matrix multiplication (GEMM). The critical
                 insight behind GETT is the identification of three
                 index sets, involved in the tensor contraction, which
                 enable us to systematically reduce an arbitrary tensor
                 contraction to loops around a highly tuned
                 ``macro-kernel.'' This macro-kernel operates on
                 suitably prepared (``packed'') sub-tensors that reside
                 in a specified level of the cache hierarchy. In
                 contrast to previous approaches to tensor contractions,
                 GETT exhibits desirable features such as unit-stride
                 memory accesses, cache-awareness, as well as full
                 vectorization, without requiring auxiliary memory. We
                 integrate GETT alongside the so-called
                 Transpose-Transpose-GEMM-Transpose and Loops-over-GEMM
                 approaches into an open source ``Tensor Contraction
                 Code Generator.'' The performance results for a wide
                 range of tensor contractions suggest that GETT has the
                 potential of becoming the method of choice: While GETT
                 exhibits excellent performance across the board, its
                 effectiveness for bandwidth-bound tensor contractions
                 is especially impressive, outperforming existing
                 approaches by up to $ 12.4 \times $. More precisely,
                 GETT achieves speedups of up to $ 1.41 \times $ over an
                 equivalent-sized GEMM for bandwidth-bound tensor
                 contractions while attaining up to 91.3\% of peak
                 floating-point performance for compute-bound tensor
                 contractions.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sanders:2018:EPR,
  author =       "Peter Sanders and Sebastian Lamm and Lorenz
                 H{\"u}bschle-Schneider and Emanuel Schrade and Carsten
                 Dachsbacher",
  title =        "Efficient Parallel Random Sampling-Vectorized,
                 Cache-Efficient, and Online",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "29:1--29:14",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3157734",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 22 17:49:32 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3157734",
  abstract =     "We consider the problem of sampling $n$ numbers from
                 the range $ \{ 1, \ldots {}, N \} $ without replacement
                 on modern architectures. The main result is a simple
                 divide-and-conquer scheme that makes sequential
                 algorithms more cache efficient and leads to a parallel
                 algorithm running in expected time $ O(n / p + \log p)$
                 on $p$ processors, i.e., scales to massively parallel
                 machines even for moderate values of $n$. The amount of
                 communication between the processors is very small (at
                 most $ O(\log p)$) and independent of the sample size.
                 We also discuss modifications needed for load
                 balancing, online sampling, sampling with replacement,
                 Bernoulli sampling, and vectorization on SIMD units or
                 GPUs.",
  acknowledgement = ack-nhfb,
  articleno =    "29",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Harase:2018:IBM,
  author =       "Shin Harase and Takamitsu Kimoto",
  title =        "Implementing $ 64$-bit Maximally Equidistributed {$
                 F_2$}-Linear Generators with {Mersenne} Prime Period",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "30:1--30:11",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3159444",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 22 17:49:32 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3159444",
  abstract =     "CPUs and operating systems are moving from 32 to 64
                 bits, and hence it is important to have good
                 pseudorandom number generators designed to fully
                 exploit these word lengths. However, existing 64-bit
                 very long period generators based on linear recurrences
                 modulo 2 are not completely optimized in terms of the
                 equidistribution properties. Here, we develop 64-bit
                 maximally equidistributed pseudorandom number
                 generators that are optimal in this respect and have
                 speeds equivalent to 64-bit Mersenne Twisters. We
                 provide a table of specific parameters with period
                 lengths from $ 2^{607} - 1 $ to $ 2^{44497} - 1 $.",
  acknowledgement = ack-nhfb,
  articleno =    "30",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Birkisson:2018:ARO,
  author =       "{\'A}sgeir Birkisson",
  title =        "Automatic Reformulation of {ODEs} to Systems of
                 First-Order Equations",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "31:1--31:18",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3159443",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Jan 22 17:49:32 MST 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3159443",
  abstract =     "Most numerical ODE solvers require problems to be
                 written as systems of first-order differential
                 equations. This normally requires the user to rewrite
                 higher-order differential equations as coupled
                 first-order systems. Here, we introduce the treeVar
                 class, written in object-oriented Matlab, which is
                 capable of algorithmically reformulating higher-order
                 ODEs to equivalent systems of first-order equations.
                 This allows users to specify problems using a more
                 natural syntax and saves them from having to manually
                 derive the first-order reformulation. The technique
                 works by using operator overloading to build up syntax
                 trees of expressions as mathematical programs are
                 evaluated. It then applies a set of rules to the
                 resulting trees to obtain the first-order
                 reformulation, which is returned as another program.
                 This technique has connections with
                 algorithmic/automatic differentiation. We present how
                 treeVar has been incorporated in Chebfun, greatly
                 improving the ODE capabilities of the system.",
  acknowledgement = ack-nhfb,
  articleno =    "31",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Weinzierl:2018:QMF,
  author =       "Marion Weinzierl and Tobias Weinzierl",
  title =        "Quasi-matrix-free Hybrid Multigrid on Dynamically
                 Adaptive {Cartesian} Grids",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "32:1--32:44",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3165280",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:12 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3165280",
  abstract =     "We present a family of spacetree-based multigrid
                 realizations using the tree's multiscale nature to
                 derive coarse grids. They align with matrix-free
                 geometric multigrid solvers as they never assemble the
                 system matrices, which is cumbersome for dynamically
                 adaptive grids and full multigrid. The most
                 sophisticated realizations use BoxMG to construct
                 operator-dependent prolongation and restriction in
                 combination with Galerkin/Petrov--Galerkin coarse-grid
                 operators. This yields robust solvers for nontrivial
                 elliptic problems. We embed the algebraic,
                 problem-dependent, and grid-dependent multigrid
                 operators as stencils into the grid and evaluate all
                 matrix-vector products in situ throughout the grid
                 traversals. Such an approach is not literally
                 matrix-free as the grid carries the matrix. We propose
                 to switch to a hierarchical representation of all
                 operators. Only differences of algebraic operators to
                 their geometric counterparts are held. These
                 hierarchical differences can be stored and exchanged
                 with small memory footprint. Our realizations support
                 arbitrary dynamically adaptive grids while they
                 vertically integrate the multilevel operations through
                 spacetree linearization. This yields good memory access
                 characteristics, while standard colouring of mesh
                 entities with domain decomposition allows us to use
                 parallel many-core clusters. All realization
                 ingredients are detailed such that they can be used by
                 other codes.",
  acknowledgement = ack-nhfb,
  articleno =    "32",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Babuska:2018:REG,
  author =       "Ivo Babuska and Gustaf S{\"o}derlind",
  title =        "On Roundoff Error Growth in Elliptic Problems",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "33:1--33:22",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3134444",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:12 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3134444",
  abstract =     "Large-scale linear systems arise in finite-difference
                 and finite-element discretizations of elliptic
                 problems. With increasing computer performance, ever
                 larger systems are solved using direct methods. How
                 large can such systems be without roundoff compromising
                 accuracy? Here we model roundoff dynamics in standard $
                 L U $ and $ L D L^T $ decompositions with respect to
                 problem size $N$. For the one-dimensional (1D) Poisson
                 equation with Dirichlet boundary conditions on an
                 equidistant grid, we show that the relative error in
                 the factorized matrix grows like $ O(\epsilon \sqrt N)$
                 if roundoffs are modeled as independent, expectation
                 zero random variables. With bias, the growth rate
                 changes to $ O(\epsilon N)$. Subsequent back
                 substitution results in typical error growths of $
                 O(\epsilon > N \sqrt {N})$ and $ O(\epsilon N^2)$,
                 respectively. Error growth is governed by the dynamics
                 of the computational process and by the structure of
                 the boundary conditions rather than by the condition
                 number. Computational results are demonstrated in
                 several examples, including a few fourth-order 1D
                 problems and second-order 2D problems, showing that
                 error accumulation depends strongly on the solution
                 method. Thus, the same $ L U$ solver may exhibit
                 different growth rates for the same 2D Poisson problem,
                 depending on whether the five-point or nine-point FDM
                 operator is used.",
  acknowledgement = ack-nhfb,
  articleno =    "33",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Karol:2018:DSL,
  author =       "Sven Karol and Tobias Nett and Jeronimo Castrillon and
                 Ivo F. Sbalzarini",
  title =        "A Domain-Specific Language and Editor for Parallel
                 Particle Methods",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "34:1--34:32",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3175659",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:12 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3175659",
  abstract =     "Domain-specific languages (DSLs) are of increasing
                 importance in scientific high-performance computing to
                 reduce development costs, raise the level of
                 abstraction, and, thus, ease scientific programming.
                 However, designing DSLs is not easy, as it requires
                 knowledge of the application domain and experience in
                 language engineering and compilers. Consequently, many
                 DSLs follow a weak approach using macros or text
                 generators, which lack many of the features that make a
                 DSL comfortable for programmers. Some of these
                 features-e.g., syntax highlighting, type inference,
                 error reporting-are easily provided by language
                 workbenches, which combine language engineering
                 techniques and tools in a common ecosystem. In this
                 article, we present the Parallel Particle-Mesh
                 Environment (PPME), a DSL and development environment
                 for numerical simulations based on particle methods and
                 hybrid particle-mesh methods. PPME uses the Meta
                 Programming System, a projectional language workbench.
                 PPME is the successor of the Parallel Particle-Mesh
                 Language, a Fortran-based DSL that uses conventional
                 implementation strategies. We analyze and compare both
                 languages and demonstrate how the programmer's
                 experience is improved using static analyses and
                 projectional editing, i.e., code-structure editing,
                 constrained by syntax, as opposed to free-text editing.
                 We present an explicit domain model for particle
                 abstractions and the first formal type system for
                 particle methods.",
  acknowledgement = ack-nhfb,
  articleno =    "34",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Zottou:2018:AMC,
  author =       "Dimitra-Nefeli A. Zottou and Dimitris J. Kavvadias and
                 Frosso S. Makri and Michael N. Vrahatis",
  title =        "Algorithm 987: {MANBIS} --- a {C++} Mathematical
                 Software Package for Locating and Computing Efficiently
                 Many Roots of a Function: Theoretical Issues",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "35:1--35:7",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3155744",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:12 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3155744",
  acknowledgement = ack-nhfb,
  articleno =    "35",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Johnson:2018:AAE,
  author =       "Robert W. Johnson",
  title =        "Algorithm 988: {AMGKQ}: An Efficient Implementation of
                 Adaptive Multivariate {Gauss--Kronrod} Quadrature for
                 Simultaneous Integrands in {Octave\slash MATLAB}",
  journal =      j-TOMS,
  volume =       "44",
  number =       "3",
  pages =        "36:1--36:19",
  month =        apr,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3157735",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:12 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3157735",
  acknowledgement = ack-nhfb,
  articleno =    "36",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hwang:2018:CAC,
  author =       "John T. Hwang and Joaquim R. R. A. Martins",
  title =        "A Computational Architecture for Coupling
                 Heterogeneous Numerical Models and Computing Coupled
                 Derivatives",
  journal =      j-TOMS,
  volume =       "44",
  number =       "4",
  pages =        "37:1--37:39",
  month =        aug,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3182393",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:13 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3182393",
  abstract =     "One of the challenges in computational modeling is
                 coupling models to solve multidisciplinary problems.
                 Flow-based computational frameworks alleviate part of
                 the challenge through a modular approach, where data
                 flows from component to component. However, existing
                 flow-based frameworks are inefficient when coupled
                 derivatives are needed for optimization. To address
                 this, we develop the modular analysis and unified
                 derivatives (MAUD) architecture. MAUD formulates the
                 multidisciplinary model as a nonlinear system of
                 equations, which leads to a linear equation that
                 unifies all methods for computing derivatives. This
                 enables flow-based frameworks that use the MAUD
                 architecture to provide a common interface for the
                 chain rule, adjoint method, coupled adjoint method, and
                 hybrid methods; MAUD automatically uses the appropriate
                 method for the problem. A hierarchical, matrix-free
                 approach enables modern solution techniques such as
                 Newton--Krylov solvers to be used within this
                 monolithic formulation without computational overhead.
                 Two demonstration problems are solved using a Python
                 implementation of MAUD: a nanosatellite optimization
                 with more than 2 million unknowns and 25,000 design
                 variables, and an aircraft optimization involving over
                 6,000 design variables and 23,000 constraints. MAUD is
                 now implemented in the open source framework OpenMDAO,
                 which has been used to solve aircraft, satellite, wind
                 turbine, and turbofan engine design problems.",
  acknowledgement = ack-nhfb,
  articleno =    "37",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Emiris:2018:PPV,
  author =       "Ioannis Z. Emiris and Vissarion Fisikopoulos",
  title =        "Practical Polytope Volume Approximation",
  journal =      j-TOMS,
  volume =       "44",
  number =       "4",
  pages =        "38:1--38:21",
  month =        aug,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3194656",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:13 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3194656",
  abstract =     "We experimentally study the fundamental problem of
                 computing the volume of a convex polytope given as an
                 intersection of linear halfspaces. We implement and
                 evaluate randomized polynomial-time algorithms for
                 accurately approximating the polytope's volume in high
                 dimensions (e.g., few hundreds) based onhit-and-run
                 random walks. To carry out this efficiently, we
                 experimentally correlate the effect of parameters, such
                 as random walk length and number of sample points, with
                 accuracy and runtime. Our method is based on Monte
                 Carlo algorithms with guaranteed speed and provably
                 high probability of success for arbitrarily high
                 precision. We exploit the problem's features in
                 implementing a practical rounding procedure of
                 polytopes, in computing only partial ``generations'' of
                 random points, and in designing fast polytope boundary
                 oracles. Our publicly available software is
                 significantly faster than exact computation and more
                 accurate than existing approximation methods. For
                 illustration, volume approximations of Birkhoff
                 polytopes $B_{11},\ldots{}, B_{15}$ are computed, in
                 dimensions up to 196, whereas exact methods have only
                 computed volumes of up to $B_{10}$.",
  acknowledgement = ack-nhfb,
  articleno =    "38",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Dambra:2018:BSP,
  author =       "Pasqua D'ambra and Salvatore Filippone and Panayot S.
                 Vassilevski",
  title =        "{BootCMatch}: A Software Package for Bootstrap {AMG}
                 Based on Graph Weighted Matching",
  journal =      j-TOMS,
  volume =       "44",
  number =       "4",
  pages =        "39:1--39:25",
  month =        aug,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3190647",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:13 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3190647",
  abstract =     "This article has two main objectives: one is to
                 describe some extensions of an adaptive Algebraic
                 Multigrid (AMG) method of the form previously proposed
                 by the first and third authors, and a second one is to
                 present a new software framework, named BootCMatch,
                 which implements all the components needed to build and
                 apply the described adaptive AMG both as a stand-alone
                 solver and as a preconditioner in a Krylov method. The
                 adaptive AMG presented is meant to handle general
                 symmetric and positive definite (SPD) sparse linear
                 systems, without assuming any a priori information of
                 the problem and its origin; the goal of adaptivity is
                 to achieve a method with a prescribed convergence rate.
                 The presented method exploits a general coarsening
                 process based on aggregation of unknowns, obtained by a
                 maximum weight matching in the adjacency graph of the
                 system matrix. More specifically, a maximum product
                 matching is employed to define an effective smoother
                 subspace (complementary to the coarse space), a process
                 referred to as compatible relaxation, at every level of
                 the recursive two-level hierarchical AMG process.
                 Results on a large variety of test cases and
                 comparisons with related work demonstrate the
                 reliability and efficiency of the method and of the
                 software.",
  acknowledgement = ack-nhfb,
  articleno =    "39",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Escobedo:2018:SDL,
  author =       "Adolfo R. Escobedo and Erick Moreno-Centeno and
                 Christopher Lourenco",
  title =        "Solution of Dense Linear Systems via
                 Roundoff-Error-Free Factorization Algorithms:
                 Theoretical Connections and Computational Comparisons",
  journal =      j-TOMS,
  volume =       "44",
  number =       "4",
  pages =        "40:1--40:24",
  month =        aug,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3199571",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:13 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3199571",
  abstract =     "Exact solving of systems of linear equations (SLEs) is
                 a fundamental subroutine within number theory, formal
                 verification of mathematical proofs, and
                 exact-precision mathematical programming. Moreover,
                 efficient exact SLE solution methods could be valuable
                 for a growing body of science and engineering
                 applications where current fixed-precision standards
                 have been deemed inadequate. This article contains key
                 derivations relating, and computational tests
                 comparing, two exact direct solution frameworks:
                 roundoff-error-free (REF) LU factorization and rational
                 arithmetic LU factorization. Specifically, both
                 approaches solve the linear system Ax = b by factoring
                 the matrix A into the product of a lower triangular (L)
                 and upper triangular (U) matrix, A = LU. Most
                 significantly, the featured findings reveal that the
                 integer-preserving REF factorization framework solves
                 dense SLEs one order of magnitude faster than the exact
                 rational arithmetic approach while requiring half the
                 memory. Since rational LU is utilized for basic
                 solution validation in exact linear and mixed-integer
                 programming, these results offer preliminary evidence
                 of the potential of the REF factorization framework to
                 be utilized within this specific context. Additionally,
                 this article develops and analyzes an efficient
                 streamlined version of Edmonds's Q-matrix approach that
                 can be implemented as another basic solution validation
                 approach. Further experiments demonstrate that the REF
                 factorization framework also outperforms this
                 alternative integer-preserving approach in terms of
                 memory requirements and computational effort. General
                 purpose codes to solve dense SLEs exactly via any of
                 the aforementioned methods have been made available to
                 the research and academic communities.",
  acknowledgement = ack-nhfb,
  articleno =    "40",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Magron:2018:IEU,
  author =       "Victor Magron",
  title =        "Interval Enclosures of Upper Bounds of Roundoff Errors
                 Using Semidefinite Programming",
  journal =      j-TOMS,
  volume =       "44",
  number =       "4",
  pages =        "41:1--41:18",
  month =        aug,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3206430",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:13 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3206430",
  abstract =     "A long-standing problem related to floating-point
                 implementation of numerical programs is to provide
                 efficient yet precise analysis of output errors. We
                 present a framework to compute lower bounds on largest
                 absolute roundoff errors, for a particular rounding
                 model. This method applies to numerical programs
                 implementing polynomial functions with box constrained
                 input variables. Our study is based on three different
                 hierarchies, relying respectively on generalized
                 eigenvalue problems, elementary computations, and
                 semidefinite programming (SDP) relaxations. This is
                 complementary of over-approximation frameworks,
                 consisting of obtaining upper bounds on the largest
                 absolute roundoff error. Combining the results of both
                 frameworks allows one to get enclosures for upper
                 bounds on roundoff errors. The under-approximation
                 framework provided by the third hierarchy is based on a
                 new sequence of convergent robust SDP approximations
                 for certain classes of polynomial optimization
                 problems. Each problem in this hierarchy can be solved
                 exactly via SDP. By using this hierarchy, one can
                 provide a monotone nondecreasing sequence of lower
                 bounds converging to the absolute roundoff error of a
                 program implementing a polynomial function, applying
                 for a particular rounding model. We investigate the
                 efficiency and precision of our method on nontrivial
                 polynomial programs coming from space control,
                 optimization, and computational biology.",
  acknowledgement = ack-nhfb,
  articleno =    "41",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Frison:2018:BBL,
  author =       "Gianluca Frison and Dimitris Kouzoupis and Tommaso
                 Sartor and Andrea Zanelli and Moritz Diehl",
  title =        "{BLASFEO}: Basic Linear Algebra Subroutines for
                 Embedded Optimization",
  journal =      j-TOMS,
  volume =       "44",
  number =       "4",
  pages =        "42:1--42:30",
  month =        aug,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3210754",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:13 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3210754",
  abstract =     "Basic Linear Algebra Subroutines for Embedded
                 Optimization (BLASFEO) is a dense linear algebra
                 library providing high-performance implementations of
                 BLAS- and LAPACK-like routines for use in embedded
                 optimization and small-scale high-performance
                 computing, in general. A key difference with respect to
                 existing high-performance implementations of BLAS is
                 that the computational performance is optimized for
                 small- to medium-scale matrices, i.e., for sizes up to
                 a few hundred. BLASFEO comes with three different
                 implementations: a high-performance implementation
                 aimed at providing the highest performance for matrices
                 fitting in cache, a reference implementation providing
                 portability and embeddability and optimized for very
                 small matrices, and a wrapper to standard BLAS and
                 LAPACK providing high performance on large matrices.
                 The three implementations of BLASFEO together provide
                 high-performance dense linear algebra routines for
                 matrices ranging from very small to large. Compared to
                 both open-source and proprietary highly tuned BLAS
                 libraries, for matrices of size up to about 100, the
                 high-performance implementation of BLASFEO is about
                 20--30\% faster than the corresponding level 3 BLAS
                 routines and two to three times faster than the
                 corresponding LAPACK routines.",
  acknowledgement = ack-nhfb,
  articleno =    "42",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Huang:2018:ROO,
  author =       "Wen Huang and P.-A. Absil and Kyle A. Gallivan and
                 Paul Hand",
  title =        "{ROPTLIB}: An Object-Oriented {C++} Library for
                 Optimization on {Riemannian} Manifolds",
  journal =      j-TOMS,
  volume =       "44",
  number =       "4",
  pages =        "43:1--43:21",
  month =        aug,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3218822",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:13 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3218822",
  abstract =     "Riemannian optimization is the task of finding an
                 optimum of a real-valued function defined on a
                 Riemannian manifold. Riemannian optimization has been a
                 topic of much interest over the past few years due to
                 many applications including computer vision, signal
                 processing, and numerical linear algebra. The
                 substantial background required to successfully design
                 and apply Riemannian optimization algorithms is a
                 significant impediment for many potential users.
                 Therefore, multiple packages, such as Manopt (in
                 Matlab) and Pymanopt (in Python), have been developed.
                 This article describes ROPTLIB, a C++ library for
                 Riemannian optimization. Unlike prior packages, ROPTLIB
                 simultaneously achieves the following goals: (i) it has
                 user-friendly interfaces in Matlab, Julia, and C++;
                 (ii) users do not need to implement manifold- and
                 algorithm-related objects; (iii) it provides efficient
                 computational time due to its C++ core; (iv) it
                 implements state-of-the-art generic Riemannian
                 optimization algorithms, including quasi-Newton
                 algorithms; and (v) it is based on object-oriented
                 programming, allowing users to rapidly add new
                 algorithms and manifolds.",
  acknowledgement = ack-nhfb,
  articleno =    "43",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Brehard:2018:VNE,
  author =       "Florent Br{\'e}hard and Nicolas Brisebarre and Mioara
                 Joldes",
  title =        "Validated and Numerically Efficient {Chebyshev}
                 Spectral Methods for Linear Ordinary Differential
                 Equations",
  journal =      j-TOMS,
  volume =       "44",
  number =       "4",
  pages =        "44:1--44:42",
  month =        aug,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3208103",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:13 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3208103",
  abstract =     "In this work, we develop a validated numeric method
                 for the solution of linear ordinary differential
                 equations (LODEs). A wide range of algorithms (i.e.,
                 Runge--Kutta, collocation, spectral methods) exist for
                 numerically computing approximations of the solutions.
                 Most of these come with proofs of asymptotic
                 convergence, but usually, provided error bounds are
                 nonconstructive. However, in some domains like critical
                 systems and computer-aided mathematical proofs, one
                 needs validated effective error bounds. We focus on
                 both the theoretical and practical complexity analysis
                 of a so-called a posteriori quasi-Newton validation
                 method, which mainly relies on a fixed-point argument
                 of a contracting map. Specifically, given a polynomial
                 approximation, obtained by some numerical algorithm and
                 expressed on a Chebyshev basis, our algorithm
                 efficiently computes an accurate and rigorous error
                 bound. For this, we study theoretical properties like
                 compactness, convergence, and invertibility of
                 associated linear integral operators and their
                 truncations in a suitable coefficient space of
                 Chebyshev series. Then, we analyze the almost-banded
                 matrix structure of these operators, which allows for
                 very efficient numerical algorithms for both numerical
                 solutions of LODEs and rigorous computation of the
                 approximation error. Finally, several representative
                 examples show the advantages of our algorithms as well
                 as their theoretical and practical limits.",
  acknowledgement = ack-nhfb,
  articleno =    "44",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Deng:2018:SFE,
  author =       "Lih-Yuan Deng and Jyh-Jen Horng Shiau and Henry
                 Horng-Shing Lu and Dale Bowman",
  title =        "{Secure and Fast Encryption (SAFE)} with Classical
                 Random Number Generators",
  journal =      j-TOMS,
  volume =       "44",
  number =       "4",
  pages =        "45:1--45:17",
  month =        aug,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3212673",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:13 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3212673",
  abstract =     "Pseudo-random number generators (PRNGs) play an
                 important role in both areas of computer simulation and
                 computer security. Currently, there appears to be a
                 huge divide between the types of PRNGs used in these
                 two areas. For PRNGs in computer security applications,
                 the security concern is extremely important. For PRNGs
                 in computer simulation applications, the properties of
                 high-dimensional equi-distribution, efficiency, long
                 period-length, and portability are important. In recent
                 years, there have been many PRNGs proposed in the area
                 of computer simulation satisfying these nice
                 properties. However, most of them are linear
                 generators, thus sharing the same weakness in
                 predictability. The major aim of this article is to
                 propose a general class of secure generators, called
                 SAFE (secure and fast encryption) generators, by
                 properly ``mixing'' two baseline generators with the
                 aforementioned properties to obtain a secure generator
                 that would inherit these nice properties. Specifically,
                 we propose applying a general mutual-shuffling method
                 to certain linear generators, such as the currently
                 most popular MT19937 generator and large-order multiple
                 recursive generators, as well as outputting certain
                 nonlinear transformations of the generated variates to
                 construct secure PRNGS.",
  acknowledgement = ack-nhfb,
  articleno =    "45",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Tan:2018:DIA,
  author =       "Guangming Tan and Junhong Liu and Jiajia Li",
  title =        "Design and Implementation of Adaptive {SpMV} Library
                 for Multicore and Many-Core Architecture",
  journal =      j-TOMS,
  volume =       "44",
  number =       "4",
  pages =        "46:1--46:25",
  month =        aug,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3218823",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:13 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3218823",
  abstract =     "Sparse matrix vector multiplication (SpMV) is an
                 important computational kernel in traditional
                 high-performance computing and emerging data-intensive
                 applications. Previous SpMV libraries are optimized by
                 either application-specific or architecture-specific
                 approaches but present difficulties for use in real
                 applications. In this work, we develop an auto-tuning
                 system (SMATER) to bridge the gap between specific
                 optimizations and general-purpose use. SMATER provides
                 programmers a unified interface based on the compressed
                 sparse row (CSR) sparse matrix format by implicitly
                 choosing the best format and fastest implementation for
                 any input sparse matrix during runtime. SMATER
                 leverages a machine-learning model and retargetable
                 back-end library to quickly predict the optimal
                 combination. Performance parameters are extracted from
                 2,386 matrices in the SuiteSparse matrix collection.
                 The experiments show that SMATER achieves good
                 performance (up to 10 times that of the Intel Math
                 Kernel Library (MKL) on Intel E5-2680 v3) while being
                 portable on state-of-the-art x86 multicore processors,
                 NVIDIA GPUs, and Intel Xeon Phi accelerators. Compared
                 with the Intel MKL library, SMATER runs faster by more
                 than 2.5 times on average. We further demonstrate its
                 adaptivity in an algebraic multigrid solver from the
                 Hypre library and report greater than 20\% performance
                 improvement.",
  acknowledgement = ack-nhfb,
  articleno =    "46",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Irurozki:2018:APM,
  author =       "Ekhine Irurozki and Josu Ceberio and Josean Santamaria
                 and Roberto Santana and Alexander Mendiburu",
  title =        "Algorithm 989: {\tt perm\_mateda}: a {Matlab} Toolbox
                 of Estimation of Distribution Algorithms for
                 Permutation-based Combinatorial Optimization Problems",
  journal =      j-TOMS,
  volume =       "44",
  number =       "4",
  pages =        "47:1--47:13",
  month =        aug,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3206429",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Oct 5 11:23:13 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3206429",
  acknowledgement = ack-nhfb,
  articleno =    "47",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ozkan:2018:AEA,
  author =       "Aysegul Ozkan and Rahul Prabhu and Troy Baker and
                 James Pence and J{\"o}rg Peters and Meera Sitharam",
  title =        "Algorithm 990: Efficient Atlasing and Search of
                 Configuration Spaces of Point-Sets Constrained by
                 Distance Intervals",
  journal =      j-TOMS,
  volume =       "44",
  number =       "4",
  pages =        "48:1--48:30",
  month =        aug,
  year =         "2018",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3204472",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  MRclass =      "65Y15 (65D18)",
  MRnumber =     "3865836",
  bibdate =      "Fri Oct 5 11:23:13 MDT 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/p/peters-jorg.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3204472",
  acknowledgement = ack-nhfb,
  articleno =    "48",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Aktas:2019:CBM,
  author =       "Mehmet E. Aktas and Esra Akbas",
  title =        "Computing the Braid Monodromy of Completely Reducible
                 $n$-gonal Curves",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "1:1--1:11",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3291040",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3291040",
  abstract =     "Braid monodromy is an important tool for computing
                 invariants of curves and surfaces. In this paper, the
                 rectangular braid diagram (RBD) method is proposed to
                 compute the braid monodromy of a completely reducible
                 $n$-gonal curve, i.e., the curves in the form $ (y -
                 y_1 (x)) \ldots {} (y - y_n(x)) = 0$, where $ n \in
                 Z^+$ and $ y_i \in C[x]$. Also, an algorithm is
                 presented to compute the Alexander polynomial of these
                 curve complements using Burau representations of braid
                 groups. Examples for each computation are provided.",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Amestoy:2019:PSB,
  author =       "Patrick R. Amestoy and Alfredo Buttari and Jean-Yves
                 L'Excellent and Theo Mary",
  title =        "Performance and Scalability of the Block Low-Rank
                 Multifrontal Factorization on Multicore Architectures",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "2:1--2:26",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3242094",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/multithreading.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3242094",
  abstract =     "Matrices coming from elliptic Partial Differential
                 Equations have been shown to have a low-rank property
                 that can be efficiently exploited in multifrontal
                 solvers to provide a substantial reduction of their
                 complexity. Among the possible low-rank formats, the
                 Block Low-Rank format (BLR) is easy to use in a general
                 purpose multifrontal solver and its potential compared
                 to standard (full-rank) solvers has been demonstrated.
                 Recently, new variants have been introduced and it was
                 proved that they can further reduce the complexity but
                 their performance has never been analyzed. In this
                 article, we present a multithreaded BLR factorization
                 and analyze its efficiency and scalability in
                 shared-memory multicore environments. We identify the
                 challenges posed by the use of BLR approximations in
                 multifrontal solvers and put forward several
                 algorithmic variants of the BLR factorization that
                 overcome these challenges by improving its efficiency
                 and scalability. We illustrate the performance analysis
                 of the BLR multifrontal factorization with numerical
                 experiments on a large set of problems coming from a
                 variety of real-life applications.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Boukaram:2019:HMO,
  author =       "Wajih Boukaram and George Turkiyyah and David Keyes",
  title =        "Hierarchical Matrix Operations on {GPUs}:
                 Matrix--Vector Multiplication and Compression",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "3:1--3:28",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3232850",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3232850",
  abstract =     "Hierarchical matrices are space- and time-efficient
                 representations of dense matrices that exploit the
                 low-rank structure of matrix blocks at different levels
                 of granularity. The hierarchically low-rank block
                 partitioning produces representations that can be
                 stored and operated on in near-linear complexity
                 instead of the usual polynomial complexity of dense
                 matrices. In this article, we present high-performance
                 implementations of matrix vector multiplication and
                 compression operations for the H 2 variant of
                 hierarchical matrices on GPUs. The H 2 variant
                 exploits, in addition to the hierarchical block
                 partitioning, hierarchical bases for the block
                 representations and results in a scheme that requires
                 only O ( n ) storage and O ( n ) complexity for the
                 mat-vec and compression kernels. These two operations
                 are at the core of algebraic operations for
                 hierarchical matrices, the mat-vec being a ubiquitous
                 operation in numerical algorithms while
                 compression/recompression represents a key building
                 block for other algebraic operations, which require
                 periodic recompression during execution. The
                 difficulties in developing efficient GPU algorithms
                 come primarily from the irregular tree data structures
                 that underlie the hierarchical representations, and the
                 key to performance is to recast the computations on
                 flattened trees in ways that allow batched linear
                 algebra operations to be performed. This requires
                 marshaling the irregularly laid out data in a way that
                 allows them to be used by the batched routines.
                 Marshaling operations only involve pointer arithmetic
                 with no data movement and as a result have minimal
                 overhead. Our numerical results on covariance matrices
                 from 2D and 3D problems from spatial statistics show
                 the high efficiency our routines achieve over 550GB/s
                 for the bandwidth-limited matrix--vector operation and
                 over 850GFLOPS/s in sustained performance for the
                 compression operation on the P100 Pascal GPU.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Martinsson:2019:RBR,
  author =       "P. G. Martinsson and G. Quintana-Ort{\'\i} and N.
                 Heavner",
  title =        "{randUTV}: A Blocked Randomized Algorithm for
                 Computing a Rank-Revealing {$ U T V $} Factorization",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "4:1--4:26",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3242670",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3242670",
  abstract =     "A randomized algorithm for computing a so-called UTV
                 factorization efficiently is presented. Given a matrix
                 A, the algorithm `randUTV' computes a factorization A =
                 UTV *, where U and V have orthonormal columns, and T is
                 triangular (either upper or lower, whichever is
                 preferred). The algorithm randUTV is developed
                 primarily to be a fast and easily parallelized
                 alternative to algorithms for computing the Singular
                 Value Decomposition (SVD). randUTV provides accuracy
                 very close to that of the SVD for problems such as
                 low-rank approximation, solving ill-conditioned linear
                 systems, and determining bases for various subspaces
                 associated with the matrix. Moreover, randUTV produces
                 highly accurate approximations to the singular values
                 of A. Unlike the SVD, the randomized algorithm proposed
                 builds a UTV factorization in an incremental,
                 single-stage, and noniterative way, making it possible
                 to halt the factorization process once a specified
                 tolerance has been met. Numerical experiments comparing
                 the accuracy and speed of randUTV to the SVD are
                 presented. Other experiments also demonstrate that in
                 comparison to column-pivoted QR, which is another
                 factorization that is often used as a relatively
                 economic alternative to the SVD, randUTV compares
                 favorably in terms of speed while providing far higher
                 accuracy.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kulisch:2019:MSI,
  author =       "Ulrich Kulisch",
  title =        "Mathematics and Speed for Interval Arithmetic: A
                 Complement to {IEEE 1788}",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "5:1--5:22",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3264448",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3264448",
  abstract =     "After a short introduction, the article begins with an
                 axiomatic definition of rounded arithmetic. The
                 concepts of rounding and of rounded arithmetic
                 operations are defined in an axiomatic manner fully
                 independent of special data formats and encodings.
                 Basic properties of floating-point and interval
                 arithmetic can directly be derived from this abstract
                 mathematical model. Interval operations are defined as
                 set operations for elements of the set {\=I}R of closed
                 and connected sets of real numbers. As such, they form
                 an algebraically closed subset of the powerset of the
                 real numbers. This property leads to explicit formulas
                 for the arithmetic operations of floating-point
                 intervals of {\=I}F, which are executable on the
                 computer. Arithmetic for intervals of {\=I}F forms an
                 exception free calculus, i.e., arithmetic operations
                 for intervals of {\=I}F always lead to intervals of
                 {\=I}F again. Later sections are concerned with
                 programming support and hardware for interval
                 arithmetic. Both are a must and absolutely necessary to
                 move interval arithmetic more into the center of
                 scientific computing. With some minor hardware
                 additions, interval operations can be made as fast as
                 simple floating-point operations. In vector and matrix
                 spaces for real, complex, and interval data, the dot
                 product is a fundamental arithmetic operation.
                 Computing the dot product of two vectors with
                 floating-point components exactly substantially speeds
                 up floating-point and interval arithmetic as well as
                 the accuracy of the computed result. Hardware needed
                 for the exact dot product is very modest. The exact dot
                 product is essential for long real and long interval
                 arithmetic. Section 9 illustrates that interval
                 arithmetic as developed in this article already has a
                 long tradition. Products based on these ideas have been
                 available since 1980. Implementing what the article
                 advocates would have a profound effect on mathematical
                 software. Modern processor architecture from Intel, for
                 example, comes quite close to what is requested in this
                 article.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Wang:2019:PAA,
  author =       "Shouxiang Wang and Kai Wang and Lei Wu and Chengshan
                 Wang",
  title =        "Polar Affine Arithmetic: Optimal Affine Approximation
                 and Operation Development for Computation in Polar Form
                 Under Uncertainty",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "6:1--6:29",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3274659",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3274659",
  abstract =     "Uncertainties practically arise from numerous factors,
                 such as ambiguous information, inaccurate model, and
                 environment disturbance. Interval arithmetic has
                 emerged to solve problems with uncertain parameters,
                 especially in the computational process where only the
                 upper and lower bounds of parameters can be
                 ascertained. In rectangular coordinate systems, the
                 basic interval operations and improved interval
                 algorithms have been developed in the numerical
                 analysis. However, in polar coordinate systems,
                 interval arithmetic still suffers from issues of
                 complex computation and overestimation. This article
                 defines a polar affine variable and develops a polar
                 affine arithmetic (PAA) that extends affine arithmetic
                 to the polar coordinate systems, which performs better
                 in many aspects than the corresponding polar interval
                 arithmetic (PIA). Basic arithmetic operations are
                 developed based on the complex affine arithmetic. The
                 Chebyshev approximation theory and the min-range
                 approximation theory are used to identify the best
                 affine approximation. PAA can accurately keep track of
                 the interdependency among multiple variables throughout
                 the calculation procedure, which prominently reduces
                 the solution conservativeness. Numerical examples
                 implemented in MATLAB programs show that, compared with
                 benchmark results from the Monte Carlo method, the
                 proposed PAA ensures completeness of the exact solution
                 and presents a more compact solution region than PIA
                 when dependency exists in the calculation process.
                 Meanwhile, a comparison of affine arithmetic in polar
                 and rectangular coordinates is presented. An
                 application of PAA in circuit analysis is
                 quantitatively presented and potential applications in
                 other research fields involving complex variables in
                 polar form will be gradually developed.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{DaSilva:2019:ULS,
  author =       "Curt {Da Silva} and Felix Herrmann",
  title =        "A Unified {$2$D\slash $3$D} Large-Scale Software
                 Environment for Nonlinear Inverse Problems",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "7:1--7:35",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3291042",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3291042",
  abstract =     "Large-scale parameter estimation problems are among
                 some of the most computationally demanding problems in
                 numerical analysis. An academic researcher's
                 domain-specific knowledge often precludes that of
                 software design, which results in inversion frameworks
                 that are technically correct but not scalable to
                 realistically sized problems. On the other hand, the
                 computational demands for realistic problems result in
                 industrial codebases that are geared solely for high
                 performance, rather than comprehensibility or
                 flexibility. We propose a new software design for
                 inverse problems constrained by partial differential
                 equations that bridges the gap between these two
                 seemingly disparate worlds. A hierarchical and modular
                 design reduces the cognitive burden on the user while
                 exploiting high-performance primitives at the lower
                 levels. Our code has the added benefit of actually
                 reflecting the underlying mathematics of the problem,
                 which lowers the cognitive load on the user using it
                 and reduces the initial startup period before a
                 researcher can be fully productive. We also introduce a
                 new preconditioner for the {$3$D} Helmholtz equation
                 that is suitable for fault-tolerant distributed
                 systems. Numerical experiments on a variety of {$2$D}
                 and {$3$D} test problems demonstrate the effectiveness
                 of this approach on scaling algorithms from small- to
                 large-scale problems with minimal code changes.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Green:2019:EBS,
  author =       "Kevin R. Green and Raymond J. Spiteri",
  title =        "Extended {BACOLI}: Solving One-Dimensional Multiscale
                 Parabolic {PDE} Systems With Error Control",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "8:1--8:19",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3301320",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3301320",
  abstract =     "BACOLI is a Fortran software package for solving
                 one-dimensional parabolic partial differential
                 equations (PDEs) with separated boundary conditions by
                 B-spline adaptive collocation methods. A distinguishing
                 feature of BACOLI is its ability to estimate and
                 control error and correspondingly adapt meshes in both
                 space and time. Many models of scientific interest,
                 however, can be formulated as multiscale parabolic PDE
                 systems, that is, models that couple a system of
                 parabolic PDEs describing dynamics on a global scale
                 with a system of ordinary differential equations
                 describing dynamics on a local scale. This article
                 describes the Fortran software eBACOLI, the extension
                 of BACOLI to solve such multiscale models. The
                 performance of the extended software is demonstrated to
                 be statistically equivalent to the original for purely
                 parabolic PDE systems. Results from eBACOLI are given
                 for various multiscale models from the extended problem
                 class considered.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Walther:2019:VNR,
  author =       "Christoph Walther",
  title =        "Verified {Newton--Raphson} Iteration for
                 Multiplicative Inverses Modulo Powers of Any Base",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "9:1--9:7",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3301317",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  note =         "See \cite{Dumas:2014:NRI}.",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3301317",
  abstract =     "We identify two faults in a published algorithm for
                 fast computation of multiplicative inverses modulo
                 prime powers. We patch the algorithm and present
                 machine-assisted proofs of correctness of the repair.
                 Our formal proofs also reveal that being prime is an
                 unnecessary demand for the power base, thus attributing
                 a wider scope of applications to the repaired
                 algorithm.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Springer:2019:SSH,
  author =       "Paul Springer and Devin Matthews and Paolo
                 Bientinesi",
  title =        "Spin Summations: A High-Performance Perspective",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "10:1--10:22",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3301319",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3301319",
  abstract =     "In addition to tensor contractions, one of the most
                 pronounced computational bottlenecks in the
                 nonorthogonally spin-adapted forms of the quantum
                 chemistry methods CCSDT and CCSDTQ, and their
                 approximate forms-including CCSD(T) and CCSDT(Q)-are
                 spin summations. At a first sight, spin summations are
                 operations similar to tensor transpositions, but a
                 closer look reveals additional challenges to
                 high-performance calculations, including temporal
                 locality and scattered memory accesses. This article
                 explores a sequence of algorithmic solutions for spin
                 summations, each exploiting individual properties of
                 either the underlying hardware (e.g., caches,
                 vectorization) or the problem itself (e.g.,
                 factorizability). The final algorithm combines the
                 advantages of all the solutions while avoiding their
                 drawbacks; this algorithm achieves high performance
                 through parallelization and vectorization, and by
                 exploiting the temporal locality inherent to spin
                 summations. Combined, these optimizations result in
                 speedups between $2.4 \times $ and $5.5 \times $ over
                 the NCC quantum chemistry software package. In addition
                 to such a performance boost, our algorithm can perform
                 the spin summations in-place, thus reducing the memory
                 footprint by $2 \times $ over an out-of-place
                 variant.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Shterenlikht:2019:QIF,
  author =       "A. Shterenlikht",
  title =        "On Quality of Implementation of {Fortran 2008} Complex
                 Intrinsic Functions on Branch Cuts",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "11:1--11:9",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3301318",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3301318",
  abstract =     "Branch cuts in complex functions have important uses
                 in fracture mechanics, jet flow, and aerofoil analysis.
                 This article introduces tests for validating Fortran
                 2008 complex functions-LOG, SQRT, ASIN, ACOS, ATAN,
                 ASINH, ACOSH, and ATANH-on branch cuts with arguments
                 of all 3 IEEE floating-point binary formats: binary32,
                 binary64, and binary128, including signed zero and
                 signed infinity. Multiple test failures were revealed,
                 such as wrong signs of results or unexpected overflow,
                 underflow, or NaN. We conclude that the quality of
                 implementation of these Fortran 2008 intrinsics in many
                 compilers is not yet sufficient to remove the need for
                 special code for branch cuts. The electronic appendix
                 contains the full test results with 8 Fortran 2008
                 compilers: GCC, Flang, Cray, Oracle, PGI, Intel, NAG,
                 and IBM, detailed derivations of the values of these
                 functions on branch cuts and conformal maps of the
                 branch cuts, to be used as a reference. The tests and
                 the results are freely available from
                 https://cmplx.sourceforge.io. This work will be of
                 interest to engineers who use complex functions, as
                 well as to compiler and math library developers.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Richardson:2019:ATS,
  author =       "Lee F. Richardson and William F. Eddy",
  title =        "Algorithm 991: The {$2$D} Tree Sliding Window
                 {Discrete Fourier Transform}",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "12:1--12:12",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3264426",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3264426",
  abstract =     "We present a new algorithm for the $2$D sliding window
                 discrete Fourier transform. Our algorithm avoids
                 repeating calculations in overlapping windows by
                 storing them in a tree data-structure based on the
                 ideas of the Cooley-Tukey fast Fourier transform. For
                 an $N_0 \times N_1$ array and $n_0 \times n_1$ windows,
                 our algorithm takes $O(N_0 N_1 n_0 n_1)$ operations. We
                 provide a C implementation of our algorithm for the
                 Radix-2 case, compare ours to existing algorithms, and
                 show how our algorithm easily extends to higher
                 dimensions.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Roth:2019:AOC,
  author =       "{\'A}goston R{\'o}th",
  title =        "Algorithm 992: An {OpenGL}- and {C++}-based Function
                 Library for Curve and Surface Modeling in a Large Class
                 of Extended {Chebyshev} Spaces",
  journal =      j-TOMS,
  volume =       "45",
  number =       "1",
  pages =        "13:1--13:32",
  month =        mar,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3284979",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/multithreading.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Roth:2021:RAO}.",
  URL =          "https://dl.acm.org/citation.cfm?id=3284979",
  abstract =     "We propose a platform-independent multi-threaded
                 function library that provides data structures to
                 generate, differentiate, and render both the ordinary
                 basis and the normalized B-basis of a user-specified
                 extended Chebyshev (EC) space that comprises the
                 constants and can be identified with the solution space
                 of a constant-coefficient homogeneous linear
                 differential equation defined on a sufficiently small
                 interval. Using the obtained normalized B-bases, our
                 library can also generate, (partially) differentiate,
                 modify, and visualize a large family of so-called
                 B-curves and tensor product B-surfaces. Moreover, the
                 library also implements methods that can be used to
                 perform dimension elevation, to subdivide B-curves and
                 B-surfaces by means of de Casteljau-like B-algorithms,
                 and to generate basis transformations for the
                 B-representation of arbitrary integral curves and
                 surfaces that are described in traditional parametric
                 form by means of the ordinary bases of the underlying
                 EC spaces. Independently of the algebraic, exponential,
                 trigonometric, or mixed type of the applied EC space,
                 the proposed library is numerically stable and
                 efficient up to a reasonable dimension number and may
                 be useful for academics and engineers in the fields of
                 Approximation Theory, Computer Aided Geometric Design,
                 Computer Graphics, and Isogeometric and Numerical
                 Analysis.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Weinzierl:2019:PSP,
  author =       "Tobias Weinzierl",
  title =        "The {Peano} Software --- Parallel, Automaton-based,
                 Dynamically Adaptive Grid Traversals",
  journal =      j-TOMS,
  volume =       "45",
  number =       "2",
  pages =        "14:1--14:41",
  month =        apr,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3319797",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3319797",
  abstract =     "We discuss the design decisions, design alternatives,
                 and rationale behind the third generation of Peano, a
                 framework for dynamically adaptive Cartesian meshes
                 derived from spacetrees. Peano ties the mesh traversal
                 to the mesh storage and supports only one element-wise
                 traversal order resulting from space-filling curves.
                 The user is not free to choose a traversal order
                 herself. The traversal can exploit regular grid
                 subregions and shared memory as well as distributed
                 memory systems with almost no modifications to a serial
                 application code. We formalize the software design by
                 means of two interacting automata-one automaton for the
                 multiscale grid traversal and one for the
                 application-specific algorithmic steps. This yields a
                 callback-based programming paradigm. We further sketch
                 the supported application types and the two data
                 storage schemes realized before we detail
                 high-performance computing aspects and lessons learned.
                 Special emphasis is put on observations regarding the
                 used programming idioms and algorithmic concepts. This
                 transforms our report from a `one way to implement
                 things' code description into a generic discussion and
                 summary of some alternatives, rationale, and design
                 decisions to be made for any tree-based adaptive mesh
                 refinement software.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Charara:2019:BTD,
  author =       "Ali Charara and David Keyes and Hatem Ltaief",
  title =        "Batched Triangular Dense Linear Algebra Kernels for
                 Very Small Matrix Sizes on {GPUs}",
  journal =      j-TOMS,
  volume =       "45",
  number =       "2",
  pages =        "15:1--15:28",
  month =        apr,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3267101",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3267101",
  abstract =     "Batched dense linear algebra kernels are becoming
                 ubiquitous in scientific applications, ranging from
                 tensor contractions in deep learning to data
                 compression in hierarchical low-rank matrix
                 approximation. Within a single API call, these kernels
                 are capable of simultaneously launching up to thousands
                 of similar matrix computations, removing the expensive
                 overhead of multiple API calls while increasing the
                 occupancy of the underlying hardware. A challenge is
                 that for the existing hardware landscape (x86, GPUs,
                 etc.), only a subset of the required batched operations
                 is implemented by the vendors, with limited support for
                 very small problem sizes. We describe the design and
                 performance of a new class of batched triangular dense
                 linear algebra kernels on very small data sizes (up to
                 256) using single and multiple GPUs. By deploying
                 recursive formulations, stressing the register usage,
                 maintaining data locality, reducing threads
                 synchronization, and fusing successive kernel calls,
                 the new batched kernels outperform existing
                 state-of-the-art implementations.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Dongarra:2019:PPL,
  author =       "Jack Dongarra and Mark Gates and Azzam Haidar and
                 Jakub Kurzak and Piotr Luszczek and Panruo Wu and
                 Ichitaro Yamazaki and Asim Yarkhan and Maksims
                 Abalenkovs and Negin Bagherpour and Sven Hammarling and
                 Jakub S{\'\i}stek and David Stevens and Mawussi Zounon
                 and Samuel D. Relton",
  title =        "{PLASMA}: Parallel Linear Algebra Software for
                 Multicore Using {OpenMP}",
  journal =      j-TOMS,
  volume =       "45",
  number =       "2",
  pages =        "16:1--16:35",
  month =        apr,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3264491",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3264491",
  abstract =     "The recent version of the Parallel Linear Algebra
                 Software for Multicore Architectures (PLASMA) library
                 is based on tasks with dependencies from the OpenMP
                 standard. The main functionality of the library is
                 presented. Extensive benchmarks are targeted on three
                 recent multicore and manycore architectures, namely, an
                 Intel Xeon, Intel Xeon Phi, and IBM POWER 8
                 processors.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Luporini:2019:ATU,
  author =       "Fabio Luporini and Michael Lange and Christian T.
                 Jacobs and Gerard J. Gorman and J. Ramanujam and Paul
                 H. J. Kelly",
  title =        "Automated Tiling of Unstructured Mesh Computations
                 with Application to Seismological Modeling",
  journal =      j-TOMS,
  volume =       "45",
  number =       "2",
  pages =        "17:1--17:30",
  month =        apr,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3302256",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3302256",
  abstract =     "Sparse tiling is a technique to fuse loops that access
                 common data, thus increasing data locality. Unlike
                 traditional loop fusion or blocking, the loops may have
                 different iteration spaces and access shared datasets
                 through indirect memory accesses, such as
                 A[map[i]]-hence the name `sparse.' One notable example
                 of such loops arises in discontinuous-Galerkin finite
                 element methods, because of the computation of
                 numerical integrals over different domains (e.g.,
                 cells, facets). The major challenge with sparse tiling
                 is implementation --- not only is it cumbersome to
                 understand and synthesize, but it is also onerous to
                 maintain and generalize, as it requires a complete
                 rewrite of the bulk of the numerical computation. In
                 this article, we propose an approach to extend the
                 applicability of sparse tiling based on raising the
                 level of abstraction. Through a sequence of compiler
                 passes, the mathematical specification of a problem is
                 progressively lowered, and eventually sparse-tiled C
                 for-loops are generated. Besides automation, we advance
                 the state-of-the-art by introducing a revisited, more
                 efficient sparse tiling algorithm; support for
                 distributed-memory parallelism; a range of fine-grained
                 optimizations for increased runtime performance;
                 implementation in a publicly available library, SLOPE;
                 and an in-depth study of the performance impact in
                 Seigen, a real-world elastic wave equation solver for
                 seismological problems, which shows speed-ups up to
                 $1.28 \times $ on a platform consisting of 896 Intel
                 Broadwell cores.",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sukkari:2019:QBS,
  author =       "Dalal Sukkari and Hatem Ltaief and Aniello Esposito
                 and David Keyes",
  title =        "A {QDWH}-based {SVD} Software Framework on
                 Distributed-memory Manycore Systems",
  journal =      j-TOMS,
  volume =       "45",
  number =       "2",
  pages =        "18:1--18:21",
  month =        apr,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3309548",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Nakatsukasa:2013:SES}.",
  URL =          "https://dl.acm.org/citation.cfm?id=3309548",
  abstract =     "This article presents a high-performance software
                 framework for computing a dense SVD on
                 distributed-memory manycore systems. Originally
                 introduced by Nakatsukasa et al. (2010) and Nakatsukasa
                 and Higham (2013), the SVD solver relies on the polar
                 decomposition using the QR Dynamically Weighted Halley
                 algorithm (QDWH). Although the QDWH-based SVD algorithm
                 performs a significant amount of extra floating-point
                 operations compared to the traditional SVD with the
                 one-stage bidiagonal reduction, the inherent high level
                 of concurrency associated with Level 3 BLAS
                 compute-bound kernels ultimately compensates for the
                 arithmetic complexity overhead. Using the ScaLAPACK
                 two-dimensional block cyclic data distribution with a
                 rectangular processor topology, the resulting QDWH-SVD
                 further reduces excessive communications during the
                 panel factorization, while increasing the degree of
                 parallelism during the update of the trailing
                 submatrix, as opposed to relying on the default square
                 processor grid. After detailing the algorithmic
                 complexity and the memory footprint of the algorithm,
                 we conduct a thorough performance analysis and study
                 the impact of the grid topology on the performance by
                 looking at the communication and computation profiling
                 trade-offs. We report performance results against
                 state-of-the-art existing QDWH software implementations
                 (e.g., Elemental) and their SVD extensions on
                 large-scale distributed-memory manycore systems based
                 on commodity Intel x86 Haswell processors and Knights
                 Landing (KNL) architecture. The QDWH-SVD framework
                 achieves up to 3/8-fold speedups on the
                 Haswell/KNL-based platforms, respectively, against
                 ScaLAPACK PDGESVD and turns out to be a competitive
                 alternative for well- and ill-conditioned matrices. We
                 finally come up herein with a performance model based
                 on these empirical results. Our QDWH-based polar
                 decomposition and its SVD extension are freely
                 available at https://github.com/ecrc/qdwh.git and
                 https://github.com/ecrc/ksvd.git, respectively, and
                 have been integrated into the Cray Scientific numerical
                 library LibSci v17.11.1.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Maniezzo:2019:CSC,
  author =       "Vittorio Maniezzo and Marco A. Boschetti and Antonella
                 Carbonaro and Moreno Marzolla and Francesco
                 Strappaveccia",
  title =        "Client-side Computational Optimization",
  journal =      j-TOMS,
  volume =       "45",
  number =       "2",
  pages =        "19:1--19:16",
  month =        apr,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3309549",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3309549",
  abstract =     "Mobile platforms have matured to a point where they
                 can provide the infrastructure required to support
                 sophisticated optimization codes. This opens the
                 possibility to envisage new interest for distributed
                 application codes and the opportunity to intensify
                 research on optimization algorithms requiring limited
                 computational resources, as provided by mobile
                 platforms. In this article, we report on some
                 exploratory experience in this area. We illustrate some
                 practical, real-world cases where running optimization
                 programs on mobile or embedded devices can be useful,
                 with particular emphasis on matheuristics
                 approaches. Then, we discuss a practical use case
                 involving the feasibility version of the generalized
                 assignment problem (GAP). We present a JavaScript
                 implementation of a GAP solver that can be executed
                 inside an ordinary browser supporting ECMAScript. We
                 tested the code on different smartphones of varying age
                 and power, as well as on desktop PCs and other embedded
                 devices. Our experiments confirm the viability of
                 mobile devices for computational intensive tasks.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Porcelli:2019:NUP,
  author =       "Margherita Porcelli and Philippe L. Toint",
  title =        "A Note on Using Performance and Data Profiles for
                 Training Algorithms",
  journal =      j-TOMS,
  volume =       "45",
  number =       "2",
  pages =        "20:1--20:10",
  month =        apr,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3310362",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3310362",
  abstract =     "This article shows how to use performance and data
                 profile benchmarking tools to improve the performance
                 of algorithms. We propose to achieve this goal by
                 defining and approximately solving suitable
                 optimization problems involving the parameters of the
                 algorithm under consideration. Because these problems
                 do not have derivatives and may involve integer
                 variables, we suggest using a mixed-integer
                 derivative-free optimizer for this task. A numerical
                 illustration is presented (using the BFO package),
                 which indicates that the obtained gains are potentially
                 significant.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Winkelmann:2019:CCA,
  author =       "Jan Winkelmann and Paul Springer and Edoardo {Di
                 Napoli}",
  title =        "{ChASE}: {Chebyshev} Accelerated Subspace Iteration
                 Eigensolver for Sequences of {Hermitian} Eigenvalue
                 Problems",
  journal =      j-TOMS,
  volume =       "45",
  number =       "2",
  pages =        "21:1--21:34",
  month =        apr,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3313828",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3313828",
  abstract =     "Solving dense Hermitian eigenproblems arranged in a
                 sequence with direct solvers fails to take advantage of
                 those spectral properties that are pertinent to the
                 entire sequence and not just to the single problem.
                 When such features take the form of correlations
                 between the eigenvectors of consecutive problems, as is
                 the case in many real-world applications, the potential
                 benefit of exploiting them can be substantial. We
                 present the Chebyshev Accelerated Subspace iteration
                 Eigensolver (ChASE), a modern algorithm and library
                 based on subspace iteration with polynomial
                 acceleration. Novel to ChASE is the computation of the
                 spectral estimates that enter in the filter and an
                 optimization of the polynomial degree that further
                 reduces the necessary floating-point operations. ChASE
                 is written in C++ using the modern software engineering
                 concepts that favor a simple integration in application
                 codes and a straightforward portability over
                 heterogeneous platforms. When solving sequences of
                 Hermitian eigenproblems for a portion of their extremal
                 spectrum, ChASE greatly benefits from the sequence's
                 spectral properties and outperforms direct solvers in
                 many scenarios. The library ships with two distinct
                 parallelization schemes, supports execution over
                 distributed GPUs, and is easily extensible to other
                 parallel computing architectures.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fackler:2019:AEC,
  author =       "Paul L. Fackler",
  title =        "Algorithm 993: Efficient Computation with {Kronecker}
                 Products",
  journal =      j-TOMS,
  volume =       "45",
  number =       "2",
  pages =        "22:1--22:9",
  month =        apr,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3291041",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3291041",
  abstract =     "An algorithm for multiplying a chain of Kronecker
                 products by a matrix is described. The algorithm does
                 not require that the Kronecker chain actually be
                 computed and the main computational work is a series of
                 matrix--matrix multiplications. Use of the algorithm
                 can lead to substantial savings in both memory
                 requirements and computational speed. Although similar
                 algorithms have been described before, this article
                 makes two novel contributions. First, it shows how
                 shuffling of data can be (largely) avoided. Second, it
                 provides a simple method to determine the optimal
                 ordering of the workflow.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Zaghloul:2019:RO,
  author =       "Mofreh R. Zaghloul",
  title =        "Remark on {`Algorithm 680: Evaluation of the Complex
                 Error Function': Cause and Remedy for the Loss of
                 Accuracy Near the Real Axis}",
  journal =      j-TOMS,
  volume =       "45",
  number =       "2",
  pages =        "24:1--24:3",
  month =        apr,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3309681",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon May 6 18:23:42 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3309681",
  abstract =     "In this remark, we identify the cause of the loss of
                 accuracy in the computation of the Faddeyeva function,
                 $w(z)$, near the real axis when using Algorithm 680. We
                 provide a simple correction to this problem that allows
                 us to restore this code as one of the important
                 reference routines for accuracy comparisons.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Faz-Hernandez:2019:HPI,
  author =       "Armando Faz-Hern{\'a}ndez and Julio L{\'o}pez and
                 Ricardo Dahab",
  title =        "High-performance Implementation of Elliptic Curve
                 Cryptography Using Vector Instructions",
  journal =      j-TOMS,
  volume =       "45",
  number =       "3",
  pages =        "25:1--25:35",
  month =        jul,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3309759",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 31 08:06:08 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3309759",
  abstract =     "Elliptic curve cryptosystems are considered an
                 efficient alternative to conventional systems such as
                 DSA and RSA. Recently, Montgomery and Edwards elliptic
                 curves have been used to implement cryptosystems. In
                 particular, the elliptic curves Curve25519 and Curve448
                 were used for instantiating Diffie--Hellman protocols
                 named X25519 and X448. Mapping these curves to twisted
                 Edwards curves allowed deriving two new signature
                 instances, called Ed25519 and Ed448, of the Edwards
                 Digital Signature Algorithm. In this work, we focus on
                 the secure and efficient software implementation of
                 these algorithms using SIMD parallel processing. We
                 present software techniques that target the Intel AVX2
                 vector instruction set for accelerating prime field
                 arithmetic and elliptic curve operations. Our
                 contributions result in a high-performance software
                 library for AVX2-ready processors. For example, our
                 library computes digital signatures 19\% (for Ed25519)
                 and 29\% (for Ed448) faster than previous optimized
                 implementations. Also, our library improves by 10\% and
                 20\% the execution time of X25519 and X448,
                 respectively.",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Naumann:2019:ACD,
  author =       "Uwe Naumann",
  title =        "Adjoint Code Design Patterns",
  journal =      j-TOMS,
  volume =       "45",
  number =       "3",
  pages =        "26:1--26:32",
  month =        jul,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3326162",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 31 08:06:08 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3326162",
  abstract =     "Adjoint methods have become fundamental ingredients of
                 the scientific computing toolbox over the past decades.
                 Large-scale parameter sensitivity analysis, uncertainty
                 quantification, and nonlinear optimization would
                 otherwise turn out computationally infeasible. The
                 symbolic derivation of adjoint mathematical models for
                 relevant problems in science and engineering and their
                 implementation in consistency with the implementation
                 of the underlying primal model frequently proves highly
                 challenging. Hence, an increased interest in
                 algorithmic adjoints can be observed. The algorithmic
                 derivation of adjoint numerical simulation programs
                 shifts some of the problems faced from functional and
                 numerical analysis to computer science. It becomes a
                 highly complex software engineering task requiring
                 expertise in software analysis, transformation, and
                 optimization. Despite rather mature software tool
                 support for algorithmic differentiation, substantial
                 user intervention is typically required when targeting
                 nontrivial numerical programs. A large number of
                 patterns shared by numerous application codes results
                 in repeated duplication of development effort. The
                 adjoint code design patterns introduced in this article
                 aim to reduce this problem through improved
                 formalization from the software engineering
                 perspective. Fully functional reference implementations
                 are provided through github.",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hashemi:2019:ECE,
  author =       "Behnam Hashemi",
  title =        "Enclosing {Chebyshev} Expansions in Linear Time",
  journal =      j-TOMS,
  volume =       "45",
  number =       "3",
  pages =        "27:1--27:33",
  month =        jul,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3319395",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 31 08:06:08 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3319395",
  abstract =     "We consider the problem of computing rigorous
                 enclosures for polynomials represented in the Chebyshev
                 basis. Our aim is to compare and develop algorithms
                 with a linear complexity in terms of the polynomial
                 degree. A first category of methods relies on a direct
                 interval evaluation of the given Chebyshev expansion in
                 which Chebyshev polynomials are bounded, e.g., with a
                 divide-and-conquer strategy. Our main category of
                 methods that are based on the Clenshaw recurrence
                 includes interval Clenshaw with defect correction
                 (ICDC), and the spectral transformation of Clenshaw
                 recurrence rewritten as a discrete dynamical system. An
                 extension of the barycentric representation to interval
                 arithmetic is also considered that has a log-linear
                 complexity as it takes advantage of a verified discrete
                 cosine transform. We compare different methods and
                 provide illustrative numerical experiments. In
                 particular, our eigenvalue-based methods are
                 interesting for bounding the range of high-degree
                 interval polynomials. Some of the methods rigorously
                 compute narrow enclosures for high-degree Chebyshev
                 expansions at thousands of points in a few seconds on
                 an average computer. We also illustrate how to employ
                 our methods as an automatic a posteriori forward error
                 analysis tool to monitor the accuracy of the Chebfun
                 feval command.",
  acknowledgement = ack-nhfb,
  articleno =    "27",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lee:2019:ICA,
  author =       "Christopher T. Lee and John B. Moody and Rommie E.
                 Amaro and J. Andrew Mccammon and Michael J. Holst",
  title =        "The Implementation of the Colored Abstract Simplicial
                 Complex and Its Application to Mesh Generation",
  journal =      j-TOMS,
  volume =       "45",
  number =       "3",
  pages =        "28:1--28:20",
  month =        aug,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3321515",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 3 17:49:22 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3321515",
  abstract =     "We introduce the Colored Abstract Simplicial Complex
                 library (CASC): a new, modern, and header-only C++
                 library that provides a data structure to represent
                 arbitrary dimension abstract simplicial complexes (ASC)
                 with user-defined classes stored directly on the
                 simplices at each dimension. This is accomplished by
                 using the latest C++ language features including
                 variadic template parameters introduced in C++11 and
                 automatic function return type deduction from C++14.
                 Effectively, CASC decouples the representation of the
                 topology from the interactions of user data. We present
                 the innovations and design principles of the data
                 structure and related algorithms. This includes a
                 metadata-aware decimation algorithm, which is general
                 for collapsing simplices of any dimension. We also
                 present an example application of this library to
                 represent an orientable surface mesh.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kronbichler:2019:FMF,
  author =       "Martin Kronbichler and Katharina Kormann",
  title =        "Fast Matrix-Free Evaluation of Discontinuous
                 {Galerkin} Finite Element Operators",
  journal =      j-TOMS,
  volume =       "45",
  number =       "3",
  pages =        "29:1--29:40",
  month =        aug,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3325864",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 3 17:49:22 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3325864",
  abstract =     "We present an algorithmic framework for matrix-free
                 evaluation of discontinuous Galerkin finite element
                 operators. It relies on fast quadrature with sum
                 factorization on quadrilateral and hexahedral meshes,
                 targeting general weak forms of linear and nonlinear
                 partial differential equations. Different algorithms
                 and data structures are compared in an in-depth
                 performance analysis. The implementations of the local
                 integrals are optimized by vectorization over several
                 cells and faces and an even-odd decomposition of the
                 one-dimensional interpolations. Up to 60\% of the
                 arithmetic peak on Intel Haswell, Broadwell, and
                 Knights Landing processors is reached when running from
                 caches and up to 40\% of peak when also considering the
                 access to vectors from main memory. On 2$ \times $14
                 Broadwell cores, the throughput is up to 2.2 billion
                 unknowns per second for the 3D Laplacian and up to 4
                 billion unknowns per second for the 3D advection on
                 affine geometries, close to a simple copy operation at
                 4.7 billion unknowns per second. Our experiments show
                 that MPI ghost exchange has a considerable impact on
                 performance and we present strategies to mitigate this
                 effect. Finally, various options for evaluating
                 geometry terms and their performance are discussed. Our
                 implementations are publicly available through the
                 deal.II finite element library.",
  acknowledgement = ack-nhfb,
  articleno =    "29",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Johansson:2019:CHF,
  author =       "Fredrik Johansson",
  title =        "Computing Hypergeometric Functions Rigorously",
  journal =      j-TOMS,
  volume =       "45",
  number =       "3",
  pages =        "30:1--30:26",
  month =        aug,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3328732",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 3 17:49:22 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3328732",
  abstract =     "We present an efficient implementation of
                 hypergeometric functions in arbitrary-precision
                 interval arithmetic. The functions $_0 F_1$, $_1 F_1$,
                 $_2 F_1$, and $_2 F_0$ (or the Kummer $U$-function) are
                 supported for unrestricted complex parameters and
                 argument, and, by extension, we cover exponential and
                 trigonometric integrals, error functions, Fresnel
                 integrals, incomplete gamma and beta functions, Bessel
                 functions, Airy functions, Legendre functions, Jacobi
                 polynomials, complete elliptic integrals, and other
                 special functions. The output can be used directly for
                 interval computations or to generate provably correct
                 floating-point approximations in any format.
                 Performance is competitive with earlier
                 arbitrary-precision software and sometimes orders of
                 magnitude faster. We also partially cover the
                 generalized hypergeometric function $_p F_q$ and
                 computation of high-order parameter derivatives.",
  acknowledgement = ack-nhfb,
  articleno =    "30",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Dieguez:2019:TPR,
  author =       "Adri{\'a}n P. Di{\'e}guez and Margarita Amor and
                 Ram{\'o}n Doallo",
  title =        "Tree Partitioning Reduction: A New Parallel Partition
                 Method for Solving Tridiagonal Systems",
  journal =      j-TOMS,
  volume =       "45",
  number =       "3",
  pages =        "31:1--31:26",
  month =        aug,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3328731",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 3 17:49:22 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3328731",
  abstract =     "Solving tridiagonal linear-equation systems is a
                 fundamental computing kernel in a wide range of
                 scientific and engineering applications, and its
                 computation can be modeled with parallel algorithms.
                 These parallel solvers are typically designed to
                 compute problems whose data fit in a common
                 shared-memory space where all the cores taking part in
                 the computation have access. However, when the problem
                 size is large, data cannot be entirely stored in the
                 common shared-memory space, and a high number of
                 high-latency communications are performed. One
                 alternative is to partition the problem among different
                 memory spaces. At this point, conventional parallel
                 algorithms do not facilitate the partition of
                 computation in independent tiles, since each reduction
                 depends on equations that may be in different tiles.
                 This article proposes an algorithm based on a tree
                 reduction, called the Tree Partitioning Reduction (TPR)
                 method, which partitions the problem into independent
                 slices that can be partially computed in parallel
                 within different common shared-memory spaces. The TPR
                 method can be implemented for any parallel and
                 distributed programming paradigm. Furthermore, in this
                 work, TPR is efficiently implemented for CUDA GPUs to
                 solve large size problems, providing highly competitive
                 performance results with respect to existing packages,
                 being, on average, 22.03$ \times $ faster than
                 CUSPARSE.",
  acknowledgement = ack-nhfb,
  articleno =    "31",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cartis:2019:IFR,
  author =       "Coralia Cartis and Jan Fiala and Benjamin Marteau and
                 Lindon Roberts",
  title =        "Improving the Flexibility and Robustness of
                 Model-based Derivative-free Optimization Solvers",
  journal =      j-TOMS,
  volume =       "45",
  number =       "3",
  pages =        "32:1--32:41",
  month =        aug,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3338517",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 3 17:49:22 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3338517",
  abstract =     "We present two software packages for derivative-free
                 optimization (DFO): DFO-LS for nonlinear least-squares
                 problems and Py-BOBYQA for general objectives, both
                 with optional bound constraints. Inspired by the
                 Gauss--Newton method, DFO-LS constructs simplified
                 linear regression models for the residuals and allows
                 flexible initialization for expensive problems, whereby
                 it can begin making progress after as few as two
                 objective evaluations. Numerical results show DFO-LS
                 can gain reasonable progress on some medium-scale
                 problems with fewer objective evaluations than is
                 needed for one gradient evaluation. DFO-LS has improved
                 robustness to noise, allowing sample averaging,
                 regression-based model construction, and multiple
                 restart strategies with an auto-detection mechanism.
                 Our extensive numerical experimentation shows that
                 restarting the solver when stagnation is detected is a
                 cheap and effective mechanism for achieving robustness,
                 with superior performance over sampling and regression
                 techniques. The package Py-BOBYQA is a Python
                 implementation of BOBYQA (Powell 2009), with novel
                 features such as the implementation of robustness to
                 noise strategies. Our numerical experiments show that
                 Py-BOBYQA is comparable to or better than existing
                 general DFO solvers for noisy problems. In our
                 comparisons, we introduce an adaptive accuracy measure
                 for data profiles of noisy functions, striking a
                 balance between measuring the true and the noisy
                 objective improvement.",
  acknowledgement = ack-nhfb,
  articleno =    "32",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pardue:2019:AEP,
  author =       "Juliette Pardue and Andrey Chernikov",
  title =        "{Algorithm 995}: An Efficient Parallel Anisotropic
                 {Delaunay} Mesh Generator for Two-Dimensional Finite
                 Element Analysis",
  journal =      j-TOMS,
  volume =       "45",
  number =       "3",
  pages =        "33:1--33:30",
  month =        jul,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3301321",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 31 08:06:08 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3301321",
  abstract =     "A bottom-up approach to parallel anisotropic mesh
                 generation is presented by building a mesh generator
                 starting from the basic operations of vertex insertion
                 and Delaunay triangles. Applications focusing on
                 high-lift design or dynamic stall, or numerical methods
                 and modeling test cases, still focus on two-dimensional
                 domains. This automated parallel mesh generation
                 approach can generate high-fidelity unstructured meshes
                 with anisotropic boundary layers for use in the
                 computational fluid dynamics field. The anisotropy
                 requirement adds a level of complexity to a parallel
                 meshing algorithm by making computation depend on the
                 local alignment of elements, which in turn is dictated
                 by geometric boundaries and the density functions-
                 one-dimensional spacing functions generated from an
                 exponential distribution. This approach yields
                 computational savings in mesh generation and flow
                 solution through well-shaped anisotropic triangles
                 instead of isotropic triangles. The validity of the
                 meshes is shown through solution characteristic
                 comparisons to verified reference solutions. A 79\%
                 parallel weak scaling efficiency on 1,024 distributed
                 memory nodes, and a 72\% parallel efficiency over the
                 fastest sequential isotropic mesh generator on 512
                 distributed memory nodes, is shown through numerical
                 experiments.",
  acknowledgement = ack-nhfb,
  articleno =    "33",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ito:2019:ABS,
  author =       "Naoki Ito and Sunyoung Kim and Masakazu Kojima and
                 Akiko Takeda and Kim-Chuan Toh",
  title =        "{Algorithm 996}: {BBCPOP}: A Sparse Doubly Nonnegative
                 Relaxation of Polynomial Optimization Problems With
                 Binary, Box, and Complementarity Constraints",
  journal =      j-TOMS,
  volume =       "45",
  number =       "3",
  pages =        "34:1--34:16",
  month =        jul,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3309988",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 31 08:06:08 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3309988",
  abstract =     "The software package BBCPOP is a MATLAB implementation
                 of a hierarchy of sparse doubly nonnegative relaxations
                 of a class of polynomial optimization (minimization)
                 problems (POPs) with binary, box, and complementarity
                 (BBC) constraints. Given a POP in the class and a
                 relaxation order, BBCPOP constructs a simple conic
                 optimization problem (COP), which serves as a doubly
                 nonnegative relaxation of the POP, and then solves the
                 COP by applying the bisection and projection method.
                 The COP is expressed with a linear objective function
                 and constraints described as a single hyperplane and
                 two cones, which are the Cartesian product of positive
                 semidefinite cones and a polyhedral cone induced from
                 the BBC constraints. BBCPOP aims to compute a tight
                 lower bound for the optimal value of a large-scale POP
                 in the class that is beyond the comfort zone of
                 existing software packages. The robustness,
                 reliability, and efficiency of BBCPOP are demonstrated
                 in comparison to the state-of-the-art software SDP
                 package SDPNAL+ on randomly generated sparse POPs of
                 degree 2 and 3 with up to a few thousands variables,
                 and ones of degree from 5 to 8 with up to a few hundred
                 variables. Numerical results on BBC-constrained POPs
                 that arise from quadratic assignment problems are also
                 reported. The software package BBCPOP is available at
                 https://sites.google.com/site/bbcpop1/.",
  acknowledgement = ack-nhfb,
  articleno =    "34",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Speck:2019:APP,
  author =       "Robert Speck",
  title =        "{Algorithm 997}: {pySDC}-Prototyping Spectral Deferred
                 Corrections",
  journal =      j-TOMS,
  volume =       "45",
  number =       "3",
  pages =        "35:1--35:23",
  month =        aug,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3310410",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 3 17:49:22 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3310410",
  abstract =     "In this article, we present the Python framework pySDC
                 for solving collocation problems with spectral deferred
                 correction (SDC) methods and their time-parallel
                 variant PFASST, the parallel full approximation scheme
                 in space and time. pySDC features many implementations
                 of SDC and PFASST, from simple implicit timestepping to
                 high-order implicit-explicit or multi-implicit
                 splitting and multilevel SDCs. The software package
                 comes with many different, preimplemented examples and
                 has seven tutorials to help new users with their first
                 steps. Time parallelism is implemented either in an
                 emulated way for debugging and prototyping or using MPI
                 for benchmarking. The code is fully documented and
                 tested using continuous integration, including most
                 results of previous publications. Here, we describe the
                 structure of the code by taking two different
                 perspectives: those of the user and those of the
                 developer. The first sheds light on the front-end, the
                 examples, and the tutorials, and the second is used to
                 describe the underlying implementation and the data
                 structures. We show three different examples to
                 highlight various aspects of the implementation, the
                 capabilities, and the usage of pySDC. In addition,
                 couplings to the FEniCS framework and PETSc, the latter
                 including spatial parallelism with MPI, are
                 described.",
  acknowledgement = ack-nhfb,
  articleno =    "35",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Agulhari:2019:ARL,
  author =       "Cristiano M. Agulhari and Alexandre Felipe and Ricardo
                 C. L. F. Oliveira and Pedro L. D. Peres",
  title =        "{Algorithm 998}: The Robust {LMI} Parser --- a Toolbox
                 to Construct {LMI} Conditions for Uncertain Systems",
  journal =      j-TOMS,
  volume =       "45",
  number =       "3",
  pages =        "36:1--36:25",
  month =        aug,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3323925",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Sep 3 17:49:22 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3323925",
  abstract =     "The ROLMIP (Robust LMI Parser) is a toolbox
                 specialized in control theory for uncertain linear
                 systems, built to work under MATLAB jointly with
                 YALMIP, to ease the programming of sufficient Linear
                 Matrix Inequality (LMI) conditions that, if feasible,
                 assure the validity of parameter-dependent LMIs in the
                 entire set of uncertainty considered. This article
                 presents the new version of the ROLMIP toolbox, which
                 was completely remodeled to provide a high-level
                 user-friendly interface to cope with distinct uncertain
                 domains (hypercube and multi-simplex) and to treat
                 time-varying parameters in discrete- and
                 continuous-time. By means of simple commands, the user
                 is able to define polynomial matrices as well as to
                 describe the desired parameter-dependent LMIs in an
                 easy way, considerably reducing the programming time to
                 end up with implementable LMI conditions. Therefore,
                 ROLMIP helps the popularization of the state-of-the-art
                 robust control methods for uncertain systems based on
                 LMIs among graduate students, researchers, and
                 engineers in control systems.",
  acknowledgement = ack-nhfb,
  articleno =    "36",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{LucambioPerez:2019:WLS,
  author =       "L. R. {Lucambio P{\'e}rez} and L. F. Prudente",
  title =        "A {Wolfe} Line Search Algorithm for Vector
                 Optimization",
  journal =      j-TOMS,
  volume =       "45",
  number =       "4",
  pages =        "37:1--37:23",
  month =        dec,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3342104",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 27 14:56:25 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3342104",
  abstract =     "In a recent article, Lucambio P{\'e}rez and Prudente
                 extended the Wolfe conditions for the vector-valued
                 optimization. Here, we propose a line search algorithm
                 for finding a step size satisfying the strong Wolfe
                 conditions in the vector optimization setting. Well
                 definedness and finite termination results are
                 provided. We discuss practical aspects related to the
                 algorithm and present some numerical experiments
                 illustrating its applicability. Codes supporting this
                 article are written in Fortran 90 and are freely
                 available for download.",
  acknowledgement = ack-nhfb,
  articleno =    "37",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sagebaum:2019:HPD,
  author =       "Max Sagebaum and Tim Albring and Nicolas R. Gauger",
  title =        "High-Performance Derivative Computations using
                 {CoDiPack}",
  journal =      j-TOMS,
  volume =       "45",
  number =       "4",
  pages =        "38:1--38:27",
  month =        dec,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3356900",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 27 14:56:25 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3356900",
  abstract =     "There are several AD tools available that all
                 implement different strategies for the reverse mode of
                 AD. The most common strategies are primal value taping
                 (implemented e.g. by ADOL-C) and Jacobian taping
                 (implemented e.g. by Adept and dco/c++). Particularly
                 for Jacobian taping, recent advances using expression
                 templates make it very attractive for large scale
                 software. However, the current implementations are
                 either closed source or miss essential features and
                 flexibility. Therefore, we present the new AD tool
                 CoDiPack (Code Differentiation Package) in this paper.
                 It is specifically designed for minimal memory
                 consumption and optimal runtime, such that it can be
                 used for the differentiation of large scale software.
                 An essential part of the design of CoDiPack is the
                 modular layout and the recursive data structures which
                 not only allow the efficient implementation of the
                 Jacobian taping approach but will also enable other
                 approaches like the primal value taping or new research
                 ideas. We will finally present the performance values
                 of CoDiPack on a generic PDE example and on the SU2
                 code.",
  acknowledgement = ack-nhfb,
  articleno =    "38",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hisil:2019:KLF,
  author =       "Huseyin Hisil and Joost Renes",
  title =        "On {Kummer} Lines with Full Rational 2-torsion and
                 Their Usage in Cryptography",
  journal =      j-TOMS,
  volume =       "45",
  number =       "4",
  pages =        "39:1--39:17",
  month =        dec,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3361680",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 27 14:56:25 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cryptography2010.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3361680",
  abstract =     "A paper by Karati and Sarkar at Asiacrypt'17 has
                 pointed out the potential for Kummer lines in genus 1,
                 by observing that their SIMD-friendly arithmetic is
                 competitive with the status quo. A more recent preprint
                 explores the connection with (twisted) Edwards curves.
                 In this article, we extend this work and significantly
                 simplify the treatment of Karati and Sarkar. We show
                 that their Kummer line is the x -line of a Montgomery
                 curve translated by a point of order two, and exhibit a
                 natural isomorphism to the y -line of a twisted Edwards
                 curve. Moreover, we show that the Kummer line presented
                 by Gaudry and Lubicz can be obtained via the action of
                 a point of order two on the y -line of an Edwards
                 curve. The maps connecting these curves and lines are
                 all very simple. As a result, a cryptographic
                 implementation can use the arithmetic that is optimal
                 for its instruction set at negligible cost.",
  acknowledgement = ack-nhfb,
  articleno =    "39",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Flegar:2019:FCL,
  author =       "Goran Flegar and Florian Scheidegger and Vedran
                 Novakovi{\'c} and Giovani Mariani and Andr{\'e}s E.
                 Tom{\'a}s and A. Cristiano I. Malossi and Enrique S.
                 Quintana-Ort{\'\i}",
  title =        "{FloatX}: A {C++} Library for Customized
                 Floating-Point Arithmetic",
  journal =      j-TOMS,
  volume =       "45",
  number =       "4",
  pages =        "40:1--40:23",
  month =        dec,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3368086",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 27 14:56:25 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3368086",
  abstract =     "We present FloatX (Float eXtended), a C ++ framework
                 to investigate the effect of leveraging customized
                 floating-point formats in numerical applications.
                 FloatX formats are based on binary IEEE 754 with
                 smaller significand and exponent bit counts specified
                 by the user. Among other properties, FloatX facilitates
                 an incremental transformation of the code, relies on
                 hardware-supported floating-point types as back-end to
                 preserve efficiency, and incurs no storage overhead.
                 The article discusses in detail the design principles,
                 programming interface, and datatype casting rules
                 behind FloatX. Furthermore, it demonstrates FloatX's
                 usage and benefits via several case studies from
                 well-known numerical dense linear algebra libraries,
                 such as BLAS and LAPACK; the Ginkgo library for sparse
                 linear systems; and two neural network applications
                 related with image processing and text recognition.",
  acknowledgement = ack-nhfb,
  articleno =    "40",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kirby:2019:CGG,
  author =       "Robert C. Kirby and Lawrence Mitchell",
  title =        "Code Generation for Generally Mapped Finite Elements",
  journal =      j-TOMS,
  volume =       "45",
  number =       "4",
  pages =        "41:1--41:23",
  month =        dec,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3361745",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 27 14:56:25 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See also replication report
                 \cite{Lindquist:2019:RCR}.",
  URL =          "https://dl.acm.org/citation.cfm?id=3361745",
  abstract =     "Many classical finite elements such as the Argyris and
                 Bell elements have long been absent from high-level PDE
                 software. Building on recent theoretical work, we
                 describe how to implement very general finite-element
                 transformations in FInAT and hence into the Firedrake
                 finite-element system. Numerical results evaluate the
                 new elements, comparing them to existing methods for
                 classical problems. For a second-order model problem,
                 we find that new elements give smooth solutions at a
                 mild increase in cost over standard Lagrange elements.
                 For fourth-order problems, however, the newly enabled
                 methods significantly outperform interior penalty
                 formulations. We also give some advanced use cases,
                 solving the nonlinear Cahn--Hilliard equation and some
                 biharmonic eigenvalue problems (including Chladni
                 plates) using C 1 discretizations.",
  acknowledgement = ack-nhfb,
  articleno =    "41",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lindquist:2019:RCR,
  author =       "Neil Lindquist",
  title =        "Replicated Computational Results {(RCR)} Report for
                 {``\booktitle{Code Generation for Generally Mapped
                 Finite Elements}''}",
  journal =      j-TOMS,
  volume =       "45",
  number =       "4",
  pages =        "42:1--42:7",
  month =        dec,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3360984",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 27 14:56:25 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Kirby:2019:CGG}.",
  URL =          "https://dl.acm.org/citation.cfm?id=3360984",
  abstract =     "``\booktitle{Code Generation for Generally Mapped
                 Finite Elements}'' includes performance results for the
                 finite element methods discussed in that manuscript.
                 The authors provided a Zenodo archive with the
                 Firedrake components and dependencies used, as well as
                 the scripts that generated the results. The software
                 was installed on two similar platforms; then, new
                 results were gathered and compared to the original
                 results. After completing this process, the results
                 have been deemed replicable by the reviewer.",
  acknowledgement = ack-nhfb,
  articleno =    "42",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Speleers:2019:ACM,
  author =       "Hendrik Speleers",
  title =        "{Algorithm 999}: {Computation} of Multi-Degree
                 {B}-Splines",
  journal =      j-TOMS,
  volume =       "45",
  number =       "4",
  pages =        "43:1--43:15",
  month =        dec,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3321514",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 27 14:56:25 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3321514",
  abstract =     "Multi-degree splines are smooth piecewise-polynomial
                 functions where the pieces can have different degrees.
                 We describe a simple algorithmic construction of a set
                 of basis functions for the space of multi-degree
                 splines with similar properties to standard B-splines.
                 These basis functions are called multi-degree B-splines
                 (or MDB-splines ). The construction relies on an
                 extraction operator that represents all MDB-splines as
                 linear combinations of local B-splines of different
                 degrees. This enables the use of existing efficient
                 algorithms for B-spline evaluations and refinements in
                 the context of multi-degree splines. A M ATLAB
                 implementation is provided to illustrate the
                 computation and use of MDB-splines.",
  acknowledgement = ack-nhfb,
  articleno =    "43",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Davis:2019:ASG,
  author =       "Timothy A. Davis",
  title =        "{Algorithm 1000}: {SuiteSparse:GraphBLAS}: Graph
                 Algorithms in the Language of Sparse Linear Algebra",
  journal =      j-TOMS,
  volume =       "45",
  number =       "4",
  pages =        "44:1--44:25",
  month =        dec,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3322125",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 27 14:56:25 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3322125",
  abstract =     "SuiteSparse:GraphBLAS is a full implementation of the
                 GraphBLAS standard, which defines a set of sparse
                 matrix operations on an extended algebra of semirings
                 using an almost unlimited variety of operators and
                 types. When applied to sparse adjacency matrices, these
                 algebraic operations are equivalent to computations on
                 graphs. GraphBLAS provides a powerful and expressive
                 framework for creating graph algorithms based on the
                 elegant mathematics of sparse matrix operations on a
                 semiring. An overview of the GraphBLAS specification is
                 given, followed by a description of the key features
                 and performance of its implementation in the
                 SuiteSparse:GraphBLAS package.",
  acknowledgement = ack-nhfb,
  articleno =    "44",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Burgel:2019:AIM,
  author =       "Florian B{\"u}rgel and Kamil S. Kazimierski and Armin
                 Lechleiter",
  title =        "{Algorithm 1001}: {IPscatt} --- a {MATLAB} Toolbox for
                 the Inverse Medium Problem in Scattering",
  journal =      j-TOMS,
  volume =       "45",
  number =       "4",
  pages =        "45:1--45:20",
  month =        dec,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3328525",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 27 14:56:25 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3328525",
  abstract =     "IPscatt is a free, open-source MATLAB toolbox
                 facilitating the solution for time-independent
                 scattering (also known as time-harmonic scattering) in
                 two- and three-dimensional settings. The toolbox has
                 three main application cases: simulation of the
                 scattered field for a given transmitter-receiver
                 geometry; the generation of simulated data as well as
                 the handling of the real-world data from Institute
                 Fresnel; and the reconstruction of the contrast from
                 several measured, scattered fields. In each case, a
                 variety of options tailored to the needs of
                 practitioners is provided. For example, the toolbox
                 allows the simulation of the scattered near field as
                 well as of the far field. Also, it provides methods for
                 the modeling of the incident field as point sources as
                 well as plane waves. Finally, many common geometries of
                 transmitters and receivers are included out of the box.
                 Regarding the reconstruction, the provided functions
                 implement the regularization scheme that relies on a
                 primal-dual algorithm and was introduced by F.
                 B{\"u}rgel, K. S. Kazimierski, and A. Lechleiter [
                 Journal of Computational Physics 339 (2017), 1-30].
                 This article provides a survey of the mathematical
                 concepts in scattering, connects them with the provided
                 implementation, gives an overview of the software
                 framework as well as its application areas, and
                 compares it with existing software packages solving the
                 same problem.",
  acknowledgement = ack-nhfb,
  articleno =    "45",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kara:2019:AGC,
  author =       "G{\"o}k{\c{c}}ehan Kara and Can {\"O}zturan",
  title =        "{Algorithm 1002}: {Graph} Coloring Based Parallel
                 Push-relabel Algorithm for the Maximum Flow Problem",
  journal =      j-TOMS,
  volume =       "45",
  number =       "4",
  pages =        "46:1--46:28",
  month =        dec,
  year =         "2019",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3330481",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Dec 27 14:56:25 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/citation.cfm?id=3330481",
  abstract =     "The maximum flow problem is one of the most common
                 network flow problems. This problem involves finding
                 the maximum possible amount of flow between two
                 designated nodes on a network with arcs having flow
                 capacities. The push-relabel algorithm is one of the
                 fastest algorithms to solve this problem. We present a
                 shared memory parallel push-relabel algorithm. Graph
                 coloring is used to avoid collisions between threads
                 for concurrent push and relabel operations. In
                 addition, excess values of target nodes are updated
                 using atomic instructions to prevent race conditions.
                 The experiments show that our algorithm is competitive
                 for wide graphs with low diameters. Results from three
                 different data sets are included, computer vision
                 problems, DIMACS challenge problems, and KaHIP
                 partitioning problems. These are compared with existing
                 push-relabel and pseudoflow implementations. We show
                 that high speedup rates are possible using our coloring
                 based parallelization technique on sparse networks.
                 However, we also observe that the pseudoflow algorithm
                 runs faster than the push-relabel algorithm on dense
                 and long networks.",
  acknowledgement = ack-nhfb,
  articleno =    "46",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Huang:2020:SAR,
  author =       "Jianyu Huang and Chenhan D. Yu and Robert A. van de
                 Geijn",
  title =        "{Strassen}'s Algorithm Reloaded on {GPUs}",
  journal =      j-TOMS,
  volume =       "46",
  number =       "1",
  pages =        "1:1--1:22",
  month =        mar,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3372419",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 7 10:39:23 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3372419",
  abstract =     "Conventional Graphics Processing Unit (GPU)
                 implementations of Strassen's algorithm (Strassen) rely
                 on the existing high-performance matrix multiplication
                 (gemm), trading space for time. As a result, such
                 approaches can only achieve practical speedup or
                 relatively large, ``squarish'' matrices due to the
                 extra memory overhead, and their usages are limited due
                 to the considerable workspace. We present novel
                 Strassen primitives for GPUs that can be composed to
                 generate a family of Strassen algorithms. Our
                 algorithms utilize both the memory and thread
                 hierarchies on GPUs, reusing shared memory and register
                 files inherited from gemm, fusing additional
                 operations, and avoiding extra workspace. We further
                 exploit intra- and inter-kernel parallelism by
                 batching, streaming, and employing atomic operations.
                 We develop a performance model for NVIDIA Volta GPUs to
                 select the appropriate blocking parameters and predict
                 the performance for gemm and Strassen. Overall, our
                 1-level Strassen can achieve up to $ 1.11 \times $
                 speedup with a crossover point as small as 1,536
                 compared to cublasSgemm on a NVIDIA Tesla V100 GPU.
                 With additional workspace, our 2-level Strassen can
                 achieve $ 1.19 \times $ speedup with a crossover point
                 at 7,680.",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Arevalo:2020:SPA,
  author =       "Carmen Ar{\'e}valo and Erik Jonsson-Glans and Josefine
                 Olander and Monica Selva Soto and Gustaf
                 S{\"o}derlind",
  title =        "A Software Platform for Adaptive High Order Multistep
                 Methods",
  journal =      j-TOMS,
  volume =       "46",
  number =       "1",
  pages =        "2:1--2:17",
  month =        mar,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3372159",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 7 10:39:23 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3372159",
  abstract =     "We present a software package, Modes, offering
                 $h$-adaptive and $p$-adaptive linear multistep methods
                 for first order initial value problems in ordinary
                 differential equations. The implementation is based on
                 a new parametric, grid-independent representation of
                 multistep methods [Ar{\'e}valo and S{\"o}derlind 2017].
                 Parameters are supplied for over 60 methods. For
                 nonstiff problems, all maximal order methods ($ p = k$
                 for explicit and $ p = k + 1$ for implicit methods) are
                 supported. For stiff computation, implicit methods of
                 order $ p = k$ are included.\par

                 A collection of step-size controllers based on digital
                 filters is provided, generating smooth step-size
                 sequences offering improved computational stability.
                 Controllers may be selected to match method and problem
                 classes. A new system for automatic order control is
                 also provided for designated families of multistep
                 methods, offering simultaneous $h$- and
                 $p$-adaptivity.\par

                 Implemented as a Matlab toolbox, the software covers
                 high order computations with linear multistep methods
                 within a unified, generic framework. Computational
                 experiments show that the new software is competitive
                 and offers qualitative improvements. Modes is available
                 for downloading and is primarily intended as a platform
                 for developing a new generation of state-of-the-art
                 multistep solvers, as well as for true ceteris paribus
                 evaluation of algorithmic components. This also enables
                 method comparisons within a single implementation
                 environment.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Cui:2020:HON,
  author =       "Tao Cui and Wei Leng and Huaqing Liu and Linbo Zhang
                 and Weiying Zheng",
  title =        "High-order Numerical Quadratures in a Tetrahedron with
                 an Implicitly Defined Curved Interface",
  journal =      j-TOMS,
  volume =       "46",
  number =       "1",
  pages =        "3:1--3:18",
  month =        mar,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3372144",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 7 10:39:23 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3372144",
  abstract =     "Given a shape regular tetrahedron and a curved surface
                 that is defined implicitly by a nonlinear level set
                 function and divides the tetrahedron into two
                 sub-domains, a general-purpose, robust, and high-order
                 numerical algorithm is proposed in this article for
                 computing both volume integrals in the sub-domains and
                 surface integrals on their common boundary. The
                 algorithm uses a direct approach that decomposes 3D
                 volume integrals or 2D surface integrals into multiple
                 1D integrals and computes the 1D integrals with
                 Gaussian quadratures. It only requires finding roots of
                 univariate nonlinear functions in given intervals and
                 evaluating the integrand, the level set function, and
                 the gradient of the level set function at given points.
                 It can achieve arbitrarily high accuracy by increasing
                 the orders of Gaussian quadratures, and it does not
                 need extra a priori knowledge about the integrand and
                 the level set function. The code for the algorithm is
                 freely available in the open-source finite element
                 toolbox Parallel Hierarchical Grid (PHG) and can serve
                 as a basic building block for implementing 3D
                 high-order numerical algorithms involving implicit
                 interfaces or boundaries.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Betcke:2020:PAG,
  author =       "Timo Betcke and Matthew W. Scroggs and Wojciech
                 'Smigaj",
  title =        "Product Algebras for {Galerkin} Discretisations of
                 Boundary Integral Operators and their Applications",
  journal =      j-TOMS,
  volume =       "46",
  number =       "1",
  pages =        "4:1--4:22",
  month =        mar,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3368618",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 7 10:39:23 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3368618",
  abstract =     "Operator products occur naturally in a range of
                 regularised boundary integral equation formulations.
                 However, while a Galerkin discretisation only depends
                 on the domain space and the test (or dual) space of the
                 operator, products require a notion of the range. In
                 the boundary element software package Bempp, we have
                 implemented a complete operator algebra that depends on
                 knowledge of the domain, range, and test space. The aim
                 was to develop a way of working with Galerkin operators
                 in boundary element software that is as close to
                 working with the strong form on paper as possible,
                 while hiding the complexities of Galerkin
                 discretisations. In this article, we demonstrate the
                 implementation of this operator algebra and show, using
                 various Laplace and Helmholtz example problems, how it
                 significantly simplifies the definition and solution of
                 a wide range of typical boundary integral equation
                 problems.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Abhyankar:2020:PDL,
  author =       "Shrirang Abhyankar and Getnet Betrie and Daniel Adrian
                 Maldonado and Lois C. Mcinnes and Barry Smith and Hong
                 Zhang",
  title =        "{PETSc DMNetwork}: a Library for Scalable Network
                 {PDE}-Based Multiphysics Simulations",
  journal =      j-TOMS,
  volume =       "46",
  number =       "1",
  pages =        "5:1--5:24",
  month =        apr,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3344587",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Apr 29 08:09:49 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3344587",
  abstract =     "We present DMNetwork, a high-level package included in
                 the PETSc library for the simulation of multiphysics
                 phenomena over large-scale networked systems. The
                 library aims at applications that have networked
                 structures such as those in electrical, gas, nd water
                 distribution systems. DMNetwork provides data and
                 topology management, parallelization for multiphysics
                 systems over a network, and hierarchical and composable
                 solvers to exploit the problem structure. DMNetwork
                 eases the simulation development cycle by providing the
                 necessary infrastructure through simple abstractions to
                 define and query the network components. This article
                 presents the design of DMNetwork, illustrates its user
                 interface, and demonstrates its ability to solve
                 multiphysics systems, such as an electric circuit, a
                 network of power grid and water subnetworks, and
                 transient hydraulic systems over large networks with
                 more than 2 billion variables on extreme-scale
                 computers using up to 30,000 processors.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Luporini:2020:APD,
  author =       "Fabio Luporini and Mathias Louboutin and Michael Lange
                 and Navjot Kukreja and Philipp Witte and Jan
                 H{\"u}ckelheim and Charles Yount and Paul H. J. Kelly
                 and Felix J. Herrmann and Gerard J. Gorman",
  title =        "Architecture and Performance of {Devito}, a System for
                 Automated Stencil Computation",
  journal =      j-TOMS,
  volume =       "46",
  number =       "1",
  pages =        "6:1--6:28",
  month =        apr,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3374916",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Apr 29 08:09:49 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3374916",
  abstract =     "Stencil computations are a key part of many
                 high-performance computing applications, such as image
                 processing, convolutional neural networks, and
                 finite-difference solvers for partial differential
                 equations. Devito is a framework capable of generating
                 highly optimized code given symbolic equations
                 expressed in Python, specialized in, but not limited
                 to, affine (stencil) codes. The lowering process ---
                 from mathematical equations down to C++ code --- is
                 performed by the Devito compiler through a series of
                 intermediate representations. Several performance
                 optimizations are introduced, including advanced common
                 sub-expressions elimination, tiling, and
                 parallelization. Some of these are obtained through
                 well-established stencil optimizers, integrated in the
                 backend of the Devito compiler. The architecture of the
                 Devito compiler, as well as the performance
                 optimizations that are applied when generating code,
                 are presented. The effectiveness of such performance
                 optimizations is demonstrated using operators drawn
                 from seismic imaging applications.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Davis:2020:AMG,
  author =       "Timothy A. Davis and William W. Hager and Scott P.
                 Kolodziej and S. Nuri Yeralan",
  title =        "{Algorithm 1003}: {Mongoose}, a Graph Coarsening and
                 Partitioning Library",
  journal =      j-TOMS,
  volume =       "46",
  number =       "1",
  pages =        "7:1--7:18",
  month =        mar,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3337792",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 7 10:39:23 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3337792",
  abstract =     "Partitioning graphs is a common and useful operation
                 in many areas, from parallel computing to VLSI design
                 to sparse matrix algorithms. In this article, we
                 introduce Mongoose, a multilevel hybrid graph
                 partitioning algorithm and library. Building on
                 previous work in multilevel partitioning frameworks and
                 combinatoric approaches, we introduce novel
                 stall-reducing and stall-free coarsening strategies, as
                 well as an efficient hybrid algorithm leveraging (1)
                 traditional combinatoric methods and (2) continuous
                 quadratic programming formulations. We demonstrate how
                 this new hybrid algorithm outperforms either strategy
                 in isolation, and we also compare Mongoose to METIS and
                 demonstrate its effectiveness on large and social
                 networking (power law) graphs.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Reizenstein:2020:AIL,
  author =       "Jeremy F. Reizenstein and Benjamin Graham",
  title =        "{Algorithm 1004}: The {Iisignature} Library: Efficient
                 Calculation of Iterated-Integral Signatures and Log
                 Signatures",
  journal =      j-TOMS,
  volume =       "46",
  number =       "1",
  pages =        "8:1--8:21",
  month =        mar,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3371237",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 7 10:39:23 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3371237",
  abstract =     "Iterated-integral signatures and log signatures are
                 sequences calculated from a path that characterizes its
                 shape. They originate from the work of K. T. Chen and
                 have become important through Terry Lyons's theory of
                 differential equations driven by rough paths, which is
                 an important developing area of stochastic analysis.
                 They have applications in statistics and machine
                 learning, where there can be a need to calculate finite
                 parts of them quickly for many paths. We introduce the
                 signature and the most basic information (displacement
                 and signed areas) that it contains. We present
                 algorithms for efficiently calculating these
                 signatures. For log signatures this requires
                 consideration of the structure of free Lie algebras. We
                 benchmark the performance of the algorithms. The
                 methods are implemented in C++ and released as a Python
                 extension package, which also supports differentiation.
                 In combination with a machine learning library
                 (Tensorflow, PyTorch, or Theano), this allows
                 end-to-end learning of neural networks involving
                 signatures.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Jonasson:2020:AFS,
  author =       "Kristjan Jonasson and Sven Sigurdsson and Hordur Freyr
                 Yngvason and Petur Orri Ragnarsson and Pall Melsted",
  title =        "{Algorithm 1005}: {Fortran} Subroutines for Reverse
                 Mode Algorithmic Differentiation of {BLAS} Matrix
                 Operations",
  journal =      j-TOMS,
  volume =       "46",
  number =       "1",
  pages =        "9:1--9:20",
  month =        mar,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3382191",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 7 10:39:23 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3382191",
  abstract =     "A set of Fortran subroutines for reverse mode
                 algorithmic (or automatic) differentiation of the basic
                 linear algebra subprograms (BLAS) is presented. This is
                 preceded by a description of the mathematical tools
                 used to obtain the formulae of these derivatives, with
                 emphasis on special matrices supported by the BLAS:
                 triangular, symmetric, and band. All single and double
                 precision BLAS derivatives have been implemented,
                 together with the Cholesky factorization from Linear
                 Algebra Package (LAPACK). The subroutines are written
                 in Fortran 2003 with a Fortran 77 interface to allow
                 use from C and C++, as well as dynamic languages such
                 as R, Python, Matlab, and Octave. The subroutines are
                 all implemented by calling BLAS, thereby attaining fast
                 runtime. Timing results show derivative runtimes that
                 are about twice those of the corresponding BLAS, in
                 line with theory. The emphasis is on reverse mode
                 because it is more important for the main application
                 that we have in mind, numerical optimization. Two
                 examples are presented, one dealing with the least
                 squares modeling of groundwater, and the other dealing
                 with the maximum likelihood estimation of the
                 parameters of a vector autoregressive time series. The
                 article contains comprehensive tables of formulae for
                 the BLAS derivatives as well as for several non-BLAS
                 matrix operations commonly used in optimization.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Abergel:2020:AFA,
  author =       "R{\'e}my Abergel and Lionel Moisan",
  title =        "{Algorithm 1006}: Fast and Accurate Evaluation of a
                 Generalized Incomplete Gamma Function",
  journal =      j-TOMS,
  volume =       "46",
  number =       "1",
  pages =        "10:1--10:24",
  month =        mar,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3365983",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 7 10:39:23 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3365983",
  abstract =     "We present a computational procedure to evaluate the
                 integral $ \int^y_x s^{p - 1} e^{- \mu s} \, d s $ for
                 $ 0 \leq x < y \leq + \infty $, $ \mu = \pm 1 $, $ p >
                 0 $, which generalizes the lower $ (x = 0) $ and upper
                 $ (y = + \infty) $ incomplete gamma functions. To allow
                 for large values of $x$, $y$, and $p$ while avoiding
                 under\slash overflow issues in the standard double
                 precision floating point arithmetic, we use an explicit
                 normalization that is much more efficient than the
                 classical ratio with the complete gamma function. The
                 generalized incomplete gamma function is estimated with
                 continued fractions, with integrations by parts, or,
                 when $ x \approx y$, with the Romberg numerical
                 integration algorithm. We show that the accuracy
                 reached by our algorithm improves a recent
                 state-of-the-art method by two orders of magnitude, and
                 it is essentially optimal considering the limitations
                 imposed by floating point arithmetic. Moreover, the
                 admissible parameter range of our algorithm $ (0 \leq
                 p, x, y \leq 10^{15})$ is much larger than competing
                 algorithms, and its robustness is assessed through
                 massive usage in an image processing application.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Brisebarre:2020:EAS,
  author =       "Nicolas Brisebarre and Mioara Joldes and Jean-Michel
                 Muller and Ana-Maria Nanes and Joris Picot",
  title =        "Error Analysis of Some Operations Involved in the
                 {Cooley--Tukey Fast Fourier Transform}",
  journal =      j-TOMS,
  volume =       "46",
  number =       "2",
  pages =        "11:1--11:27",
  month =        jun,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3368619",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 12 07:37:53 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3368619",
  abstract =     "We are interested in obtaining error bounds for the
                 classical Cooley--Tukey fast Fourier transform
                 algorithm in floating-point arithmetic, for the 2-norm
                 as well as for the infinity norm. For that purpose, we
                 also give some results on the relative error of the
                 complex multiplication by a root of unity, and on the
                 largest value that can take the real or imaginary part
                 of one term of the fast Fourier transform of a vector
                 $x$, assuming that all terms of $x$ have real and
                 imaginary parts less than some value $b$.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Herrmann:2020:HRF,
  author =       "Julien Herrmann and Guillaume Pallez (Aupy)",
  title =        "{H-Revolve}: a Framework for Adjoint Computation on
                 Synchronous Hierarchical Platforms",
  journal =      j-TOMS,
  volume =       "46",
  number =       "2",
  pages =        "12:1--12:25",
  month =        jun,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3378672",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 12 07:37:53 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3378672",
  abstract =     "We study the problem of checkpointing strategies for
                 adjoint computation on synchronous hierarchical
                 platforms, specifically computational platforms with
                 several levels of storage with different writing and
                 reading costs. When reversing a large adjoint chain,
                 choosing which data to checkpoint and where is a
                 critical decision for the overall performance of the
                 computation. We introduce H-Revolve, an optimal
                 algorithm for this problem. We make it available in a
                 public Python library along with the implementation of
                 several state-of-the-art algorithms for the variant of
                 the problem with two levels of storage. We provide a
                 detailed description of how one can use this library in
                 an adjoint computation software in the field of
                 automatic differentiation or backpropagation. Finally,
                 we evaluate the performance of H-Revolve and other
                 checkpointing heuristics though an extensive campaign
                 of simulation.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ballard:2020:TPC,
  author =       "Grey Ballard and Alicia Klinvex and Tamara G. Kolda",
  title =        "{TuckerMPI}: a Parallel {C++\slash MPI} Software
                 Package for Large-scale Data Compression via the
                 {Tucker} Tensor Decomposition",
  journal =      j-TOMS,
  volume =       "46",
  number =       "2",
  pages =        "13:1--13:31",
  month =        jun,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3378445",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 12 07:37:53 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3378445",
  abstract =     "Our goal is compression of massive-scale
                 grid-structured data, such as the multi-terabyte output
                 of a high-fidelity computational simulation. For such
                 data sets, we have developed a new software package
                 called TuckerMPI, a parallel C++/MPI software package
                 for compressing distributed data. The approach is based
                 on treating the data as a tensor, i.e., a
                 multidimensional array, and computing its truncated
                 Tucker decomposition, a higher-order analogue to the
                 truncated singular value decomposition of a matrix. The
                 result is a low-rank approximation of the original
                 tensor-structured data. Compression efficiency is
                 achieved by detecting latent global structure within
                 the data, which we contrast to most compression methods
                 that are focused on local structure. In this work, we
                 describe TuckerMPI, our implementation of the truncated
                 Tucker decomposition, including details of the data
                 distribution and in-memory layouts, the parallel and
                 serial implementations of the key kernels, and analysis
                 of the storage, communication, and computational costs.
                 We test the software on 4.5 and 6.7 terabyte data sets
                 distributed across 100 s of nodes (1,000 s of MPI
                 processes), achieving compression ratios between 100
                 and 200,000$ \times $, which equates to 99--99.999\%
                 compression (depending on the desired accuracy) in
                 substantially less time than it would take to even read
                 the same dataset from a parallel file system. Moreover,
                 we show that our method also allows for reconstruction
                 of partial or down-sampled data on a single node,
                 without a parallel computer so long as the
                 reconstructed portion is small enough to fit on a
                 single machine, e.g., in the instance of
                 reconstructing/visualizing a single down-sampled time
                 step or computing summary statistics. The code is
                 available at https://gitlab.com/tensors/TuckerMPI.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Marques:2020:BSC,
  author =       "Osni Marques and James Demmel and Paulo B.
                 Vasconcelos",
  title =        "Bidiagonal {SVD} Computation via an Associated
                 Tridiagonal Eigenproblem",
  journal =      j-TOMS,
  volume =       "46",
  number =       "2",
  pages =        "14:1--14:25",
  month =        jun,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3361746",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 12 07:37:53 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3361746",
  abstract =     "The Singular Value Decomposition (SVD) is widely used
                 in numerical analysis and scientific computing
                 applications, including dimensionality reduction, data
                 compression and clustering, and computation of
                 pseudo-inverses. In many cases, a crucial part of the
                 SVD of a general matrix is to find the SVD of an
                 associated bidiagonal matrix. This article discusses an
                 algorithm to compute the SVD of a bidiagonal matrix
                 through the eigenpairs of an associated symmetric
                 tridiagonal matrix. The algorithm enables the
                 computation of only a subset of singular values and
                 corresponding vectors, with potential performance
                 gains. The article focuses on a sequential version of
                 the algorithm, and discusses special cases and
                 implementation details. The implementation, called
                 BDSVDX, has been included in the LAPACK library. We use
                 a large set of bidiagonal matrices to assess the
                 accuracy of the implementation, both in single and
                 double precision, as well as to identify potential
                 shortcomings. The results show that BDSVDX can be up to
                 three orders of magnitude faster than existing
                 algorithms, which are limited to the computation of a
                 full SVD. We also show comparisons of an implementation
                 that uses BDSVDX as a building block for the
                 computation of the SVD of general matrices.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Frison:2020:BAB,
  author =       "Gianluca Frison and Tommaso Sartor and Andrea Zanelli
                 and Moritz Diehl",
  title =        "The {BLAS API} of {BLASFEO}: Optimizing Performance
                 for Small Matrices",
  journal =      j-TOMS,
  volume =       "46",
  number =       "2",
  pages =        "15:1--15:36",
  month =        jun,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3378671",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 12 07:37:53 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/java2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3378671",
  abstract =     "Basic Linear Algebra Subroutines For Embedded
                 Optimization (BLASFEO) is a dense linear algebra
                 library providing high-performance implementations of
                 BLAS- and LAPACK-like routines for use in embedded
                 optimization and other applications targeting
                 relatively small matrices. BLASFEO defines an
                 application programming interface (API) which uses a
                 packed matrix format as its native format. This format
                 is analogous to the internal memory buffers of
                 optimized BLAS, but it is exposed to the user and it
                 removes the packing cost from the routine call. For
                 matrices fitting in cache, BLASFEO outperforms
                 optimized BLAS implementations, both open source and
                 proprietary. This article investigates the addition of
                 a standard BLAS API to the BLASFEO framework, and
                 proposes an implementation switching between two or
                 more algorithms optimized for different matrix sizes.
                 Thanks to the modular assembly framework in BLASFEO,
                 tailored linear algebra kernels with mixed column- and
                 panel-major arguments are easily developed. This BLAS
                 API has lower performance than the BLASFEO API, but it
                 nonetheless outperforms optimized BLAS and especially
                 LAPACK libraries for matrices fitting in cache.
                 Therefore, it can boost a wide range of applications,
                 where standard BLAS and LAPACK libraries are employed
                 and the matrix size is moderate. In particular, this
                 article investigates the benefits in scientific
                 programming languages such as Octave, SciPy, and
                 Julia.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Michail:2020:JJL,
  author =       "Dimitrios Michail and Joris Kinable and Barak Naveh
                 and John V. Sichi",
  title =        "{JGraphT} --- a {Java} Library for Graph Data
                 Structures and Algorithms",
  journal =      j-TOMS,
  volume =       "46",
  number =       "2",
  pages =        "16:1--16:29",
  month =        jun,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3381449",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 12 07:37:53 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/java2020.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3381449",
  abstract =     "Mathematical software and graph-theoretical
                 algorithmic packages to efficiently model, analyze, and
                 query graphs are crucial in an era where large-scale
                 spatial, societal, and economic network data are
                 abundantly available. One such package is JGraphT,
                 programming library that contains very efficient and
                 generic graph data structures along with a large
                 collection of state-of-the-art algorithms. The library
                 is written in Java with stability, interoperability,
                 and performance in mind. A distinctive feature of this
                 library is its ability to model vertices and edges as
                 arbitrary objects, thereby permitting natural
                 representations of many common networks, including
                 transportation, social, and biological networks.
                 Besides classic graph algorithms such as shortest-paths
                 and spanning-tree algorithms, the library contains
                 numerous advanced algorithms: graph and subgraph
                 isomorphism, matching and flow problems, approximation
                 algorithms for NP-hard problems such as independent set
                 and the traveling salesman problem, and several more
                 exotic algorithms such as Berge graph detection. Due to
                 its versatility and generic design, JGraphT is
                 currently used in large-scale commercial products, as
                 well as noncommercial and academic research
                 projects.\par

                 In this work, we describe in detail the design and
                 underlying structure of the library, and discuss its
                 most important features and algorithms. A computational
                 study is conducted to evaluate the performance of
                 JGraphT versus several similar libraries. Experiments
                 on a large number of graphs over a variety of popular
                 algorithms show that JGraphT is highly competitive with
                 other established libraries such as NetworkX or the
                 BGL.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Amos:2020:AQQ,
  author =       "Brandon D. Amos and David R. Easterling and Layne T.
                 Watson and William I. Thacker and Brent S. Castle and
                 Michael W. Trosset",
  title =        "{Algorithm 1007}: {QNSTOP} --- Quasi-{Newton}
                 Algorithm for Stochastic Optimization",
  journal =      j-TOMS,
  volume =       "46",
  number =       "2",
  pages =        "17:1--17:20",
  month =        jun,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3374219",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 12 07:37:53 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3374219",
  abstract =     "QNSTOP consists of serial and parallel (OpenMP)
                 Fortran 2003 codes for the quasi-Newton stochastic
                 optimization method of Castle and Trosset for
                 stochastic search problems. A complete description of
                 QNSTOP for both local search with stochastic objective
                 and global search with ``noisy'' deterministic
                 objective is given here, to the best of our knowledge,
                 for the first time. For stochastic search problems,
                 some convergence theory exists for particular
                 algorithmic choices and parameter values. Both the
                 parallel driver subroutine, which offers several
                 parallel decomposition strategies, and the serial
                 driver subroutine can be used for local stochastic
                 search or global deterministic search, based on an
                 input switch. Some performance data for computational
                 systems biology problems is given.",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Casado:2020:AMN,
  author =       "Jose Maria Varas Casado and Rob Hewson",
  title =        "{Algorithm 1008}: {Multicomplex} Number Class for
                 {Matlab}, with a Focus on the Accurate Calculation of
                 Small Imaginary Terms for Multicomplex Step Sensitivity
                 Calculations",
  journal =      j-TOMS,
  volume =       "46",
  number =       "2",
  pages =        "18:1--18:26",
  month =        jun,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3378542",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 12 07:37:53 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3378542",
  abstract =     "A Matlab class for multicomplex numbers was developed
                 with particular attention paid to the robust and
                 accurate handling of small imaginary components. This
                 is primarily to allow the class to be used to obtain n
                 order derivative information using the multicomplex
                 step method for, among other applications,
                 gradient-based optimization and optimum control
                 problems. The algebra of multicomplex numbers is
                 described, as is its accurate computational
                 implementation, considering small term approximations
                 and the identification of principal values. The
                 implementation of the method in Matlab is studied, and
                 a class definition is constructed. This new class
                 definition enables Matlab to handle $n$-order
                 multicomplex numbers and perform arithmetic functions.
                 It was found that with this method, the step size could
                 be arbitrarily decreased toward machine precision. Use
                 of the method to obtain up to the seventh derivative of
                 functions is presented, as is timing data to
                 demonstrate the efficiency of the class
                 implementation.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hawkins:2020:AMO,
  author =       "Stuart C. Hawkins",
  title =        "{Algorithm 1009}: {MieSolver} --- an Object-Oriented
                 {Mie} Series Software for Wave Scattering by
                 Cylinders",
  journal =      j-TOMS,
  volume =       "46",
  number =       "2",
  pages =        "19:1--19:28",
  month =        jun,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3381537",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 12 07:37:53 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3381537",
  abstract =     "MieSolver provides an efficient solver for the problem
                 of wave propagation through a heterogeneous
                 configuration of nonidentical circular cylinders.
                 MieSolver allows great flexibility in the physical
                 properties of each cylinder, and the cylinders may have
                 opaque or penetrable cores, as well as an arbitrary
                 number of penetrable layers. The wave propagation is
                 governed by the two-dimensional Helmholtz equation and
                 models electromagnetic, acoustic, and elastic waves.
                 The solver is based on the Mie series solution for
                 scattering by a single circular cylinder and hence is
                 numerically stable and highly accurate. We demonstrate
                 the accuracy of our software with extensive numerical
                 experiments over a wide range of frequencies (about
                 five orders of magnitude) and up to 60 cylinders.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Orellana:2020:ABE,
  author =       "Alberto Giacomo Orellana and Cristiano {De Michele}",
  title =        "{Algorithm 1010}: {Boosting} Efficiency in Solving
                 Quartic Equations with No Compromise in Accuracy",
  journal =      j-TOMS,
  volume =       "46",
  number =       "2",
  pages =        "20:1--20:28",
  month =        jun,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3386241",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Jun 12 07:37:53 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See improvement \cite{DeMichele:2022:RAB}.",
  URL =          "https://dl.acm.org/doi/abs/10.1145/3386241",
  abstract =     "Aiming to provide a very accurate, efficient, and
                 robust quartic equation solver for physical
                 applications, we have proposed an algorithm that builds
                 on the previous works of P. Strobach and S. L. Shmakov.
                 It is based on the decomposition of the quartic
                 polynomial into two quadratics, whose coefficients are
                 first accurately estimated by handling carefully
                 numerical errors and afterward refined through the use
                 of the Newton--Raphson method. Our algorithm is very
                 accurate in comparison with other state-of-the-art
                 solvers that can be found in the literature, but (most
                 importantly) it turns out to be very efficient
                 according to our timing tests. A crucial issue for us
                 is the robustness of the algorithm, i.e., its ability
                 to cope with the detrimental effect of round-off
                 errors, no matter what set of quartic coefficients is
                 provided in a practical application. In this respect,
                 we extensively tested our algorithm in comparison to
                 other quartic equation solvers both by considering
                 specific extreme cases and by carrying out a
                 statistical analysis over a very large set of quartics.
                 Our algorithm has also been heavily tested in a
                 physical application, i.e., simulations of hard
                 cylinders, where it proved its absolute reliability as
                 well as its efficiency.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lange:2020:FRF,
  author =       "Marko Lange and Siegfried M. Rump",
  title =        "Faithfully Rounded Floating-point Computations",
  journal =      j-TOMS,
  volume =       "46",
  number =       "3",
  pages =        "21:1--21:20",
  month =        sep,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3290955",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Sep 26 07:28:19 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3290955",
  abstract =     "We present a pair arithmetic for the four basic
                 operations and square root. It can be regarded as a
                 simplified, more-efficient double-double arithmetic.
                 The central assumption on the underlying arithmetic is
                 the first standard model for error analysis for
                 operations on a discrete set of real numbers. Neither
                 do we require a floating-point grid nor a rounding to
                 nearest property. Based on that, we define a relative
                 rounding error unit $u$ and prove rigorous error bounds
                 for the computed result of an arbitrary arithmetic
                 expression depending on $u$, the size of the
                 expression, and possibly a condition measure. In the
                 second part of this note, we extend the error analysis
                 by examining requirements to ensure faithfully rounded
                 outputs and apply our results to IEEE 754 standard
                 conform floating-point systems. For a class of
                 mathematical expressions, using an IEEE 754 standard
                 conform arithmetic with base $ \beta $, the result is
                 proved to be faithfully rounded for up to $ 1 / \sqrt
                 {\beta u - 2}$ operations. Our findings cover a number
                 of previously published algorithms to compute
                 faithfully rounded results, among them Horner's scheme,
                 products, sums, dot products, or Euclidean norm. Beyond
                 that, several other problems can be analyzed, such as
                 polynomial interpolation, orientation problems,
                 Householder transformations, or the smallest singular
                 value of Hilbert matrices of large size.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ahrens:2020:AER,
  author =       "Peter Ahrens and James Demmel and Hong Diep Nguyen",
  title =        "Algorithms for Efficient Reproducible Floating Point
                 Summation",
  journal =      j-TOMS,
  volume =       "46",
  number =       "3",
  pages =        "22:1--22:49",
  month =        sep,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3389360",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Sep 26 07:28:19 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3389360",
  abstract =     "We define ``reproducibility'' as getting bitwise
                 identical results from multiple runs of the same
                 program, perhaps with different hardware resources or
                 other changes that should not affect the answer. Many
                 users depend on reproducibility for debugging or
                 correctness. However, dynamic scheduling of parallel
                 computing resources, combined with nonassociative
                 floating point addition, makes reproducibility
                 challenging even for summation, or operations like the
                 BLAS. We describe a ``reproducible accumulator'' data
                 structure (the ``binned number'') and associated
                 algorithms to reproducibly sum binary floating point
                 numbers, independent of summation order. We use a
                 subset of the IEEE Floating Point Standard 754-2008 and
                 bitwise operations on the standard representations in
                 memory. Our approach requires only one read-only pass
                 over the data, and one reduction in parallel, using a
                 6-word reproducible accumulator (more words can be used
                 for higher accuracy), enabling standard tiling
                 optimization techniques. Summing $n$ words with a
                 6-word reproducible accumulator requires approximately
                 $ 9 n$ floating point operations (arithmetic,
                 comparison, and absolute value) and approximately $ 3
                 n$ bitwise operations. The final error bound with a
                 6-word reproducible accumulator and our default
                 settings can be up to 229 times smaller than the error
                 bound for conventional (recursive) summation on
                 ill-conditioned double-precision inputs",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accurate floating-point summation",
}

@Article{Aguirre-Mesa:2020:MLC,
  author =       "Andres M. Aguirre-Mesa and Manuel J. Garcia and Harry
                 Millwater",
  title =        "{MultiZ}: a Library for Computation of High-order
                 Derivatives Using Multicomplex or Multidual Numbers",
  journal =      j-TOMS,
  volume =       "46",
  number =       "3",
  pages =        "23:1--23:30",
  month =        sep,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3378538",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Sep 26 07:28:19 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fortran3.bib;
                 https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3378538",
  abstract =     "Multicomplex and multidual numbers are two
                 generalizations of complex numbers with multiple
                 imaginary axes, useful for numerical computation of
                 derivatives with machine precision. The similarities
                 between multicomplex and multidual algebras allowed us
                 to create a unified library to use either one for
                 sensitivity analysis. This library can be used to
                 compute arbitrary order derivates of functions of a
                 single variable or multiple variables. The storage of
                 matrix representations of multicomplex and multidual
                 numbers is avoided using a combination of
                 one-dimensional resizable arrays and an indexation
                 method based on binary bitwise operations. To provide
                 high computational efficiency and low memory usage, the
                 multiplication of hypercomplex numbers up to sixth
                 order is carried out using a hard-coded algorithm. For
                 higher hypercomplex orders, the library uses by default
                 a multiplication method based on binary bitwise
                 operations. The computation of algebraic and
                 transcendental functions is achieved using a Taylor
                 series approximation. Fortran and Python versions were
                 developed, and extensions to other languages are
                 self-evident.",
  acknowledgement = ack-nhfb,
  articleno =    "23",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Avramidis:2020:SOS,
  author =       "Eleftherios Avramidis and Marta Lalik and Ozgur E.
                 Akman",
  title =        "{SODECL}: an Open-Source Library for Calculating
                 Multiple Orbits of a System of Stochastic Differential
                 Equations in Parallel",
  journal =      j-TOMS,
  volume =       "46",
  number =       "3",
  pages =        "24:1--24:21",
  month =        sep,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3385076",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Sep 26 07:28:19 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3385076",
  abstract =     "Stochastic differential equations (SDEs) are widely
                 used to model systems affected by random processes. In
                 general, the analysis of an SDE model requires
                 numerical solutions to be generated many times over
                 multiple parameter combinations. However, this process
                 often requires considerable computational resources to
                 be practicable. Due to the embarrassingly parallel
                 nature of the task, devices such as multi-core
                 processors and graphics processing units (GPUs) can be
                 employed for acceleration.\par

                 Here, we present SODECL
                 (https://github.com/avramidis/sodecl), a software
                 library that utilizes such devices to calculate
                 multiple orbits of an SDE model. To evaluate the
                 acceleration provided by SODECL, we compared the time
                 required to calculate multiple orbits of an exemplar
                 stochastic model when one CPU core is used, to the time
                 required when using all CPU cores or a GPU. In
                 addition, to assess scalability, we investigated how
                 model size affected execution time on different
                 parallel compute devices.\par

                 Our results show that when using all 32 CPU cores of a
                 high-end high-performance computing node, the task is
                 accelerated by a factor of up to 6.7, compared to when
                 using a single CPU core. Executing the task on a
                 high-end GPU yielded accelerations of up to 4.5,
                 compared to a single CPU core.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Agamawi:2020:CCS,
  author =       "Yunus M. Agamawi and Anil V. Rao",
  title =        "{CGPOPS}: a {C++} Software for Solving Multiple-Phase
                 Optimal Control Problems Using Adaptive {Gaussian}
                 Quadrature Collocation and Sparse Nonlinear
                 Programming",
  journal =      j-TOMS,
  volume =       "46",
  number =       "3",
  pages =        "25:1--25:38",
  month =        sep,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3390463",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Sep 26 07:28:19 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3390463",
  abstract =     "A general-purpose C++ software program called CGPOPS
                 is described for solving multiple-phase optimal control
                 problems using adaptive direct orthogonal collocation
                 methods. The software employs a Legendre--Gauss--Radau
                 direct orthogonal collocation method o transcribe the
                 continuous optimal control problem into a large sparse
                 nonlinear programming problem (NLP). A class of hp mesh
                 refinement methods are implemented that determine the
                 number of mesh intervals and the degree of the
                 approximating polynomial within each mesh interval to
                 achieve a specified accuracy tolerance. The software is
                 interfaced with the open source Newton NLP solver
                 IPOPT. All derivatives required by the NLP solver are
                 computed via central finite differencing,
                 bicomplex-step derivative approximations, hyper-dual
                 derivative approximations, or automatic
                 differentiation. The key components of the software are
                 described in detail, and the utility of the software is
                 demonstrated on five optimal control problems of
                 varying complexity. The software described in this
                 article provides researchers a transitional platform to
                 solve a wide variety of complex constrained optimal
                 control problems.",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Davis:2020:APE,
  author =       "Brisa N. Davis and Randall J. LeVeque",
  title =        "Analysis and Performance Evaluation of Adjoint-guided
                 Adaptive Mesh Refinement for Linear Hyperbolic {PDEs}
                 Using {Clawpack}",
  journal =      j-TOMS,
  volume =       "46",
  number =       "3",
  pages =        "26:1--26:28",
  month =        sep,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3392775",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Sep 26 07:28:19 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3392775",
  abstract =     "Adaptive mesh refinement (AMR) is often used when
                 solving time-dependent partial differential equations
                 using numerical methods. It enables time-varying
                 regions of much higher resolution, which can
                 selectively refine areas to track discontinuities in
                 the solution. The open source Clawpack software
                 implements block-structured AMR to refine around
                 propagating waves in the AMRClaw package. For problems
                 where the solution must be computed over a large domain
                 but is only of interest in a small area, this approach
                 often refines waves that will not impact the target
                 area. We seek a method that enables the identification
                 and refinement of only the waves that will influence
                 the target area.\par

                 Here we show that solving the time-dependent adjoint
                 equation and using a suitable inner product allows for
                 a more precise refinement of the relevant waves. We
                 present the adjoint methodology in general and give
                 details on the implementation of this method in
                 AMRClaw. Examples and a computational performance
                 analysis for linear acoustics equations are presented.
                 The adjoint method is compared to AMR methods already
                 available in AMRClaw, and the advantages and
                 disadvantages are discussed. The approach presented
                 here is implemented in Clawpack, in Version 5.6.1, and
                 code for all examples presented is archived on
                 Github.",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bleyer:2020:AFR,
  author =       "Jeremy Bleyer",
  title =        "Automating the Formulation and Resolution of Convex
                 Variational Problems: Applications from Image
                 Processing to Computational Mechanics",
  journal =      j-TOMS,
  volume =       "46",
  number =       "3",
  pages =        "27:1--27:33",
  month =        sep,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3393881",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Sep 26 07:28:19 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3393881",
  abstract =     "Convex variational problems arise in many fields
                 ranging from image processing to fluid and solid
                 mechanics communities. Interesting applications usually
                 involve non-smooth terms, which require well-designed
                 optimization algorithms for their resolution. The
                 present manuscript presents the Python package called
                 fenics_optim built on top of the FEniCS finite element
                 software, which enables one to automate the formulation
                 and resolution of various convex variational problems.
                 Formulating such a problem relies on FEniCS
                 domain-specific language and the representation of
                 convex functions, in particular, non-smooth ones, in
                 the conic programming framework. The discrete
                 formulation of the corresponding optimization problems
                 hinges on the finite element discretization
                 capabilities offered by FEniCS, while their numerical
                 resolution is carried out by the interior-point solver
                 Mosek. Through various illustrative examples, we show
                 that convex optimization problems can be formulated
                 using only a few lines of code, discretized in a very
                 simple manner, and solved extremely efficiently.",
  acknowledgement = ack-nhfb,
  articleno =    "27",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ewart:2020:PES,
  author =       "Timoth{\'e}e Ewart and Francesco Cremonesi and Felix
                 Sch{\"u}rmann and Fabien Delalondre",
  title =        "Polynomial Evaluation on Superscalar Architecture,
                 Applied to the Elementary Function $ e^x $",
  journal =      j-TOMS,
  volume =       "46",
  number =       "3",
  pages =        "28:1--28:22",
  month =        sep,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3408893",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Sep 26 07:28:19 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3408893",
  abstract =     "The evaluation of small degree polynomials is critical
                 for the computation of elementary functions. It has
                 been extensively studied and is well documented. In
                 this article, we evaluate existing methods for
                 polynomial evaluation on superscalar architecture. In
                 addition, we have completed this work with a
                 factorization method, which is surprisingly neglected
                 in the literature. This work focuses on out-of-order
                 Intel processors, amongst others, of which
                 computational units are available. Moreover, we applied
                 our work on the elementary function $e^x$ that requires,
                 in the current implementation, an evaluation of a
                 polynomial of degree 10 for a satisfying precision and
                 performance. Our results show that the factorization
                 scheme is the fastest in benchmarks, and that latency
                 and throughput are intrinsically dependent on each
                 other on superscalar architecture.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Mejstrik:2020:AII,
  author =       "Thomas Mejstrik",
  title =        "{Algorithm 1011}: {Improved} Invariant Polytope
                 Algorithm and Applications",
  journal =      j-TOMS,
  volume =       "46",
  number =       "3",
  pages =        "29:1--29:26",
  month =        sep,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3408891",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Sep 26 07:28:19 MDT 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3408891",
  abstract =     "In several papers of 2013--2016, Guglielmi and
                 Protasov made a breakthrough in the problem of the
                 joint spectral radius computation, developing the
                 invariant polytope algorithm that for most matrix
                 families finds the exact value of the joint spectral
                 radius. This algorithm found many applications in
                 problems of functional analysis, approximation theory,
                 combinatorics, and so on. In this article, we propose a
                 modification of the invariant polytope algorithm making
                 it roughly 3 times faster (single threaded), suitable
                 for higher dimensions, and parallelise it. The modified
                 version works for most matrix families of dimensions up
                 to 25, for non-negative matrices up to 3,000. In
                 addition, we introduce a new, fast algorithm, called
                 modified Gripenberg algorithm, for computing good lower
                 bounds for the joint spectral radius. The corresponding
                 examples and statistics of numerical results are
                 provided. Several applications of our algorithms are
                 presented. In particular, we find the exact values of
                 the regularity exponents of Daubechies wavelets up to
                 order 42 and the capacities of codes that avoid certain
                 difference patterns.",
  acknowledgement = ack-nhfb,
  articleno =    "29",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Drmac:2020:NNA,
  author =       "Zlatko Drma{\v{c}} and Ivana {\v{S}}ain Glibi{\'c}",
  title =        "New Numerical Algorithm for Deflation of Infinite and
                 Zero Eigenvalues and Full Solution of Quadratic
                 Eigenvalue Problems",
  journal =      j-TOMS,
  volume =       "46",
  number =       "4",
  pages =        "30:1--30:32",
  month =        nov,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3401831",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 14 07:15:52 MST 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3401831",
  abstract =     "This article presents a new method for computing all
                 eigenvalues and eigenvectors of quadratic matrix pencil
                 $ Q (\lambda) = \lambda^2 M + \lambda C + K $. It is an
                 upgrade of the quadeig algorithm by Hammarling et al.,
                 which attempts to reveal and remove by deflation a
                 certain number of zero and infinite eigenvalues before
                 QZ iterations. Proposed modifications of the quadeig
                 framework are designed to enhance backward stability
                 and to make the process of deflating infinite and zero
                 eigenvalues more numerically robust. In particular,
                 careful preprocessing allows scaling invariant\slash
                 component-wise backward error and thus a better
                 condition number. Further, using an upper triangular
                 version of the Kronecker canonical form enables
                 deflating additional infinite eigenvalues, in addition
                 to those inferred from the rank of M. Theoretical
                 analysis and empirical evidence from thorough testing
                 of the software implementation confirm superior
                 numerical performances of the proposed method.",
  acknowledgement = ack-nhfb,
  articleno =    "30",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Thies:2020:PPH,
  author =       "Jonas Thies and Melven R{\"o}hrig-Z{\"o}llner and
                 Nigel Overmars and Achim Basermann and Dominik Ernst
                 and Georg Hager and Gerhard Wellein",
  title =        "{PHIST}: a Pipelined, Hybrid-Parallel Iterative Solver
                 Toolkit",
  journal =      j-TOMS,
  volume =       "46",
  number =       "4",
  pages =        "31:1--31:26",
  month =        nov,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3402227",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 14 07:15:52 MST 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3402227",
  abstract =     "The increasing complexity of hardware and software
                 environments in high-performance computing poses big
                 challenges on the development of sustainable and
                 hardware-efficient numerical software. This article
                 addresses these challenges in the context of \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "31",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Burstedde:2020:PTA,
  author =       "Carsten Burstedde",
  title =        "Parallel Tree Algorithms for {AMR} and Non-Standard
                 Data Access",
  journal =      j-TOMS,
  volume =       "46",
  number =       "4",
  pages =        "32:1--32:31",
  month =        nov,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3401990",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 14 07:15:52 MST 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3401990",
  abstract =     "We introduce several parallel algorithms operating on
                 a distributed forest of adaptive quadtrees/octrees.
                 They are targeted at large-scale applications relying
                 on data layouts that are more complex than required for
                 standard finite elements, such as hp -. \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "32",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pinto:2020:VSS,
  author =       "Severiano Gonz{\'a}lez Pinto and Domingo Hern{\'a}ndez
                 Abreu and Juan Ignacio Montijano",
  title =        "Variable Step-Size Control Based on Two-Steps for
                 {Radau IIA} Methods",
  journal =      j-TOMS,
  volume =       "46",
  number =       "4",
  pages =        "33:1--33:24",
  month =        nov,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3408892",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 14 07:15:52 MST 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3408892",
  abstract =     "Two-step embedded methods of order s based on s -stage
                 Radau IIA formulas are considered for the variable
                 step-size integration of stiff differential equations.
                 These embedded methods are aimed at local error control
                 and are computed through a linear \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "33",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Uphoff:2020:YAT,
  author =       "Carsten Uphoff and Michael Bader",
  title =        "Yet Another Tensor Toolbox for Discontinuous
                 {Galerkin} Methods and Other Applications",
  journal =      j-TOMS,
  volume =       "46",
  number =       "4",
  pages =        "34:1--34:40",
  month =        nov,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3406835",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 14 07:15:52 MST 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3406835",
  abstract =     "The numerical solution of partial differential
                 equations is at the heart of many grand challenges in
                 supercomputing. Solvers based on high-order
                 discontinuous Galerkin (DG) discretisation have been
                 shown to scale on large supercomputers with excellent
                 \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "34",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Williams-Young:2020:SSS,
  author =       "David B. Williams-Young and Paul G. Beckman and Chao
                 Yang",
  title =        "A Shift Selection Strategy for Parallel Shift-invert
                 Spectrum Slicing in Symmetric Self-consistent
                 Eigenvalue Computation",
  journal =      j-TOMS,
  volume =       "46",
  number =       "4",
  pages =        "35:1--35:31",
  month =        nov,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3409571",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 14 07:15:52 MST 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3409571",
  abstract =     "The central importance of large-scale eigenvalue
                 problems in scientific computation necessitates the
                 development of massively parallel algorithms for their
                 solution. Recent advances in dense numerical linear
                 algebra have enabled the routine treatment of of
                 eigenvalue problems with dimensions on the order of
                 hundreds of thousands on the world's largest
                 supercomputers. In cases where dense treatments are not
                 feasible, Krylov subspace methods offer an attractive
                 alternative due to the fact that they do not require
                 storage of the problem matrices. However, demonstration
                 of scalability of either of these classes of eigenvalue
                 algorithms on computing architectures capable of
                 expressing massive parallelism is non-trivial due to
                 communication requirements and serial bottlenecks,
                 respectively. In this work, we introduce the SISLICE
                 method: a parallel shift-invert algorithm for the
                 solution of the symmetric self-consistent field (SCF)
                 eigenvalue problem. The SISLICE method drastically
                 reduces the communication requirement of current
                 parallel shift-invert eigenvalue algorithms through
                 various shift selection and migration techniques based
                 on density of states estimation and $k$-means
                 clustering, respectively. This work demonstrates the
                 robustness and parallel performance of the SISLICE
                 method on a representative set of SCF eigenvalue
                 problems and outlines research directions that will be
                 explored in future work.",
  acknowledgement = ack-nhfb,
  articleno =    "35",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Spring:2020:FCS,
  author =       "Braegan S. Spring and Eric Polizzi and Ahmed H.
                 Sameh",
  title =        "A Feature-complete {SPIKE} Dense Banded Solver",
  journal =      j-TOMS,
  volume =       "46",
  number =       "4",
  pages =        "36:1--36:35",
  month =        nov,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3410153",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 14 07:15:52 MST 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3410153",
  abstract =     "This article presents a parallel, effective, and
                 feature-complete recursive SPIKE algorithm that
                 achieves near feature-parity with the standard linear
                 algebra package banded linear system solver. First, we
                 present a flexible parallel implementation of
                 \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "36",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Barabasz:2020:EAI,
  author =       "Barbara Barabasz and Andrew Anderson and Kirk M.
                 Soodhalter and David Gregg",
  title =        "Error Analysis and Improving the Accuracy of
                 {Winograd} Convolution for Deep Neural Networks",
  journal =      j-TOMS,
  volume =       "46",
  number =       "4",
  pages =        "37:1--37:33",
  month =        nov,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3412380",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 14 07:15:52 MST 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3412380",
  abstract =     "Popular deep neural networks (DNNs) spend the majority
                 of their execution time computing convolutions. The
                 Winograd family of algorithms can greatly reduce the
                 number of arithmetic operations required and is used in
                 many DNN software frameworks. However,. \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "37",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Chang:2020:ADI,
  author =       "Tyler H. Chang and Layne T. Watson and Thomas C. H.
                 Lux and Ali R. Butt and Kirk W. Cameron and Yili Hong",
  title =        "{Algorithm 1012}: {DELAUNAYSPARSE}: Interpolation via
                 a Sparse Subset of the {Delaunay} Triangulation in
                 Medium to High Dimensions",
  journal =      j-TOMS,
  volume =       "46",
  number =       "4",
  pages =        "38:1--38:20",
  month =        nov,
  year =         "2020",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3422818",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 14 07:15:52 MST 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3422818",
  abstract =     "DELAUNAYSPARSE contains both serial and parallel codes
                 written in Fortran 2003 (with OpenMP) for performing
                 medium- to high-dimensional interpolation via the
                 Delaunay triangulation. To accommodate the exponential
                 growth in the size of the Delaunay \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "38",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Scott:2021:SLS,
  author =       "Jennifer Scott and Miroslav Tuma",
  title =        "Strengths and Limitations of Stretching for
                 Least-squares Problems with Some Dense Rows",
  journal =      j-TOMS,
  volume =       "47",
  number =       "1",
  pages =        "1:1--1:25",
  month =        jan,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3412559",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jan 7 10:31:04 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3412559",
  abstract =     "We recently introduced a sparse stretching strategy
                 for handling dense rows that can arise in large-scale
                 linear least-squares problems and make such problems
                 challenging to solve. Sparse stretching is designed to
                 limit the amount of fill within the \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lebrun-Grandie:2021:APP,
  author =       "D. Lebrun-Grandi{\'e} and A. Prokopenko and B.
                 Turcksin and S. R. Slattery",
  title =        "{ArborX}: a Performance Portable Geometric Search
                 Library",
  journal =      j-TOMS,
  volume =       "47",
  number =       "1",
  pages =        "2:1--2:15",
  month =        jan,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3412558",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jan 7 10:31:04 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3412558",
  abstract =     "Searching for geometric objects that are close in
                 space is a fundamental component of many applications.
                 The performance of search algorithms comes to the
                 forefront as the size of a problem increases both in
                 terms of total object count as well as in the
                 \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Huang:2021:HHP,
  author =       "Hua Huang and Xin Xing and Edmond Chow",
  title =        "{H2Pack}: High-performance {$ H^2 $} Matrix Package
                 for Kernel Matrices Using the Proxy Point Method",
  journal =      j-TOMS,
  volume =       "47",
  number =       "1",
  pages =        "3:1--3:29",
  month =        jan,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3412850",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jan 7 10:31:04 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/fastmultipole.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3412850",
  abstract =     "Dense kernel matrices represented in H$^2$ matrix
                 format typically require less storage and have faster
                 matrix--vector multiplications than when these matrices
                 are represented in the standard dense format. In this
                 article, we present H2Pack, a high-performance,
                 shared-memory library for constructing and operating
                 with $ H^2$ matrix representations for kernel matrices
                 defined by non-oscillatory, translationally invariant
                 kernel functions. Using a hybrid analytic-algebraic
                 compression method called the proxy point method,
                 H2Pack can efficiently construct an $ H^2$ matrix
                 representation with linear computational complexity.
                 Storage and matrix--vector multiplication also have
                 linear complexity. H2Pack also introduces the concept
                 of ``partially admissible blocks'' for $ H^2$ matrices
                 to make $ H^2$ matrix--vector multiplication
                 mathematically identical to the fast multipole method
                 (FMM) if analytic expansions are used. We optimize
                 H2Pack from both the algorithm and software
                 perspectives. Compared to existing FMM libraries,
                 H2Pack generally has much faster $ H^2$ matrix--vector
                 multiplications, since the proxy point method is more
                 effective at producing block low-rank approximations
                 than the analytic methods used in FMM. As a tradeoff, $
                 H^2$ matrix construction in H2Pack is typically more
                 expensive than the setup cost in FMM libraries. Thus,
                 H2Pack is ideal for applications that need a large
                 number of matrix--vector multiplications for a given
                 configuration of data points.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Renard:2021:GAF,
  author =       "Yves Renard and Konstantinos Poulios",
  title =        "{GetFEM}: Automated {FE} Modeling of Multiphysics
                 Problems Based on a Generic Weak Form Language",
  journal =      j-TOMS,
  volume =       "47",
  number =       "1",
  pages =        "4:1--4:31",
  month =        jan,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3412849",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jan 7 10:31:04 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3412849",
  abstract =     "This article presents the major mathematical and
                 implementation features of a weak form language (GWFL)
                 for an automated finite-element (FE) solution of
                 partial differential equation systems. The language is
                 implemented in the GetFEM framework and \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Oliveira:2021:EBM,
  author =       "I. F. D. Oliveira and R. H. C. Takahashi",
  title =        "An Enhancement of the Bisection Method Average
                 Performance Preserving Minmax Optimality",
  journal =      j-TOMS,
  volume =       "47",
  number =       "1",
  pages =        "5:1--5:24",
  month =        jan,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3423597",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jan 7 10:31:04 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3423597",
  abstract =     "We identify a class of root-searching methods that
                 surprisingly outperform the bisection method on the
                 average performance while retaining minmax optimality.
                 The improvement on the average applies for any
                 continuous distributional hypothesis. We also
                 \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kempf:2021:ACG,
  author =       "Dominic Kempf and Ren{\'e} He{\ss} and Steffen
                 M{\"u}thing and Peter Bastian",
  title =        "Automatic Code Generation for High-performance
                 Discontinuous {Galerkin} Methods on Modern
                 Architectures",
  journal =      j-TOMS,
  volume =       "47",
  number =       "1",
  pages =        "6:1--6:31",
  month =        jan,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3424144",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jan 7 10:31:04 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3424144",
  abstract =     "SIMD vectorization has lately become a key challenge
                 in high-performance computing. However, hand-written
                 explicitly vectorized code often poses a threat to the
                 software's sustainability. In this publication, we
                 solve this sustainability and performance \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Clevenger:2021:FPA,
  author =       "Thomas C. Clevenger and Timo Heister and Guido
                 Kanschat and Martin Kronbichler",
  title =        "A Flexible, Parallel, Adaptive Geometric Multigrid
                 Method for {FEM}",
  journal =      j-TOMS,
  volume =       "47",
  number =       "1",
  pages =        "7:1--7:27",
  month =        jan,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3425193",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jan 7 10:31:04 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3425193",
  abstract =     "We present the design and implementation details of a
                 geometric multigrid method on adaptively refined meshes
                 for massively parallel computations. The method uses
                 local smoothing on the refined part of the mesh.
                 Partitioning is achieved by using a space \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Arroyo:2021:ARI,
  author =       "Daisy Arroyo and Xavier Emery",
  title =        "{Algorithm 1013}: an {R} Implementation of a
                 Continuous Spectral Algorithm for Simulating Vector
                 {Gaussian} Random Fields in {Euclidean} Spaces",
  journal =      j-TOMS,
  volume =       "47",
  number =       "1",
  pages =        "8:1--8:25",
  month =        jan,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3421316",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jan 7 10:31:04 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/s-plus.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3421316",
  abstract =     "A continuous spectral algorithm and computer routines
                 in the R programming environment that enable the
                 simulation of second-order stationary and intrinsic
                 (i.e., with second-order stationary increments or
                 generalized increments) vector Gaussian random in
                 Euclidean spaces are presented. The simulation is
                 obtained by computing a weighted sum of cosine and sine
                 waves, with weights that depend on the matrix-valued
                 spectral density associated with the spatial
                 correlation structure of the random field to
                 simulate. The computational cost is proportional to the
                 number of locations targeted for simulation, below that
                 of sequential, matrix decomposition and discrete
                 spectral algorithms. Also, the implementation is
                 versatile, as there is no restriction on the number of
                 vector components, workspace dimension, number and
                 geometrical configuration of the target locations. The
                 computer routines are illustrated with synthetic
                 examples and statistical testing is proposed to check
                 the normality of the distribution of the simulated
                 random field or of its generalized increments. A
                 by-product of this work is a spectral representation of
                 spherical, cubic, penta, Askey, J-Bessel, Cauchy,
                 Laguerre, hypergeometric, iterated exponential, gamma,
                 and stable covariance models in the $d$-dimensional
                 Euclidean space..",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Borges:2021:AIA,
  author =       "Carlos F. Borges",
  title =        "{Algorithm 1014}: an Improved Algorithm for {\tt
                 hypot(x,y)}",
  journal =      j-TOMS,
  volume =       "47",
  number =       "1",
  pages =        "9:1--9:12",
  month =        jan,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3428446",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jan 7 10:31:04 MST 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/julia.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3428446",
  abstract =     "We develop fast and accurate algorithms for evaluating
                 $ \sqrt {x^2 + y^2} $ for two floating-point numbers
                 $x$ and $y$. Library functions that perform this
                 computation are generally named {\tt hypot(x,y)}. We
                 compare five approaches that we will develop in this
                 article to the current resident library function that
                 is delivered with Julia 1.1 and to the code that has
                 been distributed with the C math library for decades.
                 We will investigate the accuracy of our algorithms by
                 simulation.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sohier:2021:CIS,
  author =       "Devan Sohier and Pablo {De Oliveira Castro} and
                 Fran{\c{c}}ois F{\'e}votte and Bruno Lathuili{\`e}re
                 and Eric Petit and Olivier Jamond",
  title =        "Confidence Intervals for Stochastic Arithmetic",
  journal =      j-TOMS,
  volume =       "47",
  number =       "2",
  pages =        "10:1--10:33",
  month =        apr,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3432184",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 27 08:23:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3432184",
  abstract =     "Quantifying errors and losses due to the use of
                 Floating-point (FP) calculations in industrial
                 scientific computing codes is an important part of the
                 Verification, Validation, and Uncertainty
                 Quantification process. Stochastic Arithmetic is one
                 way to model and estimate FP losses of accuracy, which
                 scales well to large, industrial codes. It exists in
                 different flavors, such as CESTAC or MCA, implemented
                 in various tools such as CADNA, Verificarlo, or Verrou.
                 These methodologies and tools are based on the idea
                 that FP losses of accuracy can be modeled via
                 randomness. Therefore, they share the same need to
                 perform a statistical analysis of programs results to
                 estimate the significance of the results.\par

                 In this article, we propose a framework to perform a
                 solid statistical analysis of Stochastic Arithmetic.
                 This framework unifies all existing definitions of the
                 number of significant digits (CESTAC and MCA), and also
                 proposes a new quantity of interest: the number of
                 digits contributing to the accuracy of the results.
                 Sound confidence intervals are provided for all
                 estimators, both in the case of normally distributed
                 results, and in the general case. The use of this
                 framework is demonstrated by two case studies of
                 industrial codes: Europlexus and code\aster.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Soylu:2021:IAC,
  author =       "G{\"u}ltekin Soylu",
  title =        "Improved Arithmetic of Complex Fans",
  journal =      j-TOMS,
  volume =       "47",
  number =       "2",
  pages =        "11:1--11:10",
  month =        apr,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3434400",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 27 08:23:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3434400",
  abstract =     "Complex fans are sets of complex numbers whose
                 magnitudes and angles range in closed intervals. The
                 fact that the sum of two fans is a disordered shape
                 gives rise to the need for computational methods to
                 find the minimal enclosing fan. Cases where the sum of
                 two fans contains the origin of the complex plane as a
                 boundary point are of special interest. The result of
                 the addition is then enclosed by circles in current
                 methods, but under certain circumstances this turns out
                 to be an overestimate. The focus of this article is the
                 diagnosis and treatment of such cases.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{VanZee:2021:SMD,
  author =       "Field G. {Van Zee} and Devangi N. Parikh and Robert A.
                 {Van De Geijn}",
  title =        "Supporting Mixed-domain Mixed-precision Matrix
                 Multiplication within the {BLIS} Framework",
  journal =      j-TOMS,
  volume =       "47",
  number =       "2",
  pages =        "12:1--12:26",
  month =        apr,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3402225",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 27 08:23:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3402225",
  abstract =     "We approach the problem of implementing mixed-datatype
                 support within the general matrix multiplication (gemm)
                 operation of the BLAS-like Library Instantiation
                 Software framework, whereby each matrix operand A, B,
                 and C may be stored as single- or double-precision real
                 or complex values. Another factor of complexity,
                 whereby the matrix product and accumulation are allowed
                 to take place in a precision different from the storage
                 precisions of either A or B, is also discussed. We
                 first break the problem into orthogonal dimensions,
                 considering the mixing of domains separately from
                 mixing precisions. Support for all combinations of
                 matrix operands stored in either the real or complex
                 domain is mapped out by enumerating the cases and
                 describing an implementation approach for each.
                 Supporting all combinations of storage and computation
                 precisions is handled by typecasting the matrices at
                 key stages of the computation --- during packing and/or
                 accumulation, as needed. Several optional optimizations
                 are also documented. Performance results gathered on a
                 56-core Marvell ThunderX2 and a 52-core Intel Xeon
                 Platinum demonstrate that high performance is mostly
                 preserved, with modest slowdowns incurred from
                 unavoidable typecast instructions. The mixed-datatype
                 implementation confirms that combinatorial
                 intractability is avoided, with the framework relying
                 on only two assembly microkernels to implement 128
                 datatype combinations.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Daas:2021:RKS,
  author =       "Hussam {Al Daas} and Laura Grigori and Pascal
                 H{\'e}non and Philippe Ricoux",
  title =        "Recycling {Krylov} Subspaces and Truncating Deflation
                 Subspaces for Solving Sequence of Linear Systems",
  journal =      j-TOMS,
  volume =       "47",
  number =       "2",
  pages =        "13:1--13:30",
  month =        apr,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3439746",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 27 08:23:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3439746",
  abstract =     "This article presents deflation strategies related to
                 recycling Krylov subspace methods for solving one or a
                 sequence of linear systems of equations. Besides
                 well-known strategies of deflation, Ritz-, and harmonic
                 Ritz-based deflation, we introduce a Singular Value
                 Decomposition based deflation technique. We consider
                 the recycling in two contexts: recycling the Krylov
                 subspace between the restart cycles and recycling a
                 deflation subspace when the matrix changes in a
                 sequence of linear systems. Numerical experiments on
                 real-life reservoir simulation demonstrate the impact
                 of our proposed strategy.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Flegar:2021:APB,
  author =       "Goran Flegar and Hartwig Anzt and Terry Cojean and
                 Enrique S. Quintana-Ort{\'\i}",
  title =        "Adaptive Precision Block-{Jacobi} for High Performance
                 Preconditioning in the {Ginkgo} Linear Algebra
                 Software",
  journal =      j-TOMS,
  volume =       "47",
  number =       "2",
  pages =        "14:1--14:28",
  month =        apr,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3441850",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 27 08:23:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3441850",
  abstract =     "The use of mixed precision in numerical algorithms is
                 a promising strategy for accelerating scientific
                 applications. In particular, the adoption of
                 specialized hardware and data formats for low-precision
                 arithmetic in high-end GPUs (graphics processing units)
                 has motivated numerous efforts aiming at carefully
                 reducing the working precision in order to speed up the
                 computations. For algorithms whose performance is bound
                 by the memory bandwidth, the idea of compressing its
                 data before (and after) memory accesses has received
                 considerable attention. One idea is to store an
                 approximate operator --- like a preconditioner --- in
                 lower than working precision hopefully without
                 impacting the algorithm output. We realize the first
                 high-performance implementation of an adaptive
                 precision block-Jacobi preconditioner which selects the
                 precision format used to store the preconditioner data
                 on-the-fly, taking into account the numerical
                 properties of the individual preconditioner blocks. We
                 implement the adaptive block-Jacobi preconditioner as
                 production-ready functionality in the Ginkgo linear
                 algebra library, considering not only the precision
                 formats that are part of the IEEE standard, but also
                 customized formats which optimize the length of the
                 exponent and significand to the characteristics of the
                 preconditioner blocks. Experiments run on a
                 state-of-the-art GPU accelerator show that our
                 implementation offers attractive runtime savings.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Osborn:2021:RCR,
  author =       "Sarah Osborn",
  title =        "Replicated Computational Results {(RCR)} Report for
                 {``Adaptive Precision Block-Jacobi for High Performance
                 Preconditioning in the Ginkgo Linear Algebra
                 Software''}",
  journal =      j-TOMS,
  volume =       "47",
  number =       "2",
  pages =        "15:1--15:4",
  month =        apr,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3446000",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 27 08:23:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3446000",
  abstract =     "The article by Flegar et al. titled ``Adaptive
                 Precision Block-Jacobi for High Performance
                 Preconditioning in the Ginkgo Linear Algebra Software''
                 presents a novel, practical implementation of an
                 adaptive precision block-Jacobi preconditioner.
                 Performance results using state-of-the-art GPU
                 architectures for the block-Jacobi preconditioner
                 generation and application demonstrate the practical
                 usability of the method, compared to a traditional
                 full-precision block-Jacobi preconditioner. A
                 production-ready implementation is provided in the
                 Ginkgo numerical linear algebra library.\par

                 In this report, the Ginkgo library is reinstalled and
                 performance results are generated to perform a
                 comparison to the original results when using Ginkgo's
                 Conjugate Gradient solver with either the full or the
                 adaptive precision block-Jacobi preconditioner for a
                 suite of test problems on an NVIDIA GPU accelerator.
                 After completing this process, the published results
                 are deemed reproducible.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Villa:2021:HES,
  author =       "Umberto Villa and Noemi Petra and Omar Ghattas",
  title =        "{hIPPYlib}: an Extensible Software Framework for
                 Large-Scale Inverse Problems Governed by {PDEs}: {Part
                 I}: Deterministic Inversion and Linearized {Bayesian}
                 Inference",
  journal =      j-TOMS,
  volume =       "47",
  number =       "2",
  pages =        "16:1--16:34",
  month =        apr,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3428447",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 27 08:23:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3428447",
  abstract =     "We present an extensible software framework, hIPPYlib,
                 for solution of large-scale deterministic and Bayesian
                 inverse problems governed by partial differential
                 equations (PDEs) with (possibly) infinite-dimensional
                 parameter fields (which are high-dimensional after
                 discretization). hIPPYlib overcomes the prohibitively
                 expensive nature of Bayesian inversion for this class
                 of problems by implementing state-of-the-art scalable
                 algorithms for PDE-based inverse problems that exploit
                 the structure of the underlying operators, notably the
                 Hessian of the log-posterior. The key property of the
                 algorithms implemented in hIPPYlib is that the solution
                 of the inverse problem is computed at a cost, measured
                 in linearized forward PDE solves, that is independent
                 of the parameter dimension. The mean of the posterior
                 is approximated by the MAP point, which is found by
                 minimizing the negative log-posterior with an inexact
                 matrix-free Newton-CG method. The posterior covariance
                 is approximated by the inverse of the Hessian of the
                 negative log posterior evaluated at the MAP point. The
                 construction of the posterior covariance is made
                 tractable by invoking a low-rank approximation of the
                 Hessian of the log-likelihood. Scalable tools for
                 sample generation are also discussed. hIPPYlib makes
                 all of these advanced algorithms easily accessible to
                 domain scientists and provides an environment that
                 expedites the development of new algorithms.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Theisen:2021:FTM,
  author =       "Lambert Theisen and Manuel Torrilhon",
  title =        "{fenicsR13}: a Tensorial Mixed Finite Element Solver
                 for the Linear {R13} Equations Using the {FEniCS}
                 Computing Platform",
  journal =      j-TOMS,
  volume =       "47",
  number =       "2",
  pages =        "17:1--17:29",
  month =        apr,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3442378",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 27 08:23:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3442378",
  abstract =     "We present a mixed finite element solver for the
                 linearized regularized 13-moment equations of
                 non-equilibrium gas dynamics. The Python implementation
                 builds upon the software tools provided by the FEniCS
                 computing platform. We describe a new tensorial
                 approach utilizing the extension capabilities of
                 FEniCS' Unified Form Language to define required
                 differential operators for tensors above second degree.
                 The presented solver serves as an example for
                 implementing tensorial variational formulations in
                 FEniCS, for which the documentation and literature seem
                 to be very sparse. Using the software abstraction
                 levels provided by the Unified Form Language allows an
                 almost one-to-one correspondence between the underlying
                 mathematics and the resulting source code. Test cases
                 support the correctness of the proposed method using
                 validation with exact solutions. To justify the usage
                 of extended gas flow models, we discuss typical
                 application cases involving rarefaction effects. We
                 provide the documented and validated solver publicly.",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Guthe:2021:AFS,
  author =       "Stefan Guthe and Daniel Thuerck",
  title =        "{Algorithm 1015}: a Fast Scalable Solver for the Dense
                 Linear (Sum) Assignment Problem",
  journal =      j-TOMS,
  volume =       "47",
  number =       "2",
  pages =        "18:1--18:27",
  month =        apr,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3442348",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 27 08:23:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3442348",
  abstract =     "We present a new algorithm for solving the dense
                 linear (sum) assignment problem and an efficient,
                 parallel implementation that is based on the successive
                 shortest path algorithm. More specifically, we
                 introduce the well-known epsilon scaling approach used
                 in the Auction algorithm to approximate the dual
                 variables of the successive shortest path algorithm
                 prior to solving the assignment problem to limit the
                 complexity of the path search. This improves the
                 runtime by several orders of magnitude for
                 hard-to-solve real-world problems, making the runtime
                 virtually independent of how hard the assignment is to
                 find. In addition, our approach allows for using
                 accelerators and/or external compute resources to
                 calculate individual rows of the cost matrix. This
                 enables us to solve problems that are larger than what
                 has been reported in the past, including the ability to
                 efficiently solve problems whose cost matrix exceeds
                 the available systems memory. To our knowledge, this is
                 the first implementation that is able to solve problems
                 with more than one trillion arcs in less than 100 hours
                 on a single machine.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hahne:2021:APP,
  author =       "Jens Hahne and Stephanie Friedhoff and Matthias
                 Bolten",
  title =        "{Algorithm 1016}: {PyMGRIT}: a {Python} Package for
                 the Parallel-in-time Method {MGRIT}",
  journal =      j-TOMS,
  volume =       "47",
  number =       "2",
  pages =        "19:1--19:22",
  month =        apr,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3446979",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Apr 27 08:23:28 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3446979",
  abstract =     "In this article, we introduce the Python framework
                 PyMGRIT, which implements the
                 multigrid-reduction-in-time (MGRIT) algorithm for
                 solving (non-)linear systems arising from the
                 discretization of time-dependent problems. The MGRIT
                 algorithm is a reduction-based iterative method that
                 allows parallel-in-time simulations, i.e., calculating
                 multiple time steps simultaneously in a simulation,
                 using a time-grid hierarchy. The PyMGRIT framework
                 includes many different variants of the MGRIT
                 algorithm, ranging from different multigrid cycle types
                 and relaxation schemes, various coarsening strategies,
                 including time-only and space-time coarsening, and the
                 ability to utilize different time integrators on
                 different levels in the multigrid hierarchy. The
                 comprehensive documentation with tutorials and many
                 examples and the fully documented code allow an easy
                 start into the work with the package. The functionality
                 of the code is ensured by automated serial and parallel
                 tests using continuous integration. PyMGRIT supports
                 serial runs suitable for prototyping and testing of new
                 approaches, as well as parallel runs using the Message
                 Passing Interface (MPI). In this manuscript, we
                 describe the implementation of the MGRIT algorithm in
                 PyMGRIT and present the usage from both a user and a
                 developer point of view. Three examples illustrate
                 different aspects of the package itself, especially
                 running tests with pure time parallelism, as well as
                 space-time parallelism through the coupling of PyMGRIT
                 with PETSc or Firedrake.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Eswar:2021:PPL,
  author =       "Srinivas Eswar and Koby Hayashi and Grey Ballard and
                 Ramakrishnan Kannan and Michael A. Matheson and Haesun
                 Park",
  title =        "{PLANC}: Parallel Low-rank Approximation with
                 Nonnegativity Constraints",
  journal =      j-TOMS,
  volume =       "47",
  number =       "3",
  pages =        "20:1--20:37",
  month =        jun,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3432185",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Jun 27 07:42:02 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3432185",
  abstract =     "We consider the problem of low-rank approximation of
                 massive dense nonnegative tensor data, for example, to
                 discover latent patterns in video and imaging
                 applications. As the size of data sets grows, single
                 workstations are hitting bottlenecks in both
                 computation time and available memory. We propose a
                 distributed-memory parallel computing solution to
                 handle massive data sets, loading the input data across
                 the memories of multiple nodes, and performing
                 efficient and scalable parallel algorithms to compute
                 the low-rank approximation. We present a software
                 package called Parallel Low-rank Approximation with
                 Nonnegativity Constraints, which implements our
                 solution and allows for extension in terms of data
                 (dense or sparse, matrices or tensors of any order),
                 algorithm (e.g., from multiplicative updating
                 techniques to alternating direction method of
                 multipliers), and architecture (we exploit GPUs to
                 accelerate the computation in this work). We describe
                 our parallel distributions and algorithms, which are
                 careful to avoid unnecessary communication and
                 computation, show how to extend the software to include
                 new algorithms and/or constraints, and report
                 efficiency and scalability results for both synthetic
                 and real-world data sets.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Abdelfattah:2021:SBB,
  author =       "Ahmad Abdelfattah and Timothy Costa and Jack Dongarra
                 and Mark Gates and Azzam Haidar and Sven Hammarling and
                 Nicholas J. Higham and Jakub Kurzak and Piotr Luszczek
                 and Stanimire Tomov and Mawussi Zounon",
  title =        "A Set of Batched Basic Linear Algebra Subprograms and
                 {LAPACK} Routines",
  journal =      j-TOMS,
  volume =       "47",
  number =       "3",
  pages =        "21:1--21:23",
  month =        jun,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3431921",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Jun 27 07:42:02 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3431921",
  abstract =     "This article describes a standard API for a set of
                 Batched Basic Linear Algebra Subprograms (Batched BLAS
                 or BBLAS). The focus is on many independent BLAS
                 operations on small matrices that are grouped together
                 and processed by a single routine, called a Batched
                 BLAS routine. The matrices are grouped together in
                 uniformly sized groups, with just one group if all the
                 matrices are of equal size. The aim is to provide more
                 efficient, but portable, implementations of algorithms
                 on high-performance many-core platforms. These include
                 multicore and many-core CPU processors, GPUs and
                 coprocessors, and other hardware accelerators with
                 floating-point compute facility. As well as the
                 standard types of single and double precision, we also
                 include half and quadruple precision in the standard.
                 In particular, half precision is used in many very
                 large scale applications, such as those associated with
                 machine learning.",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Barthels:2021:LAG,
  author =       "Henrik Barthels and Christos Psarras and Paolo
                 Bientinesi",
  title =        "{Linnea}: Automatic Generation of Efficient Linear
                 Algebra Programs",
  journal =      j-TOMS,
  volume =       "47",
  number =       "3",
  pages =        "22:1--22:26",
  month =        jun,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3446632",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Jun 27 07:42:02 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3446632",
  abstract =     "The translation of linear algebra computations into
                 efficient sequences of library calls is a non-trivial
                 task that requires expertise in both linear algebra and
                 high-performance computing. Almost all high-level
                 languages and libraries for matrix computations (e.g.,
                 Matlab, Eigen) internally use optimized kernels such as
                 those provided by BLAS and LAPACK; however, their
                 translation algorithms are often too simplistic and
                 thus lead to a suboptimal use of said kernels,
                 resulting in significant performance losses. To combine
                 the productivity offered by high-level languages, and
                 the performance of low-level kernels, we are developing
                 Linnea, a code generator for linear algebra problems.
                 As input, Linnea takes a high-level description of a
                 linear algebra problem; as output, it returns an
                 efficient sequence of calls to high-performance
                 kernels. Linnea uses a custom best-first search
                 algorithm to find a first solution in less than a
                 second, and increasingly better solutions when given
                 more time. In 125 test problems, the code generated by
                 Linnea almost always outperforms Matlab, Julia, Eigen,
                 and Armadillo, with speedups up to and exceeding $ 10
                 \times $.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Campos:2021:NMP,
  author =       "Carmen Campos and Jose E. Roman",
  title =        "{NEP}: a Module for the Parallel Solution of Nonlinear
                 Eigenvalue Problems in {SLEPc}",
  journal =      j-TOMS,
  volume =       "47",
  number =       "3",
  pages =        "23:1--23:29",
  month =        jun,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3447544",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Jun 27 07:42:02 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3447544",
  abstract =     "SLEPc is a parallel library for the solution of
                 various types of large-scale eigenvalue problems. Over
                 the past few years, we have been developing a module
                 within SLEPc, called NEP, that is intended for solving
                 nonlinear eigenvalue problems. These problems can be
                 defined by means of a matrix-valued function that
                 depends nonlinearly on a single scalar parameter. We do
                 not consider the particular case of polynomial
                 eigenvalue problems (which are implemented in a
                 different module in SLEPc) and focus here on rational
                 eigenvalue problems and other general nonlinear
                 eigenproblems involving square roots or any other
                 nonlinear function. The article discusses how the NEP
                 module has been designed to fit the needs of
                 applications and provides a description of the
                 available solvers, including some implementation
                 details such as parallelization. Several test problems
                 coming from real applications are used to evaluate the
                 performance and reliability of the solvers.",
  acknowledgement = ack-nhfb,
  articleno =    "23",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pruua:2021:FMP,
  author =       "Zdenek Pruua and Nicki Holighaus and Peter Balazs",
  title =        "Fast Matching Pursuit with Multi-{Gabor}
                 Dictionaries",
  journal =      j-TOMS,
  volume =       "47",
  number =       "3",
  pages =        "24:1--24:20",
  month =        jun,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3447958",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Jun 27 07:42:02 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3447958",
  abstract =     "Finding the best K-sparse approximation of a signal in
                 a redundant dictionary is an NP-hard problem.
                 Suboptimal greedy matching pursuit algorithms are
                 generally used for this task. In this work, we present
                 an acceleration technique and an implementation of the
                 matching pursuit algorithm acting on a multi-Gabor
                 dictionary, i.e., a concatenation of several Gabor-type
                 time-frequency dictionaries, each of which consists of
                 translations and modulations of a possibly different
                 window and time and frequency shift parameters. The
                 technique is based on pre-computing and thresholding
                 inner products between atoms and on updating the
                 residual directly in the coefficient domain, i.e.,
                 without the round-trip to the signal domain. Since the
                 proposed acceleration technique involves an approximate
                 update step, we provide theoretical and experimental
                 results illustrating the convergence of the resulting
                 algorithm. The implementation is written in C
                 (compatible with C99 and C++11), and we also provide
                 Matlab and GNU Octave interfaces. For some settings,
                 the implementation is up to 70 times faster than the
                 standard Matching Pursuit Toolkit.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Farrell:2021:PST,
  author =       "Patrick E. Farrell and Matthew G. Knepley and Lawrence
                 Mitchell and Florian Wechsung",
  title =        "{PCPATCH}: Software for the Topological Construction
                 of Multigrid Relaxation Methods",
  journal =      j-TOMS,
  volume =       "47",
  number =       "3",
  pages =        "25:1--25:22",
  month =        jun,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3445791",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Jun 27 07:42:02 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3445791",
  abstract =     "Effective relaxation methods are necessary for good
                 multigrid convergence. For many equations, standard
                 Jacobi and Gau{\ss}--Seidel are inadequate, and more
                 sophisticated space decompositions are required;
                 examples include problems with semidefinite terms or
                 saddle point structure. In this article, we present a
                 unifying software abstraction, PCPATCH, for the
                 topological construction of space decompositions for
                 multigrid relaxation methods. Space decompositions are
                 specified by collecting topological entities in a mesh
                 (such as all vertices or faces) and applying a
                 construction rule (such as taking all degrees of
                 freedom in the cells around each entity). The software
                 is implemented in PETSc and facilitates the elegant
                 expression of a wide range of schemes merely by varying
                 solver options at runtime. In turn, this allows for the
                 very rapid development of fast solvers for difficult
                 problems.",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lyu:2021:FFA,
  author =       "Xing-long Lyu and Tiexiang Li and Tsung-ming Huang and
                 Jia-wei Lin and Wen-wei Lin and Sheng Wang",
  title =        "{FAME}: Fast Algorithms for {Maxwell}'s Equations for
                 Three-dimensional Photonic Crystals",
  journal =      j-TOMS,
  volume =       "47",
  number =       "3",
  pages =        "26:1--26:24",
  month =        jun,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3446329",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Jun 27 07:42:02 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3446329",
  abstract =     "In this article, we propose the Fast Algorithms for
                 Maxwell's Equations (FAME) package for solving
                 Maxwell's equations for modeling three-dimensional
                 photonic crystals. FAME combines the null-space free
                 method with fast Fourier transform (FFT)-based
                 matrix-vector multiplications to solve the generalized
                 eigenvalue problems (GEPs) arising from Yee's
                 discretization. The GEPs are transformed into a
                 null-space free standard eigenvalue problem with a
                 Hermitian positive-definite coefficient matrix. The
                 computation times for FFT-based matrix-vector
                 multiplications with matrices of dimension 7 million
                 are only $ 0.33 $ and $ 3.6 \times 10^{-3} $ seconds
                 using MATLAB with an Intel Xeon CPU and CUDA C++
                 programming with a single NVIDIA Tesla P100 GPU,
                 respectively. Such multiplications significantly reduce
                 the computational costs of the conjugate gradient
                 method for solving linear systems. We successfully use
                 FAME on a single P100 GPU to solve a set of GEPs with
                 matrices of dimension more than 19 million, in 127 to
                 191 seconds per problem. These results demonstrate the
                 potential of our proposed package to enable large-scale
                 numerical simulations for novel physical discoveries
                 and engineering applications of photonic crystals.",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lakhmiri:2021:HHO,
  author =       "Dounia Lakhmiri and S{\'e}bastien {Le Digabel} and
                 Christophe Tribes",
  title =        "{HyperNOMAD}: Hyperparameter Optimization of Deep
                 Neural Networks Using Mesh Adaptive Direct Search",
  journal =      j-TOMS,
  volume =       "47",
  number =       "3",
  pages =        "27:1--27:27",
  month =        jun,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3450975",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Jun 27 07:42:02 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3450975",
  abstract =     "The performance of deep neural networks is highly
                 sensitive to the choice of the hyperparameters that
                 define the structure of the network and the learning
                 process. When facing a new application, tuning a deep
                 neural network is a tedious and time-consuming process
                 that is often described as a ``dark art.'' This
                 explains the necessity of automating the calibration of
                 these hyperparameters. Derivative-free optimization is
                 a field that develops methods designed to optimize
                 time-consuming functions without relying on
                 derivatives. This work introduces the HyperNOMAD
                 package, an extension of the NOMAD software that
                 applies the MADS algorithm [7] to simultaneously tune
                 the hyperparameters responsible for both the
                 architecture and the learning process of a deep neural
                 network (DNN). This generic approach allows for an
                 important flexibility in the exploration of the search
                 space by taking advantage of categorical variables.
                 HyperNOMAD is tested on the MNIST, Fashion-MNIST, and
                 CIFAR-10 datasets and achieves results comparable to
                 the current state of the art.",
  acknowledgement = ack-nhfb,
  articleno =    "27",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Slak:2021:MCL,
  author =       "Jure Slak and Gregor Kosec",
  title =        "{Medusa}: a {C++} Library for Solving {PDEs} Using
                 Strong Form Mesh-free Methods",
  journal =      j-TOMS,
  volume =       "47",
  number =       "3",
  pages =        "28:1--28:25",
  month =        jun,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3450966",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Jun 27 07:42:02 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3450966",
  abstract =     "Medusa, a novel library for implementation of
                 non-particle strong form mesh-free methods, such as
                 GFDM or RBF-FD, is described. We identify and present
                 common parts and patterns among many such methods
                 reported in the literature, such as node positioning,
                 stencil selection, and stencil weight computation. Many
                 different algorithms exist for each part and the
                 possible combinations offer a plethora of possibilities
                 for improvements of solution procedures that are far
                 from fully understood. As a consequence there are still
                 many unanswered questions in the mesh-free community
                 resulting in vivid ongoing research in the field.
                 Medusa implements the core mesh-free elements as
                 independent blocks, which offers users great
                 flexibility in experimenting with the method they are
                 developing, as well as easily comparing it with other
                 existing methods. The article describes the chosen
                 abstractions and their usage, illustrates aspects of
                 the philosophy and design, offers some executions time
                 benchmarks and demonstrates the application of the
                 library on cases from linear elasticity and fluid flow
                 in irregular 2D and 3D domains.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Skrabanek:2021:AFR,
  author =       "Pavel Skrab{\'a}nek and Nat{\'a}lia
                 Mart{\'\i}nkov{\'a}",
  title =        "{Algorithm 1017}: \pkg{fuzzyreg}: an {R} Package for
                 Fitting Fuzzy Regression Models",
  journal =      j-TOMS,
  volume =       "47",
  number =       "3",
  pages =        "29:1--29:18",
  month =        jun,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3451389",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sun Jun 27 07:42:02 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/s-plus.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3451389",
  abstract =     "Fuzzy regression provides an alternative to
                 statistical regression when the model is indefinite,
                 the relationships between model parameters are vague,
                 the sample size is low, or the data are hierarchically
                 structured. Such cases allow to consider the choice of
                 a regression model based on the fuzzy set theory. In
                 fuzzyreg, we implement fuzzy linear regression methods
                 that differ in the expectations of observational data
                 types, outlier handling, and parameter estimation
                 method. We provide a wrapper function that prepares
                 data for fitting fuzzy linear models with the
                 respective methods from a syntax established in R for
                 fitting regression models. The function fuzzylm thus
                 provides a novel functionality for R through
                 standardized operations with fuzzy numbers. Additional
                 functions allow for conversion of real-value variables
                 to be fuzzy numbers, printing, summarizing, model
                 plotting, and calculation of model predictions from new
                 data using supporting functions that perform arithmetic
                 operations with triangular fuzzy numbers. Goodness of
                 fit and total error of the fit measures allow model
                 comparisons. The package contains a dataset named bats
                 with measurements of temperatures of hibernating bats
                 and the mean annual surface temperature reflecting the
                 climate at the sampling sites. The predictions from
                 fuzzy linear models fitted to this dataset correspond
                 well to the observed biological phenomenon. Fuzzy
                 linear regression has great potential in predictive
                 modeling where the data structure prevents statistical
                 analysis and the modeled process exhibits inherent
                 fuzziness.",
  acknowledgement = ack-nhfb,
  articleno =    "29",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Farrell:2021:IAR,
  author =       "Patrick E. Farrell and Robert C. Kirby and Jorge
                 Marchena-Men{\'e}ndez",
  title =        "Irksome: Automating {Runge--Kutta} Time-stepping for
                 Finite Element Methods",
  journal =      j-TOMS,
  volume =       "47",
  number =       "4",
  pages =        "30:1--30:26",
  month =        dec,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3466168",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 29 06:58:41 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3466168",
  abstract =     "While implicit Runge--Kutta (RK) methods possess high
                 order accuracy and important stability properties,
                 implementation difficulties and the high expense of
                 solving the coupled algebraic system at each time step
                 are frequently cited as impediments. We present
                 Irksome, a high-level library for manipulating UFL
                 (Unified Form Language) expressions of semidiscrete
                 variational forms to obtain UFL expressions for the
                 coupled Runge--Kutta stage equations at each time step.
                 Irksome works with the Firedrake package to enable the
                 efficient solution of the resulting coupled algebraic
                 systems. Numerical examples confirm the efficacy of the
                 software and our solver techniques for various
                 problems.",
  acknowledgement = ack-nhfb,
  articleno =    "30",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Daversin-Catty:2021:AAA,
  author =       "C{\'e}cile Daversin-Catty and Chris N. Richardson and
                 Ada J. Ellingsrud and Marie E. Rognes",
  title =        "Abstractions and Automated Algorithms for Mixed Domain
                 Finite Element Methods",
  journal =      j-TOMS,
  volume =       "47",
  number =       "4",
  pages =        "31:1--31:36",
  month =        dec,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3471138",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 29 06:58:41 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3471138",
  abstract =     "Mixed dimensional partial differential equations
                 (PDEs) are equations coupling unknown fields defined
                 over domains of differing topological dimension. Such
                 equations naturally arise in a wide range of scientific
                 fields including geology, physiology, biology, and
                 fracture mechanics. Mixed dimensional PDEs are also
                 commonly encountered when imposing non-standard
                 conditions over a subspace of lower dimension, e.g.,
                 through a Lagrange multiplier. In this article, we
                 present general abstractions and algorithms for finite
                 element discretizations of mixed domain and mixed
                 dimensional PDEs of codimension up to one (i.e., nD-mD
                 with $ |n - m| \leq 1$). We introduce high-level
                 mathematical software abstractions together with
                 lower-level algorithms for expressing and efficiently
                 solving such coupled systems. The concepts introduced
                 here have also been implemented in the context of the
                 FEniCS finite element software. We illustrate the new
                 features through a range of examples, including a
                 constrained Poisson problem, a set of Stokes-type flow
                 models, and a model for ionic electrodiffusion.",
  acknowledgement = ack-nhfb,
  articleno =    "31",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Heltai:2021:PGI,
  author =       "Luca Heltai and Wolfgang Bangerth and Martin
                 Kronbichler and Andrea Mola",
  title =        "Propagating Geometry Information to Finite Element
                 Computations",
  journal =      j-TOMS,
  volume =       "47",
  number =       "4",
  pages =        "32:1--32:30",
  month =        dec,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3468428",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 29 06:58:41 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3468428",
  abstract =     "The traditional workflow in continuum mechanics
                 simulations is that a geometry description --- for
                 example obtained using Constructive Solid Geometry
                 (CSG) or Computer Aided Design (CAD) tools --- forms
                 the input for a mesh generator. The mesh is then used
                 as the sole input for the finite element, finite
                 volume, and finite difference solver, which at this
                 point no longer has access to the original,
                 ``underlying'' geometry. However, many modern
                 techniques --- for example, adaptive mesh refinement
                 and the use of higher order geometry approximation
                 methods --- really do need information about the
                 underlying geometry to realize their full potential. We
                 have undertaken an exhaustive study of where typical
                 finite element codes use geometry information, with the
                 goal of determining what information geometry tools
                 would have to provide. Our study shows that nearly all
                 geometry-related needs inside the simulators can be
                 satisfied by just two ``primitives'': elementary
                 queries posed by the simulation software to the
                 geometry description. We then show that it is possible
                 to provide these primitives in all of the frequently
                 used ways in which geometries are described in common
                 industrial workflows, and illustrate our solutions
                 using a number of examples.",
  acknowledgement = ack-nhfb,
  articleno =    "32",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Munch:2021:HDE,
  author =       "Peter Munch and Katharina Kormann and Martin
                 Kronbichler",
  title =        "\pkg{hyper.deal}: an Efficient, Matrix-free
                 Finite-element Library for High-dimensional Partial
                 Differential Equations",
  journal =      j-TOMS,
  volume =       "47",
  number =       "4",
  pages =        "33:1--33:34",
  month =        dec,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3469720",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 29 06:58:41 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3469720",
  abstract =     "This work presents the efficient, matrix-free
                 finite-element library hyper.deal for solving partial
                 differential equations in two up to six dimensions with
                 high-order discontinuous Galerkin methods. It builds
                 upon the low-dimensional finite-element library deal.II
                 to create complex low-dimensional meshes and to operate
                 on them individually. These meshes are combined via a
                 tensor product on the fly, and the library provides new
                 special-purpose highly optimized matrix-free functions
                 exploiting domain decomposition as well as shared
                 memory via MPI-3.0 features. Both node-level
                 performance analyses and strong/weak-scaling studies on
                 up to 147,456 CPU cores confirm the efficiency of the
                 implementation. Results obtained with the library
                 hyper.deal are reported for high-dimensional advection
                 problems and for the solution of the Vlasov--Poisson
                 equation in up to six-dimensional phase space.",
  acknowledgement = ack-nhfb,
  articleno =    "33",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ramachandran:2021:PPB,
  author =       "Prabhu Ramachandran and Aditya Bhosale and Kunal Puri
                 and Pawan Negi and Abhinav Muta and A. Dinesh and
                 Dileep Menon and Rahul Govind and Suraj Sanka and Amal
                 S. Sebastian and Ananyo Sen and Rohan Kaushik and
                 Anshuman Kumar and Vikas Kurapati and Mrinalgouda Patil
                 and Deep Tavker and Pankaj Pandey and Chandrashekhar
                 Kaushik and Arkopal Dutt and Arpit Agarwal",
  title =        "{PySPH}: a {Python}-based Framework for Smoothed
                 Particle Hydrodynamics",
  journal =      j-TOMS,
  volume =       "47",
  number =       "4",
  pages =        "34:1--34:38",
  month =        dec,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3460773",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 29 06:58:41 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3460773",
  abstract =     "PySPH is an open-source, Python-based, framework for
                 particle methods in general and Smoothed Particle
                 Hydrodynamics (SPH) in particular. PySPH allows a user
                 to define a complete SPH simulation using pure Python.
                 High-performance code is generated from this high-level
                 Python code and executed on either multiple cores, or
                 on GPUs, seamlessly. It also supports distributed
                 execution using MPI. PySPH supports a wide variety of
                 SPH schemes and formulations. These include,
                 incompressible and compressible fluid flow, elastic
                 dynamics, rigid body dynamics, shallow water equations,
                 and other problems. PySPH supports a variety of
                 boundary conditions including mirror, periodic, solid
                 wall, and inlet/outlet boundary conditions. The package
                 is written to facilitate reuse and reproducibility.
                 This article discusses the overall design of PySPH and
                 demonstrates many of its features. Several example
                 results are shown to demonstrate the range of features
                 that PySPH provides.",
  acknowledgement = ack-nhfb,
  articleno =    "34",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Peres:2021:ECT,
  author =       "Noah Peres and Andrew Ray Lee and Uri Keich",
  title =        "Exactly Computing the Tail of the {Poisson}-Binomial
                 Distribution",
  journal =      j-TOMS,
  volume =       "47",
  number =       "4",
  pages =        "35:1--35:19",
  month =        dec,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3460774",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 29 06:58:41 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3460774",
  abstract =     "We present ShiftConvolvePoibin, a fast exact method to
                 compute the tail of a Poisson-binomial distribution
                 (PBD). Our method employs an exponential shift to
                 retain its accuracy when computing a tail probability,
                 and in practice we find that it is immune to the
                 significant relative errors that other methods, exact
                 or approximate, can suffer from when computing very
                 small tail probabilities of the PBD. The accompanying R
                 package is also competitive with the fastest
                 implementations for computing the entire PBD.",
  acknowledgement = ack-nhfb,
  articleno =    "35",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Blackman:2021:SLP,
  author =       "David Blackman and Sebastiano Vigna",
  title =        "Scrambled Linear Pseudorandom Number Generators",
  journal =      j-TOMS,
  volume =       "47",
  number =       "4",
  pages =        "36:1--36:32",
  month =        dec,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3460772",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 29 06:58:41 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3460772",
  abstract =     "$F_2$-linear pseudorandom number generators are very
                 popular due to their high speed, to the ease with which
                 generators with a sizable state space can be created,
                 and to their provable theoretical properties. However,
                 they suffer from linear artifacts that show as failures
                 in linearity-related statistical tests such as the
                 binary-rank and the linear-complexity test. In this
                 article, we give two new contributions. First, we
                 introduce two new $F_2$-linear transformations that
                 have been handcrafted to have good statistical
                 properties and at the same time to be programmable very
                 efficiently on superscalar processors, or even directly
                 in hardware. Then, we describe some scramblers, that
                 is, nonlinear functions applied to the state array that
                 reduce or delete the linear artifacts, and propose
                 combinations of linear transformations and scramblers
                 that give extremely fast pseudorandom number generators
                 of high quality. A novelty in our approach is that we
                 use ideas from the theory of filtered linear-feedback
                 shift registers to prove some properties of our
                 scramblers, rather than relying purely on heuristics.
                 In the end, we provide simple, extremely fast
                 generators that use a few hundred bits of memory, have
                 provable properties, and pass strong statistical
                 tests.",
  acknowledgement = ack-nhfb,
  articleno =    "36",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Snyder:2021:CRA,
  author =       "W. Van Snyder",
  title =        "Corrigendum: {Remark on Algorithm 723: Fresnel
                 Integrals}",
  journal =      j-TOMS,
  volume =       "47",
  number =       "4",
  pages =        "37:1--37:1",
  month =        dec,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3452336",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 29 06:58:41 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Snyder:1993:AFI}.",
  URL =          "https://dl.acm.org/doi/10.1145/3452336",
  abstract =     "There are mistakes and typographical errors in Remark
                 on Algorithm 723: Fresnel Integrals, which appeared in
                 ACM Transactions on Mathematical Software 22, 4
                 (December 1996). This remark corrects those errors. The
                 software provided to Collected Algorithms of the ACM
                 was correct.",
  acknowledgement = ack-nhfb,
  articleno =    "37",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Roth:2021:RAO,
  author =       "{\'A}goston R{\'o}th",
  title =        "Remark on {Algorithm 992}: an {OpenGL}- and
                 {C++}-based Function Library for Curve and Surface
                 Modeling in a Large Class of Extended {Chebyshev}
                 Spaces",
  journal =      j-TOMS,
  volume =       "47",
  number =       "4",
  pages =        "38:1--38:2",
  month =        dec,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3461643",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 29 06:58:41 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Roth:2019:AOC}.",
  URL =          "https://dl.acm.org/doi/10.1145/3461643",
  abstract =     "We provide a number of corrections to the software
                 component that accompanied this Algorithm submission
                 [3]. An updated version of the code is available from
                 the ACM Collected Algorithms site [1].",
  acknowledgement = ack-nhfb,
  articleno =    "38",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gia:2021:AFF,
  author =       "Quoc T. Le Gia and Ming Li and Yu Guang Wang",
  title =        "{Algorithm 1018}: \pkg{FaVeST} --- Fast Vector
                 Spherical Harmonic Transforms",
  journal =      j-TOMS,
  volume =       "47",
  number =       "4",
  pages =        "39:1--39:24",
  month =        dec,
  year =         "2021",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3458470",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Sep 29 06:58:41 MDT 2021",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3458470",
  abstract =     "Vector spherical harmonics on the unit sphere of $
                 \mathbb {R}^3 $ have broad applications in geophysics,
                 quantum mechanics, and astrophysics. In the
                 representation of a tangent vector field, one needs to
                 evaluate the expansion and the Fourier coefficients of
                 vector spherical harmonics. In this article, we develop
                 fast algorithms (FaVeST) for vector spherical harmonic
                 transforms on these evaluations. The forward FaVeST
                 evaluates the Fourier coefficients and has a
                 computational cost proportional to $ N \log \sqrt {N} $
                 for $N$ number of evaluation points. The adjoint
                 FaVeST, which evaluates a linear combination of vector
                 spherical harmonics with a degree up to $ \dot M$ for
                 $M$ evaluation points, has cost proportional to $ M
                 \log \sqrt {M}$. Numerical examples of simulated
                 tangent fields illustrate the accuracy, efficiency, and
                 stability of FaVeST.",
  acknowledgement = ack-nhfb,
  articleno =    "39",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Yang:2022:GHP,
  author =       "Carl Yang and Aydin Bulu{\c{c}} and John D. Owens",
  title =        "\pkg{GraphBLAST}: a High-Performance Linear
                 Algebra-based Graph Framework on the {GPU}",
  journal =      j-TOMS,
  volume =       "48",
  number =       "1",
  pages =        "1:1--1:51",
  month =        mar,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3466795",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 17 08:00:57 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3466795",
  abstract =     "High-performance implementations of graph algorithms
                 are challenging to implement on new parallel hardware
                 such as GPUs because of three challenges: (1) the
                 difficulty of coming up with graph building blocks, (2)
                 load imbalance on parallel hardware, and (3) graph
                 problems having low arithmetic intensity. To address
                 some of these challenges, GraphBLAS is an innovative,
                 on-going effort by the graph analytics community to
                 propose building blocks based on sparse linear algebra,
                 which allow graph algorithms to be expressed in a
                 performant, succinct, composable, and portable manner.
                 In this paper, we examine the performance challenges of
                 a linear-algebra-based approach to building graph
                 frameworks and describe new design principles for
                 overcoming these bottlenecks. Among the new design
                 principles is exploiting input sparsity, which allows
                 users to write graph algorithms without specifying push
                 and pull direction. Exploiting output sparsity allows
                 users to tell the backend which values of the output in
                 a single vectorized computation they do not want
                 computed. Load-balancing is an important feature for
                 balancing work amongst parallel workers. We describe
                 the important load-balancing features for handling
                 graphs with different characteristics. The design
                 principles described in this paper have been
                 implemented in ``GraphBLAST'', the first
                 high-performance linear algebra-based graph framework
                 on NVIDIA GPUs that is open-source. The results show
                 that on a single GPU, GraphBLAST has on average at
                 least an order of magnitude speedup over previous
                 GraphBLAS implementations SuiteSparse and GBTL,
                 comparable performance to the fastest GPU hardwired
                 primitives and shared-memory graph frameworks Ligra and
                 Gunrock, and better performance than any other GPU
                 graph framework, while offering a simpler and more
                 concise programming model.",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Anzt:2022:GML,
  author =       "Hartwig Anzt and Terry Cojean and Goran Flegar and
                 Fritz G{\"o}bel and Thomas Gr{\"u}tzmacher and Pratik
                 Nayak and Tobias Ribizel and Yuhsiang Mike Tsai and
                 Enrique S. Quintana-Ort{\'\i}",
  title =        "\pkg{Ginkgo}: a Modern Linear Operator Algebra
                 Framework for High Performance Computing",
  journal =      j-TOMS,
  volume =       "48",
  number =       "1",
  pages =        "2:1--2:33",
  month =        mar,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3480935",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 17 08:00:57 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3480935",
  abstract =     "In this article, we present Ginkgo, a modern C++ math
                 library for scientific high performance computing.
                 While classical linear algebra libraries act on matrix
                 and vector objects, Ginkgo's design principle abstracts
                 all functionality as ``linear operators,'' motivating
                 the notation of a ``linear operator algebra library.''
                 Ginkgo's current focus is oriented toward providing
                 sparse linear algebra functionality for high
                 performance graphics processing unit (GPU)
                 architectures, but given the library design, this focus
                 can be easily extended to accommodate other algorithms
                 and hardware architectures. We introduce this
                 sophisticated software architecture that separates core
                 algorithms from architecture-specific backends and
                 provide details on extensibility and sustainability
                 measures. We also demonstrate Ginkgo's usability by
                 providing examples on how to use its functionality
                 inside the MFEM and deal.ii finite element ecosystems.
                 Finally, we offer a practical demonstration of Ginkgo's
                 high performance on state-of-the-art GPU
                 architectures.",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Balos:2022:RCR,
  author =       "Cody J. Balos",
  title =        "Reproduced Computational Results Report for
                 {``\pkg{Ginkgo}: a Modern Linear Operator Algebra
                 Framework for High Performance Computing''}",
  journal =      j-TOMS,
  volume =       "48",
  number =       "1",
  pages =        "3:1--3:7",
  month =        mar,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3480936",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 17 08:00:57 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3480936",
  abstract =     "The article titled ``Ginkgo: A Modern Linear Operator
                 Algebra Framework for High Performance Computing'' by
                 Anzt et al. presents a modern, linear operator centric,
                 C++ library for sparse linear algebra. Experimental
                 results in the article demonstrate that Ginkgo is a
                 flexible and user-friendly framework capable of
                 achieving high-performance on state-of-the-art GPU
                 architectures.In this report, the Ginkgo library is
                 installed and a subset of the experimental results are
                 reproduced. Specifically, the experiment that shows the
                 achieved memory bandwidth of the Ginkgo Krylov linear
                 solvers on NVIDIA A100 and AMD MI100 GPUs is redone and
                 the results are compared to what presented in the
                 published article. Upon completion of the comparison,
                 the published results are deemed reproducible.",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Drmac:2022:ACS,
  author =       "Zlatko Drmac and Ivana Sain Glibi{\'c}",
  title =        "An Algorithm for the Complete Solution of the Quartic
                 Eigenvalue Problem",
  journal =      j-TOMS,
  volume =       "48",
  number =       "1",
  pages =        "4:1--4:34",
  month =        mar,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3494528",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 17 08:00:57 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3494528",
  abstract =     "The quartic eigenvalue problem $ (\lambda^4 A +
                 \lambda^3 B + \lambda^2 C + \lambda^D + E) x = 0 $
                 naturally arises in a plethora of applications, such as
                 when solving the Orr Sommerfeld equation in the
                 stability analysis of the Poiseuille flow, in
                 theoretical analysis and experimental design of locally
                 resonant phononic plates, modeling a robot with
                 electric motors in the joints, calibration of
                 catadioptric vision system, or, for example,
                 computation of the guided and leaky modes of a planar
                 waveguide. This article proposes a new numerical method
                 for the full solution (all eigenvalues and all left and
                 right eigenvectors) that, starting with a suitable
                 linearization, uses an initial, structure-preserving
                 reduction designed to reveal and deflate a certain
                 number of zero and infinite eigenvalues before the
                 final linearization is forwarded to the QZ algorithm.
                 The backward error in the reduction phase is bounded
                 column wise in each coefficient matrix, which is
                 advantageous if the coefficient matrices are graded.
                 Numerical examples show that the proposed algorithm is
                 capable of computing the eigenpairs with small
                 residuals, and that it is competitive with the
                 available state-of-the-art methods.",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Scott:2022:CSU,
  author =       "Jennifer Scott and Miroslav Tuma",
  title =        "A Computational Study of Using Black-box {$ Q R $}
                 Solvers for Large-scale Sparse-dense Linear Least
                 Squares Problems",
  journal =      j-TOMS,
  volume =       "48",
  number =       "1",
  pages =        "5:1--5:24",
  month =        mar,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3494527",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 17 08:00:57 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3494527",
  abstract =     "Large-scale overdetermined linear least squares
                 problems arise in many practical applications. One
                 popular solution method is based on the backward stable
                 QR factorization of the system matrix A. This article
                 focuses on sparse-dense least squares problems in which
                 A is sparse except from a small number of rows that are
                 considered dense. For large-scale problems, the direct
                 application of a QR solver either fails because of
                 insufficient memory or is unacceptably slow. We study
                 several solution approaches based on using a sparse QR
                 solver without modification, focussing on the case that
                 the sparse part of A is rank deficient. We discuss
                 partial matrix stretching and regularization and
                 propose extending the augmented system formulation with
                 iterative refinement for sparse problems to
                 sparse-dense problems, optionally incorporating
                 multi-precision arithmetic. In summary, our
                 computational study shows that, before applying a
                 black-box QR factorization, a check should be made for
                 rows that are classified as dense and, if such rows are
                 identified, then A should be split into sparse and
                 dense blocks; a number of ways to use a black-box QR
                 factorization to exploit this splitting are possible,
                 with no single method found to be the best in all
                 cases.",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Porcelli:2022:EPS,
  author =       "Margherita Porcelli and Philippe L. Toint",
  title =        "Exploiting Problem Structure in Derivative Free
                 Optimization",
  journal =      j-TOMS,
  volume =       "48",
  number =       "1",
  pages =        "6:1--6:25",
  month =        mar,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3474054",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 17 08:00:57 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3474054",
  abstract =     "A structured version of derivative-free random pattern
                 search optimization algorithms is introduced, which is
                 able to exploit coordinate partially separable
                 structure (typically associated with sparsity) often
                 present in unconstrained and bound-constrained
                 optimization problems. This technique improves
                 performance by orders of magnitude and makes it
                 possible to solve large problems that otherwise are
                 totally intractable by other derivative-free methods. A
                 library of interpolation-based modelling tools is also
                 described, which can be associated with the structured
                 or unstructured versions of the initial pattern search
                 algorithm. The use of the library further enhances
                 performance, especially when associated with structure.
                 The significant gains in performance associated with
                 these two techniques are illustrated using a new
                 freely-available release of the Brute Force Optimizer
                 (BFO) package firstly introduced in [Porcelli and Toint
                 2017], which incorporates them. An interesting
                 conclusion of the numerical results presented is that
                 providing global structural information on a problem
                 can result in significantly less evaluations of the
                 objective function than attempting to building local
                 Taylor-like models.",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Huckelheim:2022:SSA,
  author =       "Jan H{\"u}ckelheim and Laurent Hasco{\"e}t",
  title =        "Source-to-Source Automatic Differentiation of {OpenMP}
                 Parallel Loops",
  journal =      j-TOMS,
  volume =       "48",
  number =       "1",
  pages =        "7:1--7:32",
  month =        mar,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3472796",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 17 08:00:57 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3472796",
  abstract =     "differentiation of OpenMP parallel worksharing loops
                 in forward and reverse mode. Automatic differentiation
                 is a method to obtain gradients of numerical programs,
                 which are crucial in optimization, uncertainty
                 quantification, and machine learning. The computational
                 cost to compute gradients is a common bottleneck in
                 practice. For applications that are parallelized for
                 multicore CPUs or GPUs using OpenMP, one also wishes to
                 compute the gradients in parallel. We propose a
                 framework to reason about the correctness of the
                 generated derivative code, from which we justify our
                 OpenMP extension to the differentiation model. We
                 implement this model in the automatic differentiation
                 tool Tapenade and present test cases that are
                 differentiated following our extended differentiation
                 procedure. Performance of the generated derivative
                 programs in forward and reverse mode is better than
                 sequential, although our reverse mode often scales
                 worse than the input programs.",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Crum:2022:BTS,
  author =       "Justin Crum and Cyrus Cheng and David A. Ham and
                 Lawrence Mitchell and Robert C. Kirby and Joshua A.
                 Levine and Andrew Gillette",
  title =        "Bringing Trimmed Serendipity Methods to Computational
                 Practice in \pkg{Firedrake}",
  journal =      j-TOMS,
  volume =       "48",
  number =       "1",
  pages =        "8:1--8:19",
  month =        mar,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3490485",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 17 08:00:57 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3490485",
  abstract =     "We present an implementation of the trimmed
                 serendipity finite element family, using the
                 open-source finite element package Firedrake. The new
                 elements can be used seamlessly within the software
                 suite for problems requiring H1, H(curl), or
                 H(div)-conforming elements on meshes of squares or
                 cubes. To test how well trimmed serendipity elements
                 perform in comparison to traditional tensor product
                 elements, we perform a sequence of numerical
                 experiments including the primal Poisson, mixed
                 Poisson, and Maxwell cavity eigenvalue problems.
                 Overall, we find that the trimmed serendipity elements
                 converge, as expected, at the same rate as the
                 respective tensor product elements, while being able to
                 offer significant savings in the time or memory
                 required to solve certain problems.",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Muller:2022:FDW,
  author =       "Jean-Michel Muller and Laurence Rideau",
  title =        "Formalization of Double-Word Arithmetic, and Comments
                 on {``Tight and Rigorous Error Bounds for Basic
                 Building Blocks of Double-Word Arithmetic''}",
  journal =      j-TOMS,
  volume =       "48",
  number =       "1",
  pages =        "9:1--9:24",
  month =        mar,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3484514",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 17 08:00:57 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3484514",
  abstract =     "Recently, a complete set of algorithms for
                 manipulating double-word numbers (some classical, some
                 new) was analyzed [16]. We have formally proven all the
                 theorems given in that article, using the Coq proof
                 assistant. The formal proof work led us to: (i) locate
                 mistakes in some of the original paper proofs (mistakes
                 that, however, do not hinder the validity of the
                 algorithms), (ii) significantly improve some error
                 bounds, and (iii) generalize some results by showing
                 that they are still valid if we slightly change the
                 rounding mode. The consequence is that the algorithms
                 presented in [16] can be used with high confidence, and
                 that some of them are even more accurate than what was
                 believed before. This illustrates what formal proof can
                 bring to computer arithmetic: beyond mere (yet
                 extremely useful) verification, correction, and
                 consolidation of already known results, it can help to
                 find new properties. All our formal proofs are freely
                 available.",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Snyder:2022:RAE,
  author =       "W. Van Snyder",
  title =        "Remark on {Algorithm 982: Explicit Solutions of
                 Triangular Systems of First-order Linear Initial-value
                 Ordinary Differential Equations with Constant
                 Coefficients}",
  journal =      j-TOMS,
  volume =       "48",
  number =       "1",
  pages =        "10:1--10:4",
  month =        mar,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3479429",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 17 08:00:57 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3479429",
  abstract =     "Algorithm 982: Explicit solutions of triangular
                 systems of first-order linear initial-value ordinary
                 differential equations with constant coefficients
                 provides an explicit solution for an homogeneous
                 system, and a brief description of how to compute a
                 solution for the inhomogeneous case. The method
                 described is not directly useful if the coefficient
                 matrix is singular. This remark explains more
                 completely how to compute the solution for the
                 inhomogeneous case and for the singular coefficient
                 matrix case.",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Myllykoski:2022:ATB,
  author =       "Mirko Myllykoski",
  title =        "{Algorithm 1019}: a Task-based Multi-shift {$ Q R $
                 \slash $ Q Z $} Algorithm with Aggressive Early
                 Deflation",
  journal =      j-TOMS,
  volume =       "48",
  number =       "1",
  pages =        "11:1--11:36",
  month =        mar,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3495005",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 17 08:00:57 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3495005",
  abstract =     "The $ Q R $ algorithm is one of the three phases in
                 the process of computing the eigenvalues and the
                 eigenvectors of a dense nonsymmetric matrix. This paper
                 describes a task-based $ Q R $ algorithm for reducing
                 an upper Hessenberg matrix to real Schur form. The
                 task-based algorithm also supports generalized
                 eigenvalue problems ($ Q Z $ algorithm) but this paper
                 concentrates on the standard case. The task-based
                 algorithm adopts previous algorithmic improvements,
                 such as tightly-coupled multi-shifts and Aggressive
                 Early Deflation (AED), and also incorporates several
                 new ideas that significantly improve the performance.
                 This includes, but is not limited to, the elimination
                 of several synchronization points, the dynamic merging
                 of previously separate computational steps, the
                 shortening and the prioritization of the critical path,
                 and experimental GPU support. The task-based
                 implementation is demonstrated to be multiple times
                 faster than multi-threaded LAPACK and ScaLAPACK in both
                 single-node and multi-node configurations on two
                 different machines based on Intel and AMD CPUs. The
                 implementation is built on top of the StarPU runtime
                 system and is part of the open-source StarNEig
                 library.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Speleers:2022:ACM,
  author =       "Hendrik Speleers",
  title =        "{Algorithm 1020}: Computation of Multi-Degree
                 {Tchebycheffian} {B}-Splines",
  journal =      j-TOMS,
  volume =       "48",
  number =       "1",
  pages =        "12:1--12:31",
  month =        mar,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3478686",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Feb 17 08:00:57 MST 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3478686",
  abstract =     "Multi-degree Tchebycheffian splines are splines with
                 pieces drawn from extended (complete) Tchebycheff
                 spaces, which may differ from interval to interval, and
                 possibly of different dimensions. These are a natural
                 extension of multi-degree polynomial splines. Under
                 quite mild assumptions, they can be represented in
                 terms of a so-called multi-degree Tchebycheffian
                 B-spline (MDTB-spline) basis; such basis possesses all
                 the characterizing properties of the classical
                 polynomial B-spline basis. We present a practical
                 framework to compute MDTB-splines, and provide an
                 object-oriented implementation in Matlab. The
                 implementation supports the construction,
                 differentiation, and visualization of MDTB-splines
                 whose pieces belong to Tchebycheff spaces that are
                 null-spaces of constant-coefficient linear differential
                 operators. The construction relies on an extraction
                 operator that maps local Tchebycheffian Bernstein
                 functions to the MDTB-spline basis of interest.",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Nath:2022:KVM,
  author =       "Kaushik Nath and Palash Sarkar",
  title =        "{Kummer} versus {Montgomery} Face-off over Prime Order
                 Fields",
  journal =      j-TOMS,
  volume =       "48",
  number =       "2",
  pages =        "13:1--13:28",
  month =        jun,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3503536",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 20 07:04:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3503536",
  abstract =     "This paper makes a comprehensive comparison of the
                 efficiencies of vectorized implementations of Kummer
                 lines and Montgomery curves at various security levels.
                 For the comparison, nine Kummer lines are considered,
                 out of which eight are new, and new assembly
                 implementations of all nine Kummer lines have been
                 made. Seven previously proposed Montgomery curves are
                 considered and new vectorized assembly implementations
                 have been made for three of them. Our comparisons show
                 that for all security levels, Kummer lines are
                 consistently faster than Montgomery curves, though the
                 speed-up gap is not much.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Eifler:2022:SCF,
  author =       "Leon Eifler and Ambros Gleixner and Jonad Pulaj",
  title =        "A Safe Computational Framework for Integer Programming
                 Applied to {Chv{\'a}tal's Conjecture}",
  journal =      j-TOMS,
  volume =       "48",
  number =       "2",
  pages =        "14:1--14:12",
  month =        jun,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3485630",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 20 07:04:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3485630",
  abstract =     "We describe a general and safe computational framework
                 that provides integer programming results with the
                 degree of certainty that is required for
                 machine-assisted proofs of mathematical theorems. At
                 its core, the framework relies on a rational
                 branch-and-bound certificate produced by an exact
                 integer programming solver, SCIP, in order to
                 circumvent floating-point round-off errors present in
                 most state-of-the-art solvers for mixed-integer
                 programs. The resulting certificates are self-contained
                 and checker software exists that can verify their
                 correctness independently of the integer programming
                 solver used to produce the certificate. This acts as a
                 safeguard against programming errors that may be
                 present in complex solver software. The viability of
                 this approach is tested by applying it to finite cases
                 of Chv{\'a}tal's conjecture, a long-standing open
                 question in extremal combinatorics. We take particular
                 care to verify also the correctness of the input for
                 this specific problem, using the Coq formal proof
                 assistant. As a result, we are able to provide the
                 first machine-assisted proof that Chv{\'a}tal's
                 conjecture holds for all downsets whose union of sets
                 contains seven elements or less.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gusmeroli:2022:BPB,
  author =       "Nicol{\`o} Gusmeroli and Timotej Hrga and Borut Luzar
                 and Janez Povh and Melanie Siebenhofer and Angelika
                 Wiegele",
  title =        "{BiqBin}: a Parallel Branch-and-bound Solver for
                 Binary Quadratic Problems with Linear Constraints",
  journal =      j-TOMS,
  volume =       "48",
  number =       "2",
  pages =        "15:1--15:31",
  month =        jun,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3514039",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 20 07:04:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3514039",
  abstract =     "We present BiqBin, an exact solver for linearly
                 constrained binary quadratic problems. Our approach is
                 based on an exact penalty method to first efficiently
                 transform the original problem into an instance of
                 Max-Cut, and then to solve the Max-Cut problem by a
                 branch-and-bound algorithm. All the main ingredients
                 are carefully developed using new semidefinite
                 programming relaxations obtained by strengthening the
                 existing relaxations with a set of hypermetric
                 inequalities, applying the bundle method as the
                 bounding routine and using new strategies for exploring
                 the branch-and-bound tree.\par

                 Furthermore, an efficient C implementation of a
                 sequential and a parallel branch-and-bound algorithm is
                 presented. The latter is based on a load
                 coordinator-worker scheme using MPI for multi-node
                 parallelization and is evaluated on a high-performance
                 computer.\par

                 The new solver is benchmarked against BiqCrunch,
                 GUROBI, and SCIP on four families of (linearly
                 constrained) binary quadratic problems. Numerical
                 results demonstrate that BiqBin is a highly competitive
                 solver. The serial version outperforms the other three
                 solvers on the majority of the benchmark instances. We
                 also evaluate the parallel solver and show that it has
                 good scaling properties. The general audience can use
                 it as an on-line service available at
                 http://www.biqbin.eu.",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Charumathi:2022:FAP,
  author =       "V. Charumathi and M. Ramakrishna and Vinita
                 Vasudevan",
  title =        "Fast and Accurate Proper Orthogonal Decomposition
                 using Efficient Sampling and Iterative Techniques for
                 Singular Value Decomposition",
  journal =      j-TOMS,
  volume =       "48",
  number =       "2",
  pages =        "16:1--16:24",
  month =        jun,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3506691",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 20 07:04:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3506691",
  abstract =     "In this article, we propose a computationally
                 efficient iterative algorithm for proper orthogonal
                 decomposition (POD) using random sampling based
                 techniques. In this algorithm, additional rows and
                 columns are sampled and a merging technique is used to
                 update the dominant POD modes in each iteration. We
                 derive bounds for the spectral norm of the error
                 introduced by a series of merging operations. We use an
                 existing theorem to get an approximate measure of the
                 quality of subspaces obtained on convergence of the
                 iteration. Results on various datasets indicate that
                 the POD modes and/or the subspaces are approximated
                 with excellent accuracy with a significant runtime
                 improvement over computing the truncated SVD. We also
                 propose a method to compute the POD modes of large
                 matrices that do not fit in the RAM using this
                 iterative sampling and merging algorithms.",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Mccoid:2022:PRA,
  author =       "Conor Mccoid and Martin J. Gander",
  title =        "A Provably Robust Algorithm for Triangle--triangle
                 Intersections in Floating-point Arithmetic",
  journal =      j-TOMS,
  volume =       "48",
  number =       "2",
  pages =        "17:1--17:30",
  month =        jun,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3513264",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 20 07:04:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3513264",
  abstract =     "Motivated by the unexpected failure of the triangle
                 intersection component of the Projection Algorithm for
                 Nonmatching Grids (PANG), this article provides a
                 robust version with proof of backward stability. The
                 new triangle intersection algorithm ensures consistency
                 and parsimony across three types of calculations. The
                 set of intersections produced by the algorithm, called
                 representations, is shown to match the set of geometric
                 intersections, called models. The article concludes
                 with a comparison between the old and new intersection
                 algorithms for PANG using an example found to reliably
                 generate failures in the former.",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Scroggs:2022:CAO,
  author =       "Matthew W. Scroggs and J{\o}rgen S. Dokken and Chris
                 N. Richardson and Garth N. Wells",
  title =        "Construction of Arbitrary Order Finite Element
                 Degree-of-Freedom Maps on Polygonal and Polyhedral Cell
                 Meshes",
  journal =      j-TOMS,
  volume =       "48",
  number =       "2",
  pages =        "18:1--18:23",
  month =        jun,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3524456",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 20 07:04:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3524456",
  abstract =     "We develop a method for generating degree-of-freedom
                 maps for arbitrary order Ciarlet-type finite element
                 spaces for any cell shape. The approach is based on the
                 composition of permutations and transformations by cell
                 sub-entity. Current approaches to \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Trotter:2022:MTO,
  author =       "James D. Trotter and Xing Cai and Simon W. Funke",
  title =        "On Memory Traffic and Optimisations for Low-order
                 Finite Element Assembly Algorithms on Multi-core
                 {CPUs}",
  journal =      j-TOMS,
  volume =       "48",
  number =       "2",
  pages =        "19:1--19:31",
  month =        jun,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3503925",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 20 07:04:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3503925",
  abstract =     "Motivated by the wish to understand the achievable
                 performance of finite element assembly on unstructured
                 computational meshes, we dissect the standard cellwise
                 assembly algorithm into four kernels, two of which are
                 dominated by irregular memory traffic. Several
                 optimisation schemes are studied together with
                 associated lower and upper bounds on the estimated
                 memory traffic volume. Apart from properly reordering
                 the mesh entities, the two most significant
                 optimisations include adopting a lookup table in adding
                 element matrices or vectors to their global
                 counterparts, and using a row-wise assembly algorithm
                 for multi-threaded parallelisation. Rigorous
                 benchmarking shows that, due to the various
                 optimisations, the actual volumes of memory traffic are
                 in many cases very close to the estimated lower bounds.
                 These results confirm the effectiveness of the
                 optimisations, while also providing a recipe for
                 developing efficient software for finite element
                 assembly.",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lourenco:2022:ASL,
  author =       "Christopher Lourenco and Jinhao Chen and Erick
                 Moreno-Centeno and Timothy A. Davis",
  title =        "{Algorithm 1021}: {SPEX} Left {LU}, Exactly Solving
                 Sparse Linear Systems via a Sparse Left-looking
                 Integer-preserving {LU} Factorization",
  journal =      j-TOMS,
  volume =       "48",
  number =       "2",
  pages =        "20:1--20:23",
  month =        jun,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3519024",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 20 07:04:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3519024",
  abstract =     "SPEX Left LU is a software package for exactly solving
                 unsymmetric sparse linear systems. As a component of
                 the sparse exact (SPEX) software package, SPEX Left LU
                 can be applied to any input matrix, A, whose entries
                 are integral, rational, or decimal, and provides a
                 solution to the system $ A x = b$, which is either
                 exact or accurate to user-specified precision. SPEX
                 Left LU preorders the matrix A with a user-specified
                 fill-reducing ordering and computes a left-looking LU
                 factorization with the special property that each
                 operation used to compute the L and U matrices is
                 integral. Notable additional applications of this
                 package include benchmarking the stability and accuracy
                 of state-of-the-art linear solvers and determining
                 whether singular-to-double-precision matrices are
                 indeed singular. Computationally, this article
                 evaluates the impact of several novel pivoting schemes
                 in exact arithmetic, benchmarks the exact iterative
                 solvers within Linbox, and benchmarks the accuracy of
                 MATLAB sparse backslash. Most importantly, it is shown
                 that SPEX Left LU outperforms the exact iterative
                 solvers in run time on easy instances and in stability
                 as the iterative solver fails on a sizeable subset of
                 the tested (both easy and hard) instances. The SPEX
                 Left LU package is written in ANSI C, comes with a
                 MATLAB interface, and is distributed via GitHub, as a
                 component of the SPEX software package, and as a
                 component of SuiteSparse.",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Heavner:2022:AEA,
  author =       "N. Heavner and F. D. Igual and G. Quintana-Ort{\'\i}
                 and P. G. Martinsson",
  title =        "{Algorithm 1022}: {Efficient} Algorithms for Computing
                 a Rank-Revealing {UTV} Factorization on Parallel
                 Computing Architectures",
  journal =      j-TOMS,
  volume =       "48",
  number =       "2",
  pages =        "21:1--21:42",
  month =        jun,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3507466",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 20 07:04:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3507466",
  abstract =     "Randomized singular value decomposition (RSVD) is by
                 now a well-established technique for efficiently
                 computing an approximate singular value decomposition
                 of a matrix. Building on the ideas that underpin RSVD,
                 the recently proposed algorithm ``randUTV'' computes a
                 full factorization of a given matrix that provides
                 low-rank approximations with near-optimal error.
                 Because the bulk of randUTV is cast in terms of
                 communication-efficient operations such as
                 matrix-matrix multiplication and unpivoted QR
                 factorizations, it is faster than competing
                 rank-revealing factorization methods such as
                 column-pivoted QR in most high-performance
                 computational settings. In this article, optimized
                 randUTV implementations are presented for both
                 shared-memory and distributed-memory computing
                 environments. For shared memory, randUTV is redesigned
                 in terms of an algorithm-by-blocks that, together with
                 a runtime task scheduler, eliminates bottlenecks from
                 data synchronization points to achieve acceleration
                 over the standard blocked algorithm based on a purely
                 fork-join approach. The distributed-memory
                 implementation is based on the ScaLAPACK library. The
                 performance of our new codes compares favorably with
                 competing factorizations available on both
                 shared-memory and distributed-memory architectures",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Korablev:2022:ARF,
  author =       "Yuriy Korablev",
  title =        "{Algorithm 1023}: {Restoration} of Function by
                 Integrals with Cubic Integral Smoothing Spline in {R}",
  journal =      j-TOMS,
  volume =       "48",
  number =       "2",
  pages =        "22:1--22:17",
  month =        jun,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3519384",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 20 07:04:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/s-plus.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3519384",
  abstract =     "In this paper, a cubic integral smoothing spline with
                 roughness penalty for restoring a function by integrals
                 is described. A mathematical method for building such a
                 spline is described in detail. The method is based on
                 cubic integral spline with a penalty function, which
                 minimizes the sum of squares of the difference between
                 the observed integrals of the unknown function and the
                 integrals of the spline being constructed, plus an
                 additional penalty for the nonlinearity (roughness) of
                 the spline. This method has a matrix form, and this
                 paper shows in detail how to fill in each matrix. The
                 parameter $ \alpha $ governs the desired smoothness of
                 the restored function. Spline knots can be chosen
                 independently of observations, and a weight can be
                 defined for each observation for more control over the
                 resulting spline shape. An implementation in the R
                 language as function int_spline is given. The function
                 int_spline is easy to use, with all arguments
                 completely described and corresponding examples given.
                 An example of the application of the method in rare
                 event analysis and forecasting is given.",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kalantari:2022:AST,
  author =       "Bahman Kalantari and Yikai Zhang",
  title =        "{Algorithm 1024}: Spherical Triangle Algorithm: a Fast
                 Oracle for Convex Hull Membership Queries",
  journal =      j-TOMS,
  volume =       "48",
  number =       "2",
  pages =        "23:1--23:32",
  month =        jun,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3516520",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 20 07:04:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3516520",
  abstract =     "The Convex Hull Membership (CHM) tests whether \( p
                 \in conv(S) \), where p and the n points of S lie in \(
                 \mathbb { R}^m \). CHM finds applications in Linear
                 Programming, Computational Geometry, and Machine
                 Learning. The Triangle Algorithm (TA), previously
                 developed, in $ O(1 / \epsilon^2) $ iterations computes
                 $ p' \in \conv (S) $, either an $ \epsilon
                 $-approximate solution, or a witness certifying p \not
                 \in conv(S). We first prove the equivalence of exact
                 and approximate versions of CHM and Spherical-CHM,
                 where $ p = 0$ and $ ||v|| = 1$ for each $v$ in $S$. If
                 for some $ M \geq 1$ every non-witness with $ ||p'|| >
                 \epsilon $ admits $ v \in S$ satisfying $ ||p' - v||
                 \geq \sqrt {1 + \epsilon / M}$, we prove the number of
                 iterations improves to $ O(M / \epsilon)$ and $ M \leq
                 1 / \epsilon $ always holds. Equivalence of CHM and
                 Spherical-CHM implies {\em Minimum Enclosing Ball\/}
                 (MEB) algorithms can be modified to solve CHM. However,
                 we prove $ (1 + \epsilon)$-approximation in MEB is $
                 \Omega (\sqrt {\epsilon })$-approximation in
                 Spherical-CHM. Thus, even $ O(1 / \epsilon) $ iteration
                 MEB algorithms are not superior to Spherical-TA.
                 Similar weakness is proved for MEB core sets.
                 Spherical-TA also results a variant of the {\em All
                 Vertex Triangle Algorithm\/} (AVTA) for computing all
                 vertices of $ \conv (S)$. Substantial computations on
                 distinct problems demonstrate that TA and Spherical-TA
                 generally achieve superior efficiency over algorithms
                 such as Frank--Wolfe, MEB, and LP-Solver.",
  acknowledgement = ack-nhfb,
  articleno =    "23",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Pokuri:2022:APS,
  author =       "Balaji Sesha Sarath Pokuri and Alec Lofquist and Chad
                 Risko and Baskar Ganapathysubramanian",
  title =        "{Algorithm 1025}: {PARyOpt}: a Software for Parallel
                 Asynchronous Remote {Bayesian} Optimization",
  journal =      j-TOMS,
  volume =       "48",
  number =       "2",
  pages =        "24:1--24:15",
  month =        jun,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3529517",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Jul 20 07:04:17 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3529517",
  abstract =     "PARyOpt $^1$ is a Python based implementation of the
                 Bayesian optimization routine designed for remote and
                 asynchronous function evaluations. Bayesian
                 optimization is especially attractive for computational
                 optimization due to its low cost function footprint as
                 well as the ability to account for uncertainties in
                 data. A key challenge to efficiently deploy any
                 optimization strategy on distributed computing systems
                 is the synchronization step, where data from multiple
                 function calls is assimilated to identify the next
                 campaign of function calls. Bayesian optimization
                 provides an elegant approach to overcome this issue via
                 asynchronous updates. We formulate, develop and
                 implement a parallel, asynchronous variant of Bayesian
                 optimization. The framework is robust and resilient to
                 external failures. We show how such asynchronous
                 evaluations help reduce the total optimization wall
                 clock time for a suite of test problems. Additionally,
                 we show how the software design of the framework allows
                 easy extension to response surface reconstruction
                 (Kriging), providing a high performance software for
                 autonomous exploration. The software is available on
                 PyPI, with examples and documentation.",
  acknowledgement = ack-nhfb,
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Schwarz:2022:RLB,
  author =       "Angelika Schwarz",
  title =        "Robust level-3 {BLAS} Inverse Iteration from the
                 {Hessenberg} Matrix",
  journal =      j-TOMS,
  volume =       "48",
  number =       "3",
  pages =        "25:1--25:??",
  month =        sep,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3544789",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 29 08:26:38 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3544789",
  abstract =     "Inverse iteration is known to be an effective method
                 for computing eigenvectors corresponding to simple and
                 well-separated eigenvalues. In the non-symmetric case,
                 the solution of shifted Hessenberg systems is a central
                 step. Existing inverse iteration solvers approach the
                 solution of the shifted Hessenberg systems with either
                 RQ or LU factorizations and, once factored, solve the
                 corresponding systems. This approach has limited
                 level-3 BLAS potential since distinct shifts have
                 distinct factorizations. This paper rearranges the RQ
                 approach such that data shared between distinct shifts
                 can be exploited. Thereby the backward substitution
                 with the triangular R factor can be expressed mostly
                 with matrix--matrix multiplications (level-3 BLAS). The
                 resulting algorithm computes eigenvectors in a tiled,
                 overflow-free, and task-parallel fashion. The numerical
                 experiments show that the new algorithm outperforms
                 existing inverse iteration solvers for the computation
                 of both real and complex eigenvectors.",
  acknowledgement = ack-nhfb,
  articleno =    "25",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Psarras:2022:LAM,
  author =       "Christos Psarras and Henrik Barthels and Paolo
                 Bientinesi",
  title =        "The Linear Algebra Mapping Problem. {Current} State of
                 Linear Algebra Languages and Libraries",
  journal =      j-TOMS,
  volume =       "48",
  number =       "3",
  pages =        "26:1--26:??",
  month =        sep,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3549935",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 29 08:26:38 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/julia.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/s-plus.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3549935",
  abstract =     "We observe a disconnect between developers and
                 end-users of linear algebra libraries. On the one hand,
                 developers invest significant effort in creating
                 sophisticated numerical kernels. On the other hand,
                 end-users are progressively less likely to go through
                 the time consuming process of directly using said
                 kernels; instead, languages and libraries, which offer
                 a higher level of abstraction, are becoming
                 increasingly popular. These languages offer mechanisms
                 that internally map the input program to lower level
                 kernels. Unfortunately, our experience suggests that,
                 in terms of performance, this translation is typically
                 suboptimal.\par

                 In this paper, we define the problem of mapping a
                 linear algebra expression to a set of available
                 building blocks as the ``Linear Algebra Mapping
                 Problem'' (LAMP); we discuss its NP-complete nature,
                 and investigate how effectively a benchmark of test
                 problems is solved by popular high-level programming
                 languages and libraries. Specifically, we consider
                 Matlab, Octave, Julia, R, Armadillo (C++), Eigen (C++),
                 and NumPy (Python); the benchmark is meant to test both
                 compiler optimizations, as well as linear algebra
                 specific optimizations, such as the optimal
                 parenthesization of matrix products. The aim of this
                 study is to facilitate the development of languages and
                 libraries that support linear algebra computations.",
  acknowledgement = ack-nhfb,
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Apriansyah:2022:PQF,
  author =       "M. Ridwan Apriansyah and Rio Yokota",
  title =        "Parallel {$ Q R $} Factorization of Block Low-rank
                 Matrices",
  journal =      j-TOMS,
  volume =       "48",
  number =       "3",
  pages =        "27:1--27:??",
  month =        sep,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3538647",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 29 08:26:38 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3538647",
  abstract =     "We present two new algorithms for Householder QR
                 factorization of Block Low-Rank (BLR) matrices: one
                 that performs block-column-wise QR and another that is
                 based on tiled QR. We show how the block-column-wise
                 algorithm exploits BLR structure to achieve arithmetic
                 complexity of $ O(m n) $, while the tiled BLR-QR
                 exhibits O(mn^{1.5}) complexity. However, the tiled
                 BLR-QR has finer task granularity that allows parallel
                 task-based execution on shared memory systems. We
                 compare the block-column-wise BLR-QR using fork-join
                 parallelism with tiled BLR-QR using task-based
                 parallelism. We also compare these two implementations
                 of Householder BLR-QR with a block-column-wise Modified
                 Gram--Schmidt (MGS) BLR-QR using fork-join parallelism
                 and a state-of-the-art vendor-optimized dense
                 Householder QR in Intel MKL. For a matrix of size 131k
                 $ \times $ 65k, all BLR methods are more than an order
                 of magnitude faster than the dense QR in MKL. Our
                 methods are also robust to ill conditioning and produce
                 better orthogonal factors than the existing MGS-based
                 method. On a CPU with 64 cores, our parallel tiled
                 Householder and block-column-wise Householder
                 algorithms show a speedup of 50 and 37 times,
                 respectively",
  acknowledgement = ack-nhfb,
  articleno =    "27",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lange:2022:TAF,
  author =       "Marko Lange",
  title =        "Toward Accurate and Fast Summation",
  journal =      j-TOMS,
  volume =       "48",
  number =       "3",
  pages =        "28:1--28:??",
  month =        sep,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3544488",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 29 08:26:38 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3544488",
  abstract =     "We introduce a new accurate summation algorithm based
                 on the error-free summation into floating-point
                 buckets. Our algorithm exploits ideas from Zhu and
                 Hayes' OnlineExactSum, but it uses a significantly
                 smaller number of accumulators and has a better
                 instruction-level parallelism. In the default setting,
                 our implementation aaaSum returns a faithfully rounded
                 floating-point approximation of the true sum. We also
                 discuss possible modifications for the computation of
                 reproducible, correctly rounded, and multiple precision
                 floating-point approximations. The computational
                 overhead for any of these modifications is kept
                 comparably small. Numerical tests demonstrate that
                 aaaSum performs well for very small to large problem
                 sizes, independent of the condition number of the
                 problem. We compare our algorithm with other accurate
                 and high-precision summation approaches.",
  acknowledgement = ack-nhfb,
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "accurate summation",
}

@Article{Hubschle-Schneider:2022:PWR,
  author =       "Lorenz H{\"u}bschle-Schneider and Peter Sanders",
  title =        "Parallel Weighted Random Sampling",
  journal =      j-TOMS,
  volume =       "48",
  number =       "3",
  pages =        "29:1--29:??",
  month =        sep,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3549934",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 29 08:26:38 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3549934",
  abstract =     "Data structures for efficient sampling from a set of
                 weighted items are an important building block of many
                 applications. However, few parallel solutions are
                 known. We close many of these gaps. We give efficient,
                 fast, and practicable parallel and distributed
                 algorithms for building data structures that support
                 sampling single items (alias tables, compressed data
                 structures). This also yields a simplified and more
                 space-efficient sequential algorithm for alias table
                 construction. Our approaches to sampling k out of n
                 items with/without replacement and to subset (Poisson)
                 sampling are output-sensitive, i.e., the sampling
                 algorithms use work linear in the number of different
                 samples. This is also interesting in the sequential
                 case. Weighted random permutation can be done by
                 sorting appropriate random deviates. We show that this
                 is possible with linear work. Finally, we give a
                 communication-efficient, highly scalable approach to
                 (weighted and unweighted) reservoir sampling. This
                 algorithm is based on a fully distributed model of
                 streaming algorithms that might be of independent
                 interest. Experiments for alias tables and sampling
                 with replacement show near linear speedups using up to
                 158 threads of shared-memory machines. An experimental
                 evaluation of distributed weighted reservoir sampling
                 on up to 5,120 cores also shows good speedups.",
  acknowledgement = ack-nhfb,
  articleno =    "29",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Klinkovsky:2022:COS,
  author =       "Jakub Klinkovsk{\'y} and Tom{\'a}s Oberhuber and Radek
                 Fuc{\'\i}k and V{\'\i}tezslav Zabka",
  title =        "Configurable Open-source Data Structure for
                 Distributed Conforming Unstructured Homogeneous Meshes
                 with {GPU} Support",
  journal =      j-TOMS,
  volume =       "48",
  number =       "3",
  pages =        "30:1--30:??",
  month =        sep,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3536164",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 29 08:26:38 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3536164",
  abstract =     "A general multi-purpose data structure for an
                 efficient representation of conforming unstructured
                 homogeneous meshes for scientific computations on CPU
                 and GPU-based systems is presented. The data structure
                 is provided as open-source software as part of the TNL
                 library (https://tnl-project.org/). The abstract
                 representation supports almost any cell shape and
                 common 2D quadrilateral, 3D hexahedron and arbitrarily
                 dimensional simplex shapes are currently built into the
                 library. The implementation is highly configurable via
                 templates of the C++ language, which allows avoiding
                 the storage of unnecessary dynamic data. The internal
                 memory layout is based on state-of-the-art sparse
                 matrix storage formats, which are optimized for
                 different hardware architectures in order to provide
                 high-performance computations. The proposed data
                 structure is also suitable for meshes decomposed into
                 several subdomains and distributed computing using the
                 Message Passing Interface (MPI). The efficiency of the
                 implemented data structure on CPU and GPU hardware
                 architectures is demonstrated on several benchmark
                 problems and a comparison with another library. Its
                 applicability to advanced numerical methods is
                 demonstrated with an example problem of two-phase flow
                 in porous media using a numerical scheme based on the
                 mixed-hybrid finite element method (MHFEM). We show GPU
                 speed-ups that rise above 20 in 2D and 50 in 3D when
                 compared to sequential CPU computations, and above 2 in
                 2D and 9 in 3D when compared to 12-threaded CPU
                 computations.",
  acknowledgement = ack-nhfb,
  articleno =    "30",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Gardner:2022:ENF,
  author =       "David J. Gardner and Daniel R. Reynolds and Carol S.
                 Woodward and Cody J. Balos",
  title =        "Enabling New Flexibility in the {SUNDIALS} Suite of
                 Nonlinear and Differential\slash Algebraic Equation
                 Solvers",
  journal =      j-TOMS,
  volume =       "48",
  number =       "3",
  pages =        "31:1--31:??",
  month =        sep,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3539801",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 29 08:26:38 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3539801",
  abstract =     "In recent years, the SUite of Nonlinear and
                 DIfferential/ALgebraic equation Solvers (SUNDIALS) has
                 been redesigned to better enable the use of
                 application-specific and third-party algebraic solvers
                 and data structures. Throughout this work, we have
                 adhered to specific guiding principles that minimized
                 the impact to current users while providing maximum
                 flexibility for later evolution of solvers and data
                 structures. The redesign was done through the addition
                 of new linear and nonlinear solvers classes,
                 enhancements to the vector class, and the creation of
                 modern Fortran interfaces. The vast majority of this
                 work has been performed ``behind-the-scenes,'' with
                 minimal changes to the user interface and no reduction
                 in solver capabilities or performance. These changes
                 allow SUNDIALS users to more easily utilize external
                 solver libraries and create highly customized solvers,
                 enabling greater flexibility on extreme-scale,
                 heterogeneous computational architectures.",
  acknowledgement = ack-nhfb,
  articleno =    "31",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Chen:2022:HHI,
  author =       "Qiao Chen and Xiangmin Jiao",
  title =        "{HIFIR}: Hybrid Incomplete Factorization with
                 Iterative Refinement for Preconditioning
                 Ill-Conditioned and Singular Systems",
  journal =      j-TOMS,
  volume =       "48",
  number =       "3",
  pages =        "32:1--32:??",
  month =        sep,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3536165",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 29 08:26:38 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3536165",
  abstract =     "We introduce a software package called Hybrid
                 Incomplete Factorization with Iterative Refinement
                 (HIFIR) for preconditioning sparse, unsymmetric,
                 ill-conditioned, and potentially singular systems.
                 HIFIR computes a hybrid incomplete factorization (HIF),
                 which combines multilevel incomplete LU factorization
                 with a truncated, rank-revealing QR (RRQR)
                 factorization on the final Schur complement. This novel
                 hybridization is based on the new theory of $ \epsilon
                 $-accurate approximate generalized inverse (AGI). It
                 enables near-optimal preconditioners for consistent
                 systems and enables flexible GMRES to solve
                 inconsistent systems when coupled with iterative
                 refinement. In this article, we focus on some practical
                 algorithmic and software issues of HIFIR. In
                 particular, we introduce a new inverse-based rook
                 pivoting (IBRP) into ILU, which improves the robustness
                 and the overall efficiency for some ill-conditioned
                 systems by significantly reducing the size of the final
                 Schur complement for some systems. We also describe the
                 software design of HIFIR in terms of its efficient data
                 structures for supporting rook pivoting in a multilevel
                 setting, its template-based generic programming
                 interfaces for mixed-precision real and complex values
                 in C++, and its user-friendly high-level interfaces in
                 MATLAB and Python. We demonstrate the effectiveness of
                 HIFIR for ill-conditioned or singular systems arising
                 from several applications, including the Helmholtz
                 equation, linear elasticity, stationary incompressible
                 Navier--Stokes (INS) equations, and time-dependent
                 advection-diffusion equation.",
  acknowledgement = ack-nhfb,
  articleno =    "32",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Liang:2022:QTP,
  author =       "Ling Liang and Xudong Li and Defeng Sun and Kim-Chuan
                 Toh",
  title =        "{QPPAL}: a Two-phase Proximal Augmented {Lagrangian}
                 Method for High-dimensional Convex Quadratic
                 Programming Problems",
  journal =      j-TOMS,
  volume =       "48",
  number =       "3",
  pages =        "33:1--33:??",
  month =        sep,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3476571",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 29 08:26:38 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3476571",
  abstract =     "In this article, we aim to solve high-dimensional
                 convex quadratic programming (QP) problems with a large
                 number of quadratic terms, linear equality, and
                 inequality constraints. To solve the targeted QP
                 problem to a desired accuracy efficiently, we consider
                 the restricted-Wolfe dual problem and develop a
                 two-phase Proximal Augmented Lagrangian method (QPPAL),
                 with Phase I to generate a reasonably good initial
                 point to warm start Phase II to obtain an accurate
                 solution efficiently. More specifically, in Phase I,
                 based on the recently developed symmetric Gauss-Seidel
                 (sGS) decomposition technique, we design a novel
                 sGS-based semi-proximal augmented Lagrangian method for
                 the purpose of finding a solution of low to medium
                 accuracy. Then, in Phase II, a proximal augmented
                 Lagrangian algorithm is proposed to obtain a more
                 accurate solution efficiently. Extensive numerical
                 results evaluating the performance of QPPAL against
                 existing state-of-the-art solvers Gurobi, OSQP, and
                 QPALM are presented to demonstrate the high efficiency
                 and robustness of our proposed algorithm for solving
                 various classes of large-scale convex QP problems. The
                 MATLAB implementation of the software package QPPAL is
                 available at
                 \url{https://blog.nus.edu.sg/mattohkc/softwares/qppal/}.",
  acknowledgement = ack-nhfb,
  articleno =    "33",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Psarras:2022:ACA,
  author =       "Christos Psarras and Lars Karlsson and Rasmus Bro and
                 Paolo Bientinesi",
  title =        "{Algorithm 1026}: Concurrent Alternating Least Squares
                 for Multiple Simultaneous Canonical Polyadic
                 Decompositions",
  journal =      j-TOMS,
  volume =       "48",
  number =       "3",
  pages =        "34:1--34:??",
  month =        sep,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3519383",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 29 08:26:38 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3519383",
  abstract =     "Tensor decompositions, such as CANDECOMP/PARAFAC (CP),
                 are widely used in a variety of applications, such as
                 chemometrics, signal processing, and machine learning.
                 A broadly used method for computing such decompositions
                 relies on the Alternating Least Squares (ALS)
                 algorithm. When the number of components is small,
                 regardless of its implementation, ALS exhibits low
                 arithmetic intensity, which severely hinders its
                 performance and makes GPU offloading ineffective. We
                 observe that, in practice, experts often have to
                 compute multiple decompositions of the same tensor,
                 each with a small number of components (typically fewer
                 than 20), to ultimately find the best ones to use for
                 the application at hand. In this article, we illustrate
                 how multiple decompositions of the same tensor can be
                 fused together at the algorithmic level to increase the
                 arithmetic intensity. Therefore, it becomes possible to
                 make efficient use of GPUs for further speedups; at the
                 same time, the technique is compatible with many
                 enhancements typically used in ALS, such as line
                 search, extrapolation, and non-negativity constraints.
                 We introduce the Concurrent ALS algorithm and library,
                 which offers an interface to MATLAB, and a mechanism to
                 effectively deal with the issue that decompositions
                 complete at different times. Experimental results on
                 artificial and real datasets demonstrate a shorter time
                 to completion due to increased arithmetic intensity.",
  acknowledgement = ack-nhfb,
  articleno =    "34",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Audet:2022:ANV,
  author =       "Charles Audet and S{\'e}bastien {Le Digabel} and
                 Viviane Rochon Montplaisir and Christophe Tribes",
  title =        "{Algorithm 1027}: \pkg{NOMAD} Version 4: Nonlinear
                 Optimization with the {MADS} Algorithm",
  journal =      j-TOMS,
  volume =       "48",
  number =       "3",
  pages =        "35:1--35:??",
  month =        sep,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3544489",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 29 08:26:38 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3544489",
  abstract =     "NOMADis a state-of-the-art software package for
                 optimizing blackbox problems. In continuous development
                 since 2001, it constantly evolved with the integration
                 of new algorithmic features published in scientific
                 publications. These features are motivated by real
                 applications encountered by industrial partners. The
                 latest major release of NOMAD, version 3, dates to
                 2008. Minor releases are produced as new features are
                 incorporated. The present work describes NOMAD 4, a
                 complete redesign of the previous version, with a new
                 architecture providing more flexible code, added
                 functionalities, and reusable code. We introduce
                 algorithmic components, which are building blocks for
                 more complex algorithms and can initiate other
                 components, launch nested algorithms, or perform
                 specialized tasks. They facilitate the implementation
                 of new ideas, including the MegaSearchPoll component,
                 warm and hot restarts, and a revised version of the
                 PsdMads algorithm. Another main improvement of NOMAD 4
                 is the usage of parallelism, to simultaneously compute
                 multiple blackbox evaluations and to maximize usage of
                 available cores. Running different algorithms, tuning
                 their parameters, and comparing their performance for
                 optimization are simpler than before, while overall
                 optimization performance is maintained between versions
                 3 and 4. NOMAD is freely available at
                 www.gerad.ca/nomad and the whole project is visible at
                 github.com/bbopt/nomad.",
  acknowledgement = ack-nhfb,
  articleno =    "35",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Chang:2022:AVS,
  author =       "Tyler H. Chang and Layne T. Watson and Jeffrey Larson
                 and Nicole Neveu and William I. Thacker and Shubhangi
                 Deshpande and Thomas C. H. Lux",
  title =        "{Algorithm 1028}: {VTMOP}: Solver for Blackbox
                 Multiobjective Optimization Problems",
  journal =      j-TOMS,
  volume =       "48",
  number =       "3",
  pages =        "36:1--36:??",
  month =        sep,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3529258",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Oct 29 08:26:38 MDT 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3529258",
  abstract =     "VTMOP is a Fortran 2008 software package containing
                 two Fortran modules for solving computationally
                 expensive bound-constrained blackbox multiobjective
                 optimization problems. VTMOP implements the algorithm
                 of [32], which handles two or more objectives, does not
                 require any derivatives, and produces well-distributed
                 points over the Pareto front. The first module contains
                 a general framework for solving multiobjective
                 optimization problems by combining response surface
                 methodology, trust region methodology, and an adaptive
                 weighting scheme. The second module features a driver
                 subroutine that implements this framework when the
                 objective functions can be wrapped as a Fortran
                 subroutine. Support is provided for both serial and
                 parallel execution paradigms, and VTMOP is demonstrated
                 on several test problems as well as one real-world
                 problem in the area of particle accelerator
                 optimization.",
  acknowledgement = ack-nhfb,
  articleno =    "36",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Alves:2022:COH,
  author =       "Jo{\~a}o Nuno Ferreira Alves and Lu{\'\i}s Manuel
                 Silveira Russo and Alexandre Francisco",
  title =        "Cache-oblivious {Hilbert} Curve-based Blocking Scheme
                 for Matrix Transposition",
  journal =      j-TOMS,
  volume =       "48",
  number =       "4",
  pages =        "37:1--37:??",
  month =        dec,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3555353",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3555353",
  abstract =     "This article presents a fast SIMD Hilbert
                 space-filling curve generator, which supports a new
                 cache-oblivious blocking-scheme technique applied to
                 the out-of-place transposition of general matrices.
                 Matrix operations found in high performance computing
                 \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "37",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Telen:2022:NFA,
  author =       "Simon Telen and Nick Vannieuwenhoven",
  title =        "A Normal Form Algorithm for Tensor Rank
                 Decomposition",
  journal =      j-TOMS,
  volume =       "48",
  number =       "4",
  pages =        "38:1--38:??",
  month =        dec,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3555369",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3555369",
  abstract =     "We propose a new numerical algorithm for computing the
                 tensor rank decomposition or canonical polyadic
                 decomposition of higher-order tensors subject to a rank
                 and genericity constraint. Reformulating this
                 computational problem as a system of polynomial
                 \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "38",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Jarlebring:2022:CGM,
  author =       "Elias Jarlebring and Massimiliano Fasi and Emil
                 Ringh",
  title =        "Computational Graphs for Matrix Functions",
  journal =      j-TOMS,
  volume =       "48",
  number =       "4",
  pages =        "39:1--39:??",
  month =        dec,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3568991",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3568991",
  abstract =     "Many numerical methods for evaluating matrix functions
                 can be naturally viewed as computational graphs.
                 Rephrasing these methods as directed acyclic graphs
                 (DAGs) is a particularly effective approach to study
                 existing techniques, improve them, and \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "39",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Mai:2022:ECT,
  author =       "Ngoc Hoang Anh Mai and J. B. Lasserre and Victor
                 Magron and Jie Wang",
  title =        "Exploiting Constant Trace Property in Large-scale
                 Polynomial Optimization",
  journal =      j-TOMS,
  volume =       "48",
  number =       "4",
  pages =        "40:1--40:??",
  month =        dec,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3555309",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3555309",
  abstract =     "We prove that every semidefinite moment relaxation of
                 a polynomial optimization problem (POP) with a ball
                 constraint can be reformulated as a semidefinite
                 program involving a matrix with constant trace property
                 (CTP). As a result, such moment relaxations \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "40",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Stripinis:2022:DND,
  author =       "Linas Stripinis and Remigijus Paulavicius",
  title =        "{DIRECTGO}: a New {DIRECT}-Type {MATLAB} Toolbox for
                 Derivative-Free Global Optimization",
  journal =      j-TOMS,
  volume =       "48",
  number =       "4",
  pages =        "41:1--41:??",
  month =        dec,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3559755",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3559755",
  abstract =     "In this work, we introduce DIRECTGO, a new MATLAB
                 toolbox for derivative-free global optimization.
                 DIRECTGO collects various deterministic derivative-free
                 DIRECT-type algorithms for box-constrained, generally
                 constrained, and problems with hidden constraints. Each
                 sequential algorithm is implemented in two ways: using
                 static and dynamic data structures for more efficient
                 information storage and organization. Furthermore,
                 parallel schemes are applied to some promising
                 algorithms within DIRECTGO. The toolbox is equipped
                 with a graphical user interface (GUI), ensuring the
                 user-friendly use of all functionalities available in
                 DIRECTGO. Available features are demonstrated in
                 detailed computational studies using a comprehensive
                 DIRECTGOLib v1.0 library of global optimization test
                 problems. Additionally, 11 classical engineering design
                 problems illustrate the potential of DIRECTGO to solve
                 challenging real-world problems. Finally, the appendix
                 gives examples of accompanying MATLAB programs and
                 provides a synopsis of its use on the test problems
                 with box and general constraints.",
  acknowledgement = ack-nhfb,
  articleno =    "41",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Wang:2022:CTC,
  author =       "Jie Wang and Victor Magron and J. B. Lasserre and Ngoc
                 Hoang Anh Mai",
  title =        "{CS-TSSOS}: Correlative and Term Sparsity for
                 Large-Scale Polynomial Optimization",
  journal =      j-TOMS,
  volume =       "48",
  number =       "4",
  pages =        "42:1--42:??",
  month =        dec,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3569709",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3569709",
  abstract =     "This work proposes a new moment-SOS hierarchy, called
                 CS-TSSOS, for solving large-scale sparse polynomial
                 optimization problems. Its novelty is to exploit
                 simultaneously correlative sparsity and term sparsity
                 by combining advantages of two existing \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "42",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Phipps:2022:ADC,
  author =       "Eric Phipps and Roger Pawlowski and Christian Trott",
  title =        "Automatic Differentiation of {C++} Codes on Emerging
                 Manycore Architectures with {Sacado}",
  journal =      j-TOMS,
  volume =       "48",
  number =       "4",
  pages =        "43:1--43:??",
  month =        dec,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3560262",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3560262",
  abstract =     "Automatic differentiation (AD) is a well-known
                 technique for evaluating analytic derivatives of
                 calculations implemented on a computer, with numerous
                 software tools available for incorporating AD
                 technology into complex applications. However, a
                 growing \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "43",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Sobczyk:2022:PPA,
  author =       "Aleksandros Sobczyk and Efstratios Gallopoulos",
  title =        "\pkg{pylspack}: Parallel Algorithms and Data
                 Structures for Sketching, Column Subset Selection,
                 Regression, and Leverage Scores",
  journal =      j-TOMS,
  volume =       "48",
  number =       "4",
  pages =        "44:1--44:??",
  month =        dec,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3555370",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3555370",
  abstract =     "We present parallel algorithms and data structures for
                 three fundamental operations in Numerical Linear
                 Algebra: (i) Gaussian and CountSketch random
                 projections and their combination, (ii) computation of
                 the Gram matrix, and (iii) computation of the
                 \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "44",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Meisrimel:2022:WRA,
  author =       "Peter Meisrimel and Philipp Birken",
  title =        "Waveform Relaxation with Asynchronous
                 Time-integration",
  journal =      j-TOMS,
  volume =       "48",
  number =       "4",
  pages =        "45:1--45:??",
  month =        dec,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3569578",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3569578",
  abstract =     "We consider Waveform Relaxation (WR) methods for
                 parallel and partitioned time-integration of
                 surface-coupled multiphysics problems. WR allows
                 independent time-discretizations on independent and
                 adaptive time-grids, while maintaining high
                 time-integration \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "45",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{DeMichele:2022:RAB,
  author =       "Cristiano {De Michele}",
  title =        "Remark on {Algorithm 1010}: Boosting Efficiency in
                 Solving Quartic Equations with No Compromise in
                 Accuracy",
  journal =      j-TOMS,
  volume =       "48",
  number =       "4",
  pages =        "46:1--46:??",
  month =        dec,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3564270",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Orellana:2020:ABE}.",
  URL =          "https://dl.acm.org/doi/10.1145/3564270",
  abstract =     "We present a correction and an improvement to
                 Algorithm 1010 [A. Orellana and C. De Michele 2020]",
  acknowledgement = ack-nhfb,
  articleno =    "46",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Demeure:2022:AEE,
  author =       "Nestor Demeure and C{\'e}dric Chevalier and Christophe
                 Denis and Pierre Dossantos-Uzarralde",
  title =        "{Algorithm 1029}: Encapsulated Error, a Direct
                 Approach to Evaluate Floating-Point Accuracy",
  journal =      j-TOMS,
  volume =       "48",
  number =       "4",
  pages =        "47:1--47:??",
  month =        dec,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3549205",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3549205",
  abstract =     "Floating-point numbers represent only a subset of real
                 numbers. As such, floating-point arithmetic introduces
                 approximations that can compound and have a significant
                 impact on numerical simulations. We introduce
                 encapsulated error, a new way to estimate the numerical
                 error of an application and provide a reference
                 implementation, the Shaman library. Our method uses
                 dedicated arithmetic over a type that encapsulates both
                 the result the user would have had with the original
                 computation and an approximation of its numerical
                 error. We thus can measure the number of significant
                 digits of any result or intermediate result in a
                 simulation. We show that this approach, although
                 simple, gives results competitive with state-of-the-art
                 methods. It has a smaller overhead, and it is
                 compatible with parallelism, making it suitable for the
                 study of large-scale applications.",
  acknowledgement = ack-nhfb,
  articleno =    "47",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Brust:2022:ASS,
  author =       "Johannes Brust and Oleg Burdakov and Jennifer Erway
                 and Roummel Marcia",
  title =        "{Algorithm 1030}: {SC-SR1}: {MATLAB} Software for
                 Limited-memory {SR1} Trust-region Methods",
  journal =      j-TOMS,
  volume =       "48",
  number =       "4",
  pages =        "48:1--48:??",
  month =        dec,
  year =         "2022",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3550269",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3550269",
  abstract =     "We present a MATLAB implementation of the symmetric
                 rank-one (SC-SR1) method that solves trust-region
                 subproblems when a limited-memory symmetric rank-one
                 (L-SR1) matrix is used in place of the true Hessian
                 matrix, which can be used for large-scale optimization.
                 The method takes advantage of two shape-changing norms
                 [Burdakov and Yuan 2002; Burdakov et al. 2017] to
                 decompose the trust-region subproblem into two separate
                 problems. Using one of the proposed norms, the
                 resulting subproblems have closed-form solutions.
                 Meanwhile, using the other proposed norm, one of the
                 resulting subproblems has a closed-form solution while
                 the other is easily solvable using techniques that
                 exploit the structure of L-SR1 matrices. Numerical
                 results suggest that the SC-SR1 method is able to solve
                 trust-region subproblems to high accuracy even in the
                 so-called ``hard case.'' When integrated into a
                 trust-region algorithm, extensive numerical experiments
                 suggest that the proposed algorithms perform well, when
                 compared with widely used solvers, such as truncated
                 conjugate-gradients.",
  acknowledgement = ack-nhfb,
  articleno =    "48",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lefevre:2023:ACE,
  author =       "Vincent Lef{\`e}vre and Nicolas Louvet and Jean-Michel
                 Muller and Joris Picot and Laurence Rideau",
  title =        "Accurate Calculation of {Euclidean} Norms Using
                 Double-word Arithmetic",
  journal =      j-TOMS,
  volume =       "49",
  number =       "1",
  pages =        "1:1--1:??",
  month =        mar,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3568672",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3568672",
  abstract =     "We consider the computation of the Euclidean (or $
                 L^2$) norm of an $n$-dimensional vector in
                 floating-point arithmetic. We review the classical
                 solutions used to avoid spurious overflow or underflow
                 and\slash or to obtain very accurate results. We modify
                 a recently published algorithm (that uses double-word
                 arithmetic) to allow for a very accurate solution, free
                 of spurious overflows and underflows. To that purpose,
                 we use a double-word square-root algorithm of which we
                 provide a tight error analysis. The returned $ L^2$
                 norm will be within very slightly more than 0.5 ulp
                 from the exact result, which means that we will almost
                 always provide correct rounding",
  acknowledgement = ack-nhfb,
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Reberol:2023:RTC,
  author =       "Maxence Reberol and Kilian Verhetsel and
                 Fran{\c{c}}ois Henrotte and David Bommes and
                 Jean-Fran{\c{c}}ois Remacle",
  title =        "Robust Topological Construction of All-hexahedral
                 Boundary Layer Meshes",
  journal =      j-TOMS,
  volume =       "49",
  number =       "1",
  pages =        "2:1--2:??",
  month =        mar,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3577196",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3577196",
  abstract =     "We present a robust technique to build a topologically
                 optimal all-hexahedral layer on the boundary of a model
                 with arbitrarily complex ridges and corners. The
                 generated boundary layer mesh strictly respects the
                 geometry of the input surface mesh, and it \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bluhdorn:2023:EBA,
  author =       "Johannes Bl{\"u}hdorn and Max Sagebaum and Nicolas
                 Gauger",
  title =        "Event-Based Automatic Differentiation of {OpenMP} with
                 {OpDiLib}",
  journal =      j-TOMS,
  volume =       "49",
  number =       "1",
  pages =        "3:1--3:??",
  month =        mar,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3570159",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/pvm.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3570159",
  abstract =     "We present the new software OpDiLib, a universal
                 add-on for classical operator overloading AD tools that
                 enables the automatic differentiation (AD) of OpenMP
                 parallelized code. With it, we establish support for
                 OpenMP features in a reverse mode operator \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Amestoy:2023:CSA,
  author =       "Patrick Amestoy and Alfredo Buttari and Nicholas J.
                 Higham and Jean-Yves L'Excellent and Theo Mary and
                 Bastien Vieubl{\'e}",
  title =        "Combining Sparse Approximate Factorizations with
                 Mixed-precision Iterative Refinement",
  journal =      j-TOMS,
  volume =       "49",
  number =       "1",
  pages =        "4:1--4:??",
  month =        mar,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3582493",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3582493",
  abstract =     "The standard LU factorization-based solution process
                 for linear systems can be enhanced in speed or accuracy
                 by employing mixed-precision iterative refinement. Most
                 recent work has focused on dense systems. We
                 investigate the potential of mixed-precision \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Anselmann:2023:GMM,
  author =       "Mathias Anselmann and Markus Bause",
  title =        "A Geometric Multigrid Method for Space-Time Finite
                 Element Discretizations of the {Navier--Stokes}
                 Equations and its Application to {$3$D} Flow
                 Simulation",
  journal =      j-TOMS,
  volume =       "49",
  number =       "1",
  pages =        "5:1--5:??",
  month =        mar,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3582492",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3582492",
  abstract =     "We present a parallelized geometric multigrid (GMG)
                 method, based on the cell-based Vanka smoother, for
                 higher order space-time finite element methods (STFEM)
                 to the incompressible Navier--Stokes equations. The
                 STFEM is implemented as a time marching \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lux:2023:AMM,
  author =       "Thomas Lux and Layne T. Watson and Tyler Chang and
                 William Thacker",
  title =        "{Algorithm 1031}: {MQSI}-Monotone Quintic Spline
                 Interpolation",
  journal =      j-TOMS,
  volume =       "49",
  number =       "1",
  pages =        "6:1--6:??",
  month =        mar,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3570157",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3570157",
  abstract =     "MQSI is a Fortran 2003 subroutine for constructing
                 monotone quintic spline interpolants to univariate
                 monotone data. Using sharp theoretical monotonicity
                 constraints, first and second derivative estimates at
                 data provided by a quadratic facet model are \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Peters:2023:ABC,
  author =       "J{\"o}rg Peters and Kyle Lo and K{\k{e}}stutis
                 Karciauskas",
  title =        "{Algorithm 1032}: Bi-cubic Splines for Polyhedral
                 Control Nets",
  journal =      j-TOMS,
  volume =       "49",
  number =       "1",
  pages =        "7:1--7:??",
  month =        mar,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3570158",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/p/peters-jorg.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3570158",
  abstract =     "For control nets outlining a large class of
                 topological polyhedra, not just tensor-product grids,
                 bi-cubic polyhedral splines form a piecewise
                 polynomial, first-order differentiable space that
                 associates one function with each vertex. Akin to
                 tensor-. \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Quintana-Orti:2023:API,
  author =       "Gregorio Quintana-Ort{\'\i} and Fernando Hernando and
                 Francisco D. Igual",
  title =        "{Algorithm 1033}: Parallel Implementations for
                 Computing the Minimum Distance of a Random Linear Code
                 on Distributed-memory Architectures",
  journal =      j-TOMS,
  volume =       "49",
  number =       "1",
  pages =        "8:1--8:??",
  month =        mar,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3573383",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3573383",
  abstract =     "The minimum distance of a linear code is a key concept
                 in information theory. Therefore, the time required by
                 its computation is very important to many problems in
                 this area. In this article, we introduce a family of
                 implementations of the Brouwer-\ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fahmy:2023:AAA,
  author =       "Thierry Fahmy",
  title =        "{Algorithm 1034}: an Accelerated Algorithm to Compute
                 the {$ Q_n $} Robust Statistic, with Corrections to
                 Constants",
  journal =      j-TOMS,
  volume =       "49",
  number =       "1",
  pages =        "9:1--9:??",
  month =        mar,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3576920",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3576920",
  abstract =     "The robust scale estimator Q$_n$ developed by Croux
                 and Rousseeuw [ 3 ], for the computation of which they
                 provided a deterministic algorithm, has proven to be
                 very useful in several domains including in quality
                 management and time series analysis. It has \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "9",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Li:2023:NRC,
  author =       "Xiaoye S. Li and Paul Lin and Yang Liu and Piyush
                 Sao",
  title =        "Newly Released Capabilities in the Distributed-Memory
                 {SuperLU} Sparse Direct Solver",
  journal =      j-TOMS,
  volume =       "49",
  number =       "1",
  pages =        "10:1--10:??",
  month =        mar,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3577197",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3577197",
  abstract =     "We present the new features available in the recent
                 release of SuperLU_DIST, Version 8.1.1. SuperLU_DIST is
                 a distributed-memory parallel sparse direct solver. The
                 new features include (1) a 3D communication-avoiding
                 algorithm framework that trades off \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "10",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Breiding:2023:CZP,
  author =       "Paul Breiding and Kemal Rose and Sascha Timme",
  title =        "Certifying Zeros of Polynomial Systems Using Interval
                 Arithmetic",
  journal =      j-TOMS,
  volume =       "49",
  number =       "1",
  pages =        "11:1--11:??",
  month =        mar,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3580277",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Mar 23 11:34:59 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3580277",
  abstract =     "We establish interval arithmetic as a practical tool
                 for certification in numerical algebraic geometry. Our
                 software HomotopyContinuation.jl now has a built-in
                 function certify, which proves the correctness of an
                 isolated nonsingular solution to a square system of
                 polynomial equations. The implementation rests on
                 Krawczyk's method. We demonstrate that it dramatically
                 outperforms earlier approaches to certification. We see
                 this contribution as a powerful new tool in numerical
                 algebraic geometry, which can make certification the
                 default and not just an option.",
  acknowledgement = ack-nhfb,
  articleno =    "11",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Horacsek:2023:FAG,
  author =       "Joshua Horacsek and Usman Alim",
  title =        "{FastSpline}: Automatic Generation of Interpolants for
                 Lattice Samplings",
  journal =      j-TOMS,
  volume =       "49",
  number =       "2",
  pages =        "12:1--12:??",
  month =        jun,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3577194",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 29 07:01:00 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3577194",
  abstract =     "Interpolation is a foundational concept in scientific
                 computing and is at the heart of many scientific
                 visualization techniques. There is usually a tradeoff
                 between the approximation capabilities of an
                 interpolation scheme and its evaluation efficiency.
                 \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "12",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ketcheson:2023:CBS,
  author =       "David I. Ketcheson and Hendrik Ranocha",
  title =        "Computing with {B}-series",
  journal =      j-TOMS,
  volume =       "49",
  number =       "2",
  pages =        "13:1--13:??",
  month =        jun,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3573384",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 29 07:01:00 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/julia.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3573384",
  abstract =     "We present BSeries.jl, a Julia package for the
                 computation and manipulation of B-series, which are a
                 versatile theoretical tool for understanding and
                 designing discretizations of differential equations. We
                 give a short introduction to the theory of B-series and
                 associated concepts and provide examples of their use,
                 including method composition and backward error
                 analysis. The associated software is highly performant
                 and makes it possible to work with B-series of high
                 order.",
  acknowledgement = ack-nhfb,
  articleno =    "13",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Borm:2023:DHM,
  author =       "Steffen B{\"o}rm",
  title =        "Distributed {$ \mathcal {H}_2 $}-Matrices for Boundary
                 Element Methods",
  journal =      j-TOMS,
  volume =       "49",
  number =       "2",
  pages =        "14:1--14:??",
  month =        jun,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3582494",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 29 07:01:00 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/fastmultipole.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3582494",
  abstract =     "Standard discretization techniques for boundary
                 integral equations, e.g., the Galerkin boundary element
                 method, lead to large densely populated matrices that
                 require fast and efficient compression techniques like
                 the fast multipole method or hierarchical matrices. If
                 the underlying mesh is very large, running the
                 corresponding algorithms on a distributed computer is
                 attractive, e.g., since distributed computers
                 frequently are cost-effective and offer a high
                 accumulated memory bandwidth.\par

                 Compared to the closely related particle methods, for
                 which distributed algorithms are well-established, the
                 Galerkin discretization poses a challenge, since the
                 supports of the basis functions influence the block
                 structure of the matrix and therefore the flow of data
                 in the corresponding algorithms. This article
                 introduces distributed $ \mathcal {H}_2$-matrices, a
                 class of hierarchical matrices that is closely related
                 to fast multipole methods and particularly well-suited
                 for distributed computing. While earlier efforts
                 required the global tree structure of the $ \mathcal
                 {H}_2$-matrix to be stored in every node of the
                 distributed system, the new approach needs only local
                 multilevel information that can be obtained via a
                 simple distributed algorithm, allowing us to scale to
                 significantly larger systems. Experiments show that
                 this approach can handle very large meshes with more
                 than 130 million triangles efficiently.",
  acknowledgement = ack-nhfb,
  articleno =    "14",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Agullo:2023:TBP,
  author =       "Emmanuel Agullo and Alfredo Buttari and Abdou
                 Guermouche and Julien Herrmann and Antoine Jego",
  title =        "Task-based Parallel Programming for Scalable Matrix
                 Product Algorithms",
  journal =      j-TOMS,
  volume =       "49",
  number =       "2",
  pages =        "15:1--15:??",
  month =        jun,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3583560",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 29 07:01:00 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3583560",
  abstract =     "Task-based programming models have succeeded in
                 gaining the interest of the high-performance
                 mathematical software community because they relieve
                 part of the burden of developing and implementing
                 distributed-memory parallel algorithms in an efficient
                 and \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "15",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Chalkis:2023:TLC,
  author =       "Apostolos Chalkis and Vissarion Fisikopoulos and
                 Marios Papachristou and Elias Tsigaridas",
  title =        "Truncated Log-concave Sampling for Convex Bodies with
                 Reflective {Hamiltonian Monte Carlo}",
  journal =      j-TOMS,
  volume =       "49",
  number =       "2",
  pages =        "16:1--16:??",
  month =        jun,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3589505",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 29 07:01:00 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3589505",
  abstract =     "We introduce Reflective Hamiltonian Monte Carlo
                 (ReHMC), an HMC-based algorithm to sample from a
                 log-concave distribution restricted to a convex body.
                 The random walk is based on incorporating reflections
                 to the Hamiltonian dynamics such that the support
                 \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "16",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kim:2023:HMB,
  author =       "Ki-Tae Kim and Umberto Villa and Matthew Parno and
                 Youssef Marzouk and Omar Ghattas and Noemi Petra",
  title =        "{hIPPYlib-MUQ}: a {Bayesian} Inference Software
                 Framework for Integration of Data with Complex
                 Predictive Models under Uncertainty",
  journal =      j-TOMS,
  volume =       "49",
  number =       "2",
  pages =        "17:1--17:??",
  month =        jun,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3580278",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 29 07:01:00 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3580278",
  abstract =     "Bayesian inference provides a systematic framework for
                 integration of data with mathematical models to
                 quantify the uncertainty in the solution of the inverse
                 problem. However, the solution of Bayesian inverse
                 problems governed by complex forward models \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "17",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fasi:2023:CCL,
  author =       "Massimiliano Fasi and Mantas Mikaitis",
  title =        "{CPFloat}: a {C} Library for Simulating Low-precision
                 Arithmetic",
  journal =      j-TOMS,
  volume =       "49",
  number =       "2",
  pages =        "18:1--18:??",
  month =        jun,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3585515",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 29 07:01:00 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3585515",
  abstract =     "One can simulate low-precision floating-point
                 arithmetic via software by executing each arithmetic
                 operation in hardware and then rounding the result to
                 the desired number of significant bits. For
                 IEEE-compliant formats, rounding requires only standard
                 mathematical library functions, but handling
                 subnormals, underflow, and overflow demands special
                 attention, and numerical errors can cause
                 mathematically correct formulae to behave incorrectly
                 in finite arithmetic. Moreover, the ensuing
                 implementations are not necessarily efficient, as the
                 library functions these techniques build upon are
                 typically designed to handle a broad range of cases and
                 may not be optimized for the specific needs of rounding
                 algorithms. CPFloat is a C library for simulating
                 low-precision arithmetics. It offers efficient routines
                 for rounding, performing mathematical computations, and
                 querying properties of the simulated low-precision
                 format. The software exploits the bit-level
                 floating-point representation of the format in which
                 the numbers are stored and replaces costly library
                 calls with low-level bit manipulations and integer
                 arithmetic. In numerical experiments, the new
                 techniques bring a considerable speedup (typically one
                 order of magnitude or more) over existing alternatives
                 in C, C++, and MATLAB. To our knowledge, CPFloat is
                 currently the most efficient and complete library for
                 experimenting with custom low-precision floating-point
                 arithmetic.",
  acknowledgement = ack-nhfb,
  articleno =    "18",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Reynolds:2023:AFI,
  author =       "Daniel R. Reynolds and David J. Gardner and Carol S.
                 Woodward and Rujeko Chinomona",
  title =        "{ARKODE}: a Flexible {IVP} Solver Infrastructure for
                 One-step Methods",
  journal =      j-TOMS,
  volume =       "49",
  number =       "2",
  pages =        "19:1--19:??",
  month =        jun,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3594632",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 29 07:01:00 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3594632",
  abstract =     "We describe the ARKODE library of one-step time
                 integration methods for ordinary differential equation
                 (ODE) initial-value problems (IVPs). In addition to
                 providing standard explicit and diagonally implicit
                 Runge--Kutta methods, ARKODE supports one-step
                 \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "19",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hager:2023:AGB,
  author =       "William W. Hager and Hongchao Zhang",
  title =        "{Algorithm 1035}: a Gradient-based Implementation of
                 the Polyhedral Active Set Algorithm",
  journal =      j-TOMS,
  volume =       "49",
  number =       "2",
  pages =        "20:1--20:??",
  month =        jun,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3583559",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 29 07:01:00 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3583559",
  abstract =     "The Polyhedral Active Set Algorithm (PASA) is designed
                 to optimize a general nonlinear function over a
                 polyhedron. Phase one of the algorithm is a nonmonotone
                 gradient projection algorithm, while phase two is an
                 active set algorithm that explores faces of \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "20",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Baert:2023:AAA,
  author =       "Wouter Baert and Nick Vannieuwenhoven",
  title =        "{Algorithm 1036}: {ATC}, An Advanced {Tucker}
                 Compression Library for Multidimensional Data",
  journal =      j-TOMS,
  volume =       "49",
  number =       "2",
  pages =        "21:1--21:??",
  month =        jun,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3585514",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 29 07:01:00 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/datacompression.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3585514",
  abstract =     "We present ATC, a C++ library for advanced
                 Tucker-based lossy compression of dense
                 multidimensional numerical data in a shared-memory
                 parallel setting, based on the sequentially truncated
                 higher-order singular value decomposition (ST-HOSVD)
                 and bit plane \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "21",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Bestuzheva:2023:ERT,
  author =       "Ksenia Bestuzheva and Mathieu Besan{\c{c}}on and
                 Wei-Kun Chen and Antonia Chmiela and Tim Donkiewicz and
                 Jasper van Doornmalen and Leon Eifler and Oliver Gaul
                 and Gerald Gamrath and Ambros Gleixner and Leona
                 Gottwald and Christoph Graczyk and Katrin Halbig and
                 Alexander Hoen and Christopher Hojny and Rolf van der
                 Hulst and Thorsten Koch and Marco L{\"u}bbecke and
                 Stephen J. Maher and Frederic Matter and Erik
                 M{\"u}hmer and Benjamin M{\"u}ller and Marc E. Pfetsch
                 and Daniel Rehfeldt and Steffan Schlein and Franziska
                 Schl{\"o}sser and Felipe Serrano and Yuji Shinano and
                 Boro Sofranac and Mark Turner and Stefan Vigerske and
                 Fabian Wegscheider and Philipp Wellner and Dieter
                 Weninger and Jakob Witzig",
  title =        "Enabling Research through the {SCIP Optimization Suite
                 8.0}",
  journal =      j-TOMS,
  volume =       "49",
  number =       "2",
  pages =        "22:1--22:??",
  month =        jun,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3585516",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Jun 29 07:01:00 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3585516",
  abstract =     "The SCIP Optimization Suite provides a collection of
                 software packages for mathematical optimization
                 centered around the constraint integer programming
                 framework SCIP. The focus of this article is on the
                 role of the SCIP Optimization Suite in supporting
                 \ldots{}",
  acknowledgement = ack-nhfb,
  articleno =    "22",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Deshmukh:2023:COP,
  author =       "Sameer Deshmukh and Rio Yokota and George Bosilca",
  title =        "Cache Optimization and Performance Modeling of
                 Batched, Small, and Rectangular Matrix Multiplication
                 on {Intel}, {AMD}, and {Fujitsu} Processors",
  journal =      j-TOMS,
  volume =       "49",
  number =       "3",
  pages =        "23:1--23:??",
  month =        sep,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3595178",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 29 08:05:09 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3595178",
  abstract =     "Factorization and multiplication of dense matrices and
                 tensors are critical, yet extremely expensive pieces of
                 the scientific toolbox. Careful use of low rank
                 approximation can drastically reduce the computation
                 and memory requirements of these operations. In
                 addition to a lower arithmetic complexity, such methods
                 can, by their structure, be designed to efficiently
                 exploit modern hardware architectures. The majority of
                 existing work relies on batched BLAS libraries to
                 handle the computation of many small dense matrices. We
                 show that through careful analysis of the cache
                 utilization, register accumulation using SIMD registers
                 and a redesign of the implementation, one can achieve
                 significantly higher throughput for these types of
                 batched low-rank matrices across a large range of block
                 and batch sizes. We test our algorithm on three CPUs
                 using diverse ISAs --- the Fujitsu A64FX using ARM SVE,
                 the Intel Xeon 6148 using AVX-512, and AMD EPYC 7502
                 using AVX-2, and show that our new batching methodology
                 is able to obtain more than twice the throughput of
                 vendor optimized libraries for all CPU architectures
                 and problem sizes.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "23",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Claus:2023:SAM,
  author =       "Lisa Claus and Pieter Ghysels and Yang Liu and
                 Th{\'a}i Anh Nhan and Ramakrishnan Thirumalaisamy and
                 Amneet Pal Singh Bhalla and Sherry Li",
  title =        "Sparse Approximate Multifrontal Factorization with
                 Composite Compression Methods",
  journal =      j-TOMS,
  volume =       "49",
  number =       "3",
  pages =        "24:1--24:??",
  month =        sep,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3611662",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 29 08:05:09 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3611662",
  abstract =     "This article presents a fast and approximate
                 multifrontal solver for large sparse linear systems. In
                 a recent work by Liu et al., we showed the efficiency
                 of a multifrontal solver leveraging the butterfly
                 algorithm and its hierarchical matrix extension, HODBF
                 (hierarchical off-diagonal butterfly) compression to
                 compress large frontal matrices. The resulting
                 multifrontal solver can attain quasi-linear computation
                 and memory complexity when applied to sparse linear
                 systems arising from spatial discretization of
                 high-frequency wave equations. To further reduce the
                 overall number of operations and especially the
                 factorization memory usage to scale to larger problem
                 sizes, in this article we develop a composite
                 multifrontal solver that employs the HODBF format for
                 large-sized fronts, a reduced-memory version of the
                 nonhierarchical block low-rank format for medium-sized
                 fronts, and a lossy compression format for small-sized
                 fronts. This allows us to solve sparse linear systems
                 of dimension up to $ 2.7 \times $ larger than before
                 and leads to a memory consumption that is reduced by
                 70\% while ensuring the same execution time. The code
                 is made publicly available in GitHub.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "24",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fehling:2023:APG,
  author =       "Marc Fehling and Wolfgang Bangerth",
  title =        "Algorithms for Parallel Generic {\em hp\/}-Adaptive
                 Finite Element Software",
  journal =      j-TOMS,
  volume =       "49",
  number =       "3",
  pages =        "25:1--25:??",
  month =        sep,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3603372",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 29 08:05:09 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3603372",
  abstract =     "The {\em hp\/}-adaptive finite element method ---
                 where one independently chooses the mesh size (h) and
                 polynomial degree (p) to be used on each cell --- has
                 long been known to have better theoretical convergence
                 properties than either h- or p-adaptive methods alone.
                 However, it is not widely used, owing at least in part
                 to the difficulty of the underlying algorithms and the
                 lack of widely usable implementations. This is
                 particularly true when used with continuous finite
                 elements.\par

                 Herein, we discuss algorithms that are necessary for a
                 comprehensive and generic implementation of {\em
                 hp\/}-adaptive finite element methods on
                 distributed-memory, parallel machines. In particular,
                 we will present a multistage algorithm for the unique
                 enumeration of degrees of freedom suitable for
                 continuous finite element spaces, describe
                 considerations for weighted load balancing, and discuss
                 the transfer of variable size data between processes.
                 We illustrate the performance of our algorithms with
                 numerical examples and demonstrate that they scale
                 reasonably up to at least 16,384 message passage
                 interface processes.\par

                 We provide a reference implementation of our algorithms
                 as part of the open source library deal.II.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "25",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Giles:2023:AIC,
  author =       "Michael Giles and Oliver Sheridan-Methven",
  title =        "Approximating Inverse Cumulative Distribution
                 Functions to Produce Approximate Random Variables",
  journal =      j-TOMS,
  volume =       "49",
  number =       "3",
  pages =        "26:1--26:??",
  month =        sep,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3604935",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 29 08:05:09 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/prng.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3604935",
  abstract =     "For random variables produced through the inverse
                 transform method, approximate random variables are
                 introduced, which are produced using approximations to
                 a distribution's inverse cumulative distribution
                 function. These approximations are designed to be
                 computationally inexpensive and much cheaper than
                 library functions, which are exact to within machine
                 precision and, thus, highly suitable for use in Monte
                 Carlo simulations. The approximation errors they
                 introduce can then be eliminated through use of the
                 multilevel Monte Carlo method. Two approximations are
                 presented for the Gaussian distribution: a piecewise
                 constant on equally spaced intervals and a piecewise
                 linear using geometrically decaying intervals. The
                 errors of the approximations are bounded and the
                 convergence demonstrated, and the computational savings
                 are measured for C and C++ implementations.
                 Implementations tailored for Intel and Arm hardware are
                 inspected alongside hardware agnostic implementations
                 built using OpenMP. The savings are incorporated into a
                 nested multilevel Monte Carlo framework with the
                 Euler-Maruyama scheme to exploit the speedups without
                 losing accuracy, offering speed ups by a factor of
                 5--7. These ideas are empirically extended to the
                 Milstein scheme and the non-central $ \chi^2 $
                 distribution for the Cox--Ingersoll--Ross process,
                 offering speedups of a factor of 250 or more.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "26",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Fioravanti:2023:AAM,
  author =       "Massimo Fioravanti and Daniele Cattaneo and Federico
                 Terraneo and Silvano Seva and Stefano Cherubin and
                 Giovanni Agosta and Francesco Casella and Alberto
                 Leva",
  title =        "Array-Aware Matching: Taming the Complexity of
                 Large-Scale Simulation Models",
  journal =      j-TOMS,
  volume =       "49",
  number =       "3",
  pages =        "27:1--27:??",
  month =        sep,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3611661",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 29 08:05:09 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3611661",
  abstract =     "Equation-based modelling is a powerful approach to
                 tame the complexity of large-scale simulation problems.
                 Equation-based tools automatically translate models
                 into imperative languages. When confronted with
                 nowadays' problems, however, well assessed model
                 translation techniques exhibit scalability issues that
                 are particularly severe when models contain very large
                 arrays. In fact, such models can be made very compact
                 by enclosing equations into looping constructs, but
                 reflecting the same compactness into the translated
                 imperative code is nontrivial. In this paper, we face
                 this issue by concentrating on a key step of
                 equations-to-code translation, the equation/variable
                 matching. We first show that an efficient translation
                 of models with (large) arrays needs awareness of their
                 presence, by defining a figure of merit to measure how
                 much the looping constructs are preserved along the
                 translation. We then show that the said figure of merit
                 allows to define an optimal array-aware matching, and
                 as our main result, that the so stated optimal
                 array-aware matching problem is NP-complete. As an
                 additional result, we propose a heuristic algorithm
                 capable of performing array-aware matching in
                 polynomial time. The proposed algorithm can be
                 proficiently used by model translator developers in the
                 implementation of efficient tools for large-scale
                 system simulation.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "27",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Davis:2023:ASG,
  author =       "Timothy A. Davis",
  title =        "{Algorithm 1037: SuiteSparse:GraphBLAS}: Parallel
                 Graph Algorithms in the Language of Sparse Linear
                 Algebra",
  journal =      j-TOMS,
  volume =       "49",
  number =       "3",
  pages =        "28:1--28:??",
  month =        sep,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3577195",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 29 08:05:09 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3577195",
  abstract =     "SuiteSparse:GraphBLAS is a full parallel
                 implementation of the GraphBLAS standard, which defines
                 a set of sparse matrix operations on an extended
                 algebra of semirings using an almost unlimited variety
                 of operators and types. When applied to sparse
                 adjacency matrices, these algebraic operations are
                 equivalent to computations on graphs. A description of
                 the parallel implementation of SuiteSparse:GraphBLAS is
                 given, including its novel parallel algorithms for
                 sparse matrix multiply, addition, element-wise
                 multiply, submatrix extraction and assignment, and the
                 GraphBLAS mask/accumulator operation. Its performance
                 is illustrated by solving the graph problems in the GAP
                 Benchmark and by comparing it with other sparse matrix
                 libraries",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "28",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Roman:2023:ISR,
  author =       "Jose E. Roman and Fernando Alvarruiz and Carmen Campos
                 and Lisandro Dalcin and Pierre Jolivet and Alejandro
                 Lamas Davi{\~n}a",
  title =        "Improvements to \pkg{SLEPc} in Releases 3.14--3.18",
  journal =      j-TOMS,
  volume =       "49",
  number =       "3",
  pages =        "29:1--29:??",
  month =        sep,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3603373",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 29 08:05:09 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3603373",
  abstract =     "This short article describes the main new features
                 added to SLEPc, the Scalable Library for Eigenvalue
                 Problem Computations, in the past two and a half years,
                 corresponding to five release versions. The main
                 novelty is the extension of the SVD module with new
                 problem types, such as the generalized SVD or the
                 hyperbolic SVD. Additionally, many improvements have
                 been incorporated in different parts of the library,
                 including contour integral eigensolvers,
                 preconditioning, and GPU support.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "29",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Papanikos:2023:ICL,
  author =       "Georgios Papanikos and Catherine E. Powell and David
                 J. Silvester",
  title =        "\pkg{IFISS$3$D}: a Computational Laboratory for
                 Investigating Finite Element Approximation in Three
                 Dimensions",
  journal =      j-TOMS,
  volume =       "49",
  number =       "3",
  pages =        "30:1--30:??",
  month =        sep,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3604934",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 29 08:05:09 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3604934",
  abstract =     "IFISS is an established MATLAB finite element software
                 package for studying strategies for solving partial
                 differential equations (PDEs). IFISS3D is a new add-on
                 toolbox that extends IFISS capabilities for elliptic
                 PDEs from two to three space dimensions. The
                 open-source MATLAB framework provides a computational
                 laboratory for experimentation and exploration of
                 finite element approximation and error estimation, as
                 well as iterative solvers. The package is designed to
                 be useful as a teaching tool for instructors and
                 students who want to learn about state-of-the-art
                 finite element methodology. It will also be useful for
                 researchers as a source of reproducible test matrices
                 of arbitrarily large dimension.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "30",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Himpe:2023:EEG,
  author =       "Christian Himpe",
  title =        "\pkg{emgr} --- {EMpirical GRamian} Framework Version
                 5.99",
  journal =      j-TOMS,
  volume =       "49",
  number =       "3",
  pages =        "31:1--31:??",
  month =        sep,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3609860",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Sep 29 08:05:09 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/python.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3609860",
  abstract =     "Version 5.99 of the empirical Gramian framework ---
                 emgr --- completes a development cycle which focused on
                 parametric model order reduction of gas network models
                 while preserving compatibility to the previous
                 development for the application of combined state and
                 parameter reduction for neuroscience network models.
                 Second, new features concerning empirical Gramian
                 types, perturbation design, and trajectory
                 post-processing, as well as a Python version in
                 addition to the default MATLAB / Octave implementation,
                 have been added. This work summarizes these changes,
                 particularly since emgr version 5.4, see Himpe, 2018
                 [Algorithms 11(7): 91], and gives recent as well as
                 future applications, such as parameter identification
                 in systems biology, based on the current feature set.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "31",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Rump:2023:IPP,
  author =       "Siegfried M. Rump",
  title =        "{IEEE-754} Precision-$p$ base-$ \beta $ Arithmetic
                 Implemented in Binary",
  journal =      j-TOMS,
  volume =       "49",
  number =       "4",
  pages =        "32:1--32:??",
  month =        dec,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3596218",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Dec 23 05:40:24 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3596218;
                 https://www.tuhh.de/ti3/paper/rump/Ru23b.pdf",
  abstract =     "We show how an IEEE-754 conformant precision-$p$
                 base-$ \beta $ arithmetic can be implemented based on
                 some binary floating-point and/or integer arithmetic.
                 This includes the four basic operations and square root
                 subject to the five IEEE-754 rounding modes, namely he
                 nearest roundings with roundTiesToEven and
                 roundTiesToAway, the directed roundings downwards and
                 upwards, as well as rounding towards zero. Exceptional
                 values like $ \infty $ or NaN are covered according to
                 the IEEE-754 arithmetic standard.

                 The results of the precision-$p$ base-$ \beta $
                 operations are computed using some underlying
                 precision-$q$ binary arithmetic. We distinguish two
                 cases. When using a precision-$q$ binary integer
                 arithmetic, the base-$ \beta $ precision $p$ is limited
                 for all operations by $ \beta^{2 p} \leq 2^q$, whereas
                 using a precision-$q$ binary floating-point arithmetic
                 imposes stronger limits on the base-$ \beta $
                 precision, namely $ \beta^{2p} \leq 2^q$ for addition
                 and multiplication, $ \beta^{2p} \leq 2^{q - 1}$ for
                 division and $ \beta^{2p} \leq 2^{q - 3}$ for the
                 square root. Those limitations cannot be improved.

                 The algorithms are implemented in a Matlab/Octave
                 flbeta-toolbox with the choice of using uint64 or
                 binary64 as underlying arithmetic. The former allows
                 larger precisions, the latter is advantageous for the
                 square root, whereas computing times are similar. The
                 flbeta-toolbox offers precision-$p$ base-$ \beta $
                 scalar, vector and matrix operations including sparse
                 matrices as well as corresponding interval operations.
                 The base $ \beta $ can be chosen in the range $ \beta $
                 [2,64]. The flbeta-toolbox will be part of Version 13
                 of INTLAB [18], the Matlab/Octave toolbox for reliable
                 computing.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "32",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  remark =       "Received 6 December 2021; revised 10 October 2022;
                 accepted 30 March 2023.",
}

@Article{Axen:2023:MJE,
  author =       "Seth D. Axen and Mateusz Baran and Ronny Bergmann and
                 Krzysztof Rzecki",
  title =        "\pkg{Manifolds.jl}: an Extensible {Julia} Framework
                 for Data Analysis on Manifolds",
  journal =      j-TOMS,
  volume =       "49",
  number =       "4",
  pages =        "33:1--33:??",
  month =        dec,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3618296",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Dec 23 05:40:24 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/julia.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3618296",
  abstract =     "We present the Julia package Manifolds.jl, providing a
                 fast and easy-to-use library of Riemannian manifolds
                 and Lie groups. This package enables working with data
                 defined on a Riemannian manifold, such as the circle,
                 the sphere, symmetric positive definite matrices, or
                 one of the models for hyperbolic spaces. We introduce a
                 common interface, available in \pkg{ManifoldsBase.jl},
                 with which new manifolds, applications, and algorithms
                 can be implemented. We demonstrate the utility of
                 \pkg{Manifolds.jl} using B{\'e}zier splines, an
                 optimization task on manifolds, and principal component
                 analysis on nonlinear data. In a benchmark,
                 \pkg{Manifolds.jl} outperforms all comparable packages
                 for low-dimensional manifolds in speed; over Python and
                 Matlab packages, the improvement is often several
                 orders of magnitude, while over C/C++ packages, the
                 improvement is two-fold. For high-dimensional
                 manifolds, it outperforms all packages except for
                 Tensorflow-Riemopt, which is specifically tailored for
                 high-dimensional manifolds.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "33",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Brigant:2023:PIG,
  author =       "Alice Le Brigant and Jules Deschamps and Antoine
                 Collas and Nina Miolane",
  title =        "Parametric Information Geometry with the Package
                 \pkg{Geomstats}",
  journal =      j-TOMS,
  volume =       "49",
  number =       "4",
  pages =        "34:1--34:??",
  month =        dec,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3627538",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Dec 23 05:40:24 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3627538",
  abstract =     "We introduce the information geometry module of the
                 Python package Geomstats. The module first implements
                 Fisher--Rao Riemannian manifolds of widely used
                 parametric families of probability distributions, such
                 as normal, gamma, beta, Dirichlet distributions, and
                 more. The module further gives the Fisher Rao
                 Riemannian geometry of any parametric family of
                 distributions of interest, given a parameterized
                 probability density function as input. The implemented
                 Riemannian geometry tools allow users to compare,
                 average, interpolate between distributions inside a
                 given family. Importantly, such capabilities open the
                 door to statistics and machine learning on probability
                 distributions. We present the object-oriented
                 implementation of the module along with illustrative
                 examples and show how it can be used to perform
                 learning on manifolds of parametric probability
                 distributions.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "34",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Villar-Sepulveda:2023:CTB,
  author =       "Edgardo Villar-Sep{\'u}lveda and Alan Champneys",
  title =        "Computation of {Turing} Bifurcation Normal Form for
                 $n$-Component Reaction--Diffusion Systems",
  journal =      j-TOMS,
  volume =       "49",
  number =       "4",
  pages =        "35:1--35:??",
  month =        dec,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3625560",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Dec 23 05:40:24 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3625560",
  abstract =     "General expressions are derived for the amplitude
                 equation valid at a Turing bifurcation of a system of
                 reaction--diffusion equations in one spatial dimension,
                 with an arbitrary number of components. The normal form
                 is computed up to fifth order, which \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "35",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Budisa:2023:HSC,
  author =       "Ana Budisa and Xiaozhe Hu and Miroslav Kuchta and
                 Kent-Andr{\'e} Mardal and Ludmil T. Zikatanov",
  title =        "{HAZniCS} --- Software Components for Multiphysics
                 Problems",
  journal =      j-TOMS,
  volume =       "49",
  number =       "4",
  pages =        "36:1--36:??",
  month =        dec,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3625561",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Dec 23 05:40:24 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3625561",
  abstract =     "We introduce the software toolbox HAZniCS for solving
                 interface-coupled multiphysics problems. HAZniCS is a
                 suite of modules that combines the well-known FEniCS
                 framework for finite element discretization with solver
                 and graph library HAZmath. The focus \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "36",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ranocha:2023:EIM,
  author =       "Hendrik Ranocha and Michael Schlottke-Lakemper and
                 Jesse Chan and Andr{\'e}s M. Rueda-Ram{\'\i}rez and
                 Andrew R. Winters and Florian Hindenlang and Gregor J.
                 Gassner",
  title =        "Efficient Implementation of Modern Entropy Stable and
                 Kinetic Energy Preserving Discontinuous {Galerkin}
                 Methods for Conservation Laws",
  journal =      j-TOMS,
  volume =       "49",
  number =       "4",
  pages =        "37:1--37:??",
  month =        dec,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3625559",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Dec 23 05:40:24 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3625559",
  abstract =     "Many modern discontinuous Galerkin (DG) methods for
                 conservation laws make use of summation by parts
                 operators and flux differencing to achieve kinetic
                 energy preservation or entropy stability. While these
                 techniques increase the robustness of DG methods
                 \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "37",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kusch:2023:KRE,
  author =       "Jonas Kusch and Steffen Schotth{\"o}fer and Pia
                 Stammer and Jannick Wolters and Tianbai Xiao",
  title =        "\pkg{KiT-RT}: an Extendable Framework for Radiative
                 Transfer and Therapy",
  journal =      j-TOMS,
  volume =       "49",
  number =       "4",
  pages =        "38:1--38:??",
  month =        dec,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3630001",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Dec 23 05:40:24 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3630001",
  abstract =     "In this article, we present Kinetic Transport Solver
                 for Radiation Therapy (KiT-RT), an open source
                 C++-based framework for solving kinetic equations in
                 therapy applications available at . This software
                 framework aims to \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "38",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Kimiaei:2023:NSM,
  author =       "Morteza Kimiaei and Arnold Neumaier and Parvaneh
                 Faramarzi",
  title =        "New Subspace Method for Unconstrained Derivative-Free
                 Optimization",
  journal =      j-TOMS,
  volume =       "49",
  number =       "4",
  pages =        "39:1--39:??",
  month =        dec,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3618297",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Dec 23 05:40:24 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3618297",
  abstract =     "This article defines an efficient subspace method,
                 called SSDFO, for unconstrained derivative-free
                 optimization problems where the gradients of the
                 objective function are Lipschitz continuous but only
                 exact function values are available. SSDFO employs
                 \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "39",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Lin:2023:AKM,
  author =       "Hao Lin and Hongfu Liu and Junjie Wu and Hong Li and
                 Stephan G{\"u}nnemann",
  title =        "Algorithm 1038: {KCC}: a {MATLAB} Package for
                 $k$-Means-based Consensus Clustering",
  journal =      j-TOMS,
  volume =       "49",
  number =       "4",
  pages =        "40:1--40:??",
  month =        dec,
  year =         "2023",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3616011",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Dec 23 05:40:24 MST 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3616011",
  abstract =     "Consensus clustering is gaining increasing attention
                 for its high quality and robustness. In particular,
                 $k$-means-based Consensus Clustering (KCC) converts the
                 usual computationally expensive problem to a classic
                 $k$-means clustering with generalized utility
                 functions, bringing potentials for large-scale data
                 clustering on different types of data. Despite KCC s
                 applicability and generalizability, implementing this
                 method such as representing the binary dataset in the
                 k-means heuristic is challenging and has seldom been
                 discussed in prior work. To fill this gap, we present a
                 MATLAB package, KCC, that completely implements the KCC
                 framework and utilizes a sparse representation
                 technique to achieve a low space complexity. Compared
                 to alternative consensus clustering packages, the KCC
                 package is of high flexibility, efficiency, and
                 effectiveness. Extensive numerical experiments are also
                 included to show its usability on real-world
                 datasets.",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "40",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Drmac:2024:LID,
  author =       "Zlatko Drmac",
  title =        "A {LAPACK} Implementation of the Dynamic Mode
                 Decomposition",
  journal =      j-TOMS,
  volume =       "50",
  number =       "1",
  pages =        "1:1--1:??",
  month =        mar,
  year =         "2024",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3640012",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Mar 23 16:17:51 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3640012",
  abstract =     "The Dynamic Mode Decomposition (DMD) is a method for
                 computational analysis of nonlinear dynamical systems
                 in data driven scenarios. Based on high fidelity
                 numerical simulations or experimental data, the DMD can
                 be used to reveal the latent structures in \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "1",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Drmac:2024:HDM,
  author =       "Zlatko Drmac",
  title =        "{Hermitian} Dynamic Mode Decomposition --- Numerical
                 Analysis and Software Solution",
  journal =      j-TOMS,
  volume =       "50",
  number =       "1",
  pages =        "2:1--2:??",
  month =        mar,
  year =         "2024",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3641884",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Mar 23 16:17:51 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3641884",
  abstract =     "The Dynamic Mode Decomposition (DMD) is a versatile
                 and increasingly popular method for data driven
                 analysis of dynamical systems that arise in a variety
                 of applications in, e.g., computational fluid dynamics,
                 robotics or machine learning. In the \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "2",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Hascoet:2024:DFR,
  author =       "Laurent Hasco{\"e}t",
  title =        "Data-flow Reversal and Garbage Collection",
  journal =      j-TOMS,
  volume =       "50",
  number =       "1",
  pages =        "3:1--3:??",
  month =        mar,
  year =         "2024",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3627537",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Mar 23 16:17:51 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3627537",
  abstract =     "Data-flow reversal is at the heart of
                 source-transformation reverse algorithmic
                 differentiation (reverse ST-AD), arguably the most
                 efficient way to obtain gradients of numerical models.
                 However, when the model implementation language uses
                 garbage \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "3",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Brehard:2024:EVN,
  author =       "Florent Br{\'e}hard and Nicolas Brisebarre and Mioara
                 Joldes and Warwick Tucker",
  title =        "Efficient and Validated Numerical Evaluation of
                 {Abelian} Integrals",
  journal =      j-TOMS,
  volume =       "50",
  number =       "1",
  pages =        "4:1--4:??",
  month =        mar,
  year =         "2024",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3637550",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Mar 23 16:17:51 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3637550",
  abstract =     "Abelian integrals play a key role in the infinitesimal
                 version of Hilbert's 16th problem. Being able to
                 evaluate such integrals-with guaranteed error bounds-is
                 a fundamental step in computer-aided proofs aimed at
                 this problem. Using interpolation by \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "4",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Alkamper:2024:IPM,
  author =       "Maria Alk{\"a}mper and Jim Magiera and Christian
                 Rohde",
  title =        "An Interface-Preserving Moving Mesh in Multiple Space
                 Dimensions",
  journal =      j-TOMS,
  volume =       "50",
  number =       "1",
  pages =        "5:1--5:??",
  month =        mar,
  year =         "2024",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3630000",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Mar 23 16:17:51 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3630000",
  abstract =     "An interface-preserving moving mesh algorithm in two
                 or higher dimensions is presented. It resolves a moving
                 ( d -1)-dimensional manifold directly within the d
                 -dimensional mesh, which means that the interface is
                 represented by a subset of moving mesh cell-.
                 \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "5",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Alaejos:2024:AAG,
  author =       "Guillermo Alaejos and Adri{\'a}n Castell{\'o} and
                 Pedro Alonso-Jord{\'a} and Francisco D. Igual and
                 H{\'e}ctor Mart{\'\i}nez and Enrique S.
                 Quintana-Ort{\'\i}",
  title =        "{Algorithm 1039}: Automatic Generators for a Family of
                 Matrix Multiplication Routines with {Apache TVM}",
  journal =      j-TOMS,
  volume =       "50",
  number =       "1",
  pages =        "6:1--6:??",
  month =        mar,
  year =         "2024",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3638532",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Mar 23 16:17:51 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3638532",
  abstract =     "We explore the utilization of the Apache TVM open
                 source framework to automatically generate a family of
                 algorithms that follow the approach taken by popular
                 linear algebra libraries, such as GotoBLAS2, BLIS, and
                 OpenBLAS, to obtain high-performance \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "6",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Piazzola:2024:ASG,
  author =       "Chiara Piazzola and Lorenzo Tamellini",
  title =        "{Algorithm 1040}: The {Sparse Grids Matlab Kit} --- a
                 {Matlab} implementation of sparse grids for
                 high-dimensional function approximation and uncertainty
                 quantification",
  journal =      j-TOMS,
  volume =       "50",
  number =       "1",
  pages =        "7:1--7:??",
  month =        mar,
  year =         "2024",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3630023",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Mar 23 16:17:51 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/matlab.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3630023",
  abstract =     "The Sparse Grids Matlab Kit provides a Matlab
                 implementation of sparse grids, and can be used for
                 approximating high-dimensional functions and, in
                 particular, for surrogate-model-based uncertainty
                 quantification. It is lightweight, high-level and easy
                 to \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "7",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}

@Article{Ouermi:2024:AHH,
  author =       "Timbwoga A. J. Ouermi and Robert M. Kirby and Martin
                 Berzins",
  title =        "{Algorithm 1041}: {HiPPIS} --- A High-order
                 Positivity-preserving Mapping Software for Structured
                 Meshes",
  journal =      j-TOMS,
  volume =       "50",
  number =       "1",
  pages =        "8:1--8:??",
  month =        mar,
  year =         "2024",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/3632291",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Mar 23 16:17:51 MDT 2024",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "https://dl.acm.org/doi/10.1145/3632291",
  abstract =     "Polynomial interpolation is an important component of
                 many computational problems. In several of these
                 computational problems, failure to preserve positivity
                 when using polynomials to approximate or map data
                 values between meshes can lead to negative \ldots{}",
  acknowledgement = ack-nhfb,
  ajournal =     "ACM Trans. Math. Softw.",
  articleno =    "8",
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}