@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"
}
@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,
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="}
@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"}
@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",
}
@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",
}
@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",
}
@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/elefunt.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",
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",
bibdate = "Sun Sep 4 20:00:39 1994",
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",
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 = "ϕ -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",
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",
note = "See remark \cite{Chang:2024:RAC}.",
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/bibnet/authors/h/higham-nicholas-john.bib;
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{LeBrigant: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/python.bib;
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
\url{https://github.com/CSMMLab/KiT-RT}. This software
framework aims to provide a collection of classical
deterministic solvers for unstructured meshes that
allow for easy extendability. Therefore, KiT-RT is a
convenient base to test new numerical methods in
various applications and compare them against
conventional solvers. The implementation includes
spherical harmonics, minimal entropy, neural minimal
entropy, and discrete ordinates methods. Solution
characteristics and efficiency are presented through
several test cases ranging from radiation transport to
electron radiation therapy. Due to the variety of
included numerical methods and easy extendability, the
presented open source code is attractive for both
developers, who want a basis to build their numerical
solvers, and users or application engineers, who want
to gain experimental insights without directly
interfering with the codebase.",
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--7:22",
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 se also in realistic applications. The goal of this
paper is to provide an overview of the data structure
and of the mathematical aspects forming the basis of
the software, as well as comparing the current release
of our package to similar available software.",
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",
}
@Article{Scott:2024:ABI,
author = "Jennifer Scott and Miroslav Tuma",
title = "Avoiding Breakdown in Incomplete Factorizations in Low
Precision Arithmetic",
journal = j-TOMS,
volume = "50",
number = "2",
pages = "9:1--9:25",
month = jun,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3651155",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Jul 2 07:51:57 MDT 2024",
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/10.1145/3651155",
abstract = "The emergence of low precision floating-point
arithmetic in computer hardware has led to a resurgence
of interest in the use of mixed precision numerical
linear algebra. For linear systems of equations, there
has been renewed enthusiasm for mixed precision
variants of iterative refinement. We consider the
iterative solution of large sparse systems using
incomplete factorization preconditioners. The focus is
on the robust computation of such preconditioners in
half precision arithmetic and employing them to solve
symmetric positive definite systems to higher precision
accuracy; however, the proposed ideas can be applied
more generally. Even for well-conditioned problems,
incomplete factorizations can break down when small
entries occur on the diagonal during the factorization.
When using half precision arithmetic, overflows are an
additional possible source of breakdown. We examine how
breakdowns can be avoided and implement our strategies
within new half precision Fortran sparse incomplete
Cholesky factorization software. Results are reported
for a range of problems from practical applications.
These demonstrate that, even for highly ill-conditioned
problems, half precision preconditioners can
potentially replace double precision preconditioners,
although unsurprisingly this may be at the cost of
additional iterations of a Krylov solver.",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "9",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Beaumont:2024:ORM,
author = "Olivier Beaumont and Lionel Eyraud-Dubois and Julien
Herrmann and Alexis Joly and Alena Shilova",
title = "Optimal Re-Materialization Strategies for
Heterogeneous Chains: How to Train Deep Neural Networks
with Limited Memory",
journal = j-TOMS,
volume = "50",
number = "2",
pages = "10:1--10:??",
month = jun,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3648633",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Jul 2 07:51:57 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3648633",
abstract = "Training in Feed Forward Deep Neural Networks is a
memory-intensive operation which is usually performed
on GPUs with limited memory capacities. This may force
data scientists to limit the depth of the models or the
resolution of the input data if data \ldots{}",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "10",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Chowdhary:2024:PES,
author = "Abhijit Chowdhary and Shady E. Ahmed and Ahmed Attia",
title = "{PyOED}: an Extensible Suite for Data Assimilation and
Model-Constrained Optimal Design of Experiments",
journal = j-TOMS,
volume = "50",
number = "2",
pages = "11:1--11:??",
month = jun,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3653071",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Jul 2 07:51:57 MDT 2024",
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/10.1145/3653071",
abstract = "This article describes PyOED, a highly extensible
scientific package that enables developing and testing
model-constrained optimal experimental design (OED) for
inverse problems. Specifically, PyOED aims to be a
comprehensive Python toolkit for model-. \ldots{}",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "11",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Chang:2024:RAC,
author = "Tyler H. Chang and Layne T. Watson and Sven Leyffer
and Thomas C. H. Lux and Hussain M. J. Almohri",
note = "See \cite{Chang:2020:ADI}.",
title = "Remark on {Algorithm 1012}: Computing Projections with
Large Datasets",
journal = j-TOMS,
volume = "50",
number = "2",
pages = "12:1--12:??",
month = jun,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3656581",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Jul 2 07:51:57 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3656581",
abstract = "In ACM TOMS Algorithm 1012, the DELAUNAYSPARSE
software is given for performing Delaunay interpolation
in medium to high dimensions. When extrapolating
outside the convex hull of the training set,
DELAUNAYSPARSE calls the nonnegative least squares
solver DWNNLS to compute projections onto the convex
hull. However, DWNNLS and many other available
sum-of-squares optimization solvers were not intended
for usage with many variable problems, which result
from the large training sets that are typical in
machine learning applications. Thus, a new PROJECT
subroutine is given, based on the highly customizable
quadratic program solver BQPD. This solution is shown
to be as robust as DELAUNAYSPARSE for projection onto
both synthetic and real-world datasets, where other
available solvers frequently fail. Although it is
intended as an update for DELAUNAYSPARSE, due to the
difficulty and prevalence of the problem, this solution
is likely to be of external interest as well.",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "12",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Eftekhari:2024:ASP,
author = "Aryan Eftekhari and Lisa Gaedke-Merzh{\"a}user and
Dimosthenis Pasadakis and Matthias Bollh{\"o}fer and
Simon Scheidegger and Olaf Schenk",
title = "{Algorithm 1042}: Sparse Precision Matrix Estimation
with {SQUIC}",
journal = j-TOMS,
volume = "50",
number = "2",
pages = "13:1--13:??",
month = jun,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3650108",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Jul 2 07:51:57 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3650108",
abstract = "We present SQUIC, a fast and scalable package for
sparse precision matrix estimation. The algorithm
employs a second-order method to solve the $
\ell_1$-regularized maximum likelihood problem,
utilizing highly optimized linear algebra subroutines.
In \ldots{}",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "13",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Feng:2024:AFR,
author = "Xu Feng and Wenjian Yu and Yuyang Xie and Jie Tang",
title = "{Algorithm 1043}: Faster Randomized {SVD} with Dynamic
Shifts",
journal = j-TOMS,
volume = "50",
number = "2",
pages = "14:1--14:??",
month = jun,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3660629",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Jul 2 07:51:57 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3660629",
abstract = "Aiming to provide a faster and convenient truncated
SVD algorithm for large sparse matrices from real
applications (i.e., for computing a few of the largest
singular values and the corresponding singular
vectors), a dynamically shifted power iteration
\ldots{}",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "14",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Arnaudon:2024:APM,
author = "Alexis Arnaudon and Dominik J. Schindler and Robert L.
Peach and Adam Gosztolai and Maxwell Hodges and Michael
T. Schaub and Mauricio Barahona",
title = "{Algorithm 1044: {PyGenStability}}, a Multiscale
Community Detection with Generalized {Markov}
Stability",
journal = j-TOMS,
volume = "50",
number = "2",
pages = "15:1--15:??",
month = jun,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3651225",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Jul 2 07:51:57 MDT 2024",
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/10.1145/3651225",
abstract = "We present PyGenStability, a general-use Python
software package that provides a suite of analysis and
visualization tools for unsupervised multiscale
community detection in graphs. PyGenStability finds
optimized partitions of a graph at different levels
\ldots{}",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "15",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Helwig:2024:ACD,
author = "Jacob Helwig and Sutanoy Dasgupta and Peng Zhao and
Bani K. Mallick and Debdeep Pati",
title = "{Algorithm 1045}: a Covariate-Dependent Approach to
{Gaussian} Graphical Modeling in {R}",
journal = j-TOMS,
volume = "50",
number = "2",
pages = "16:1--16:??",
month = jun,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3659206",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Tue Jul 2 07:51:57 MDT 2024",
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/10.1145/3659206",
abstract = "Graphical models are used to capture complex
multivariate relationships and have applications in
diverse disciplines such as biology, physics, and
economics. Within this field, Gaussian graphical models
aim to identify the pairs of variables whose dependence
is maintained even after conditioning on the remaining
variables in the data, known as the conditional
dependence structure of the data. There are many
existing software packages for Gaussian graphical
modeling, however, they often make restrictive
assumptions that reduce their flexibility for modeling
data that are not identically distributed. Conversely,
\pkg{covdepGE} is an R implementation of a variational
weighted pseudo-likelihood algorithm for modeling the
conditional dependence structure as a continuous
function of an extraneous covariate. To build on the
efficiency of this algorithm, \pkg{covdepGE} leverages
parallelism and C++ integration with R. Additionally,
\pkg{covdepGE} provides fully-automated and data-driven
hyperparameter specification while maintaining
flexibility for the user to decide key components of
the estimation procedure. Through an extensive
simulation study spanning diverse settings,
\pkg{covdepGE} is demonstrated to be top of its class
in recovering the ground truth conditional dependence
structure while efficiently managing computational
overhead.",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "16",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Rozanski:2024:EGA,
author = "Piotr T. R{\'o}za{\'n}ski",
title = "\pkg{empi}: {GPU}-Accelerated Matching Pursuit with
Continuous Dictionaries",
journal = j-TOMS,
volume = "50",
number = "3",
pages = "17:1--17:??",
month = sep,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3674832",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Oct 28 09:16:22 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3674832",
abstract = "This article introduces an effective approach to
performing matching pursuit calculations with
continuous (quasi-infinite) dictionaries. Simulating
continuous parameter space is accomplished by combining
optimal dictionary construction as introduced
\ldots{}",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "17",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Marzorati:2024:EML,
author = "Denise Marzorati and Joaqu{\'\i}n Fern{\'a}ndez and
Ernesto Kofman",
title = "Efficient Matching in Large {DAE} Models",
journal = j-TOMS,
volume = "50",
number = "3",
pages = "18:1--18:??",
month = sep,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3674831",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Oct 28 09:16:22 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3674831",
abstract = "This article presents a matching algorithm for
bipartite graphs containing repetitive structures and
represented by intension as Set-Based Graphs. Under
certain conditions on the structure of the graphs, the
computational cost of this novel algorithm is
\ldots{}",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "18",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Hou:2024:SSN,
author = "Di Hou and Ling Liang and Kim-Chuan Toh",
title = "A Sparse Smoothing {Newton} Method for Solving
Discrete Optimal Transport Problems",
journal = j-TOMS,
volume = "50",
number = "3",
pages = "19:1--19:??",
month = sep,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3688800",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Oct 28 09:16:22 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3688800",
abstract = "The discrete optimal transport (OT) problem, which
offers an effective computational tool for comparing
two discrete probability distributions, has recently
attracted much attention and played essential roles in
many modern applications. This paper \ldots{}",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "19",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Thompson:2024:AIR,
author = "Ian Thompson",
title = "{Algorithm 1046}: an Improved Recurrence Method for
the Scaled Complex Error Function",
journal = j-TOMS,
volume = "50",
number = "3",
pages = "20:1--20:??",
month = sep,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3688799",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Oct 28 09:16:22 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3688799",
abstract = "Calculation of the scaled complex error function $
w(z) $ by recurrence is discussed, and a new method for
determining the number of steps required to achieve a
given accuracy is introduced. This method is found to
work throughout the complex plane, except for a short
section of the real line, centred at the origin. An
algorithm based on this analysis is implemented; Taylor
series with stored coefficients are used to compute $
w(z) $ in a small region where recurrence is not
efficient. The new algorithm is tested extensively and
found to outperform earlier recurrence-based codes. It
also performs favourably against recent codes based on
other methods.",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "20",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Michele:2024: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 = "50",
number = "3",
pages = "21:1--21:??",
month = sep,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3674833",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Oct 28 09:16:22 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3674833",
abstract = "In this second remark, we present a revised correction
to Algorithm 1010 [A. Orellana and C. De Michele 2020]
with respect to the one already proposed in the remark
on Algorithm 1010 [C. De Michele 2022].",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "21",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Khalighi:2024:AFJ,
author = "Moein Khalighi and Giulio Benedetti and Leo Lahti",
title = "{Algorithm 1047}: {FdeSolver}, a {Julia} Package for
Solving Fractional Differential Equations",
journal = j-TOMS,
volume = "50",
number = "3",
pages = "22:1--22:??",
month = sep,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3680280",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Oct 28 09:16:22 MDT 2024",
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/10.1145/3680280",
abstract = "We introduce FdeSolver, an open-source Julia package
designed to solve fractional-order differential
equations efficiently. The available solutions are
based on product-integration rules,
predictor--corrector algorithms, and the Newton-Raphson
method. The package covers solutions for
one-dimensional equations with orders of positive real
numbers. For higher-dimensional systems, it supports
orders up to one. Incommensurate derivatives are
allowed and defined in the Caputo sense. Here, we
summarize the implementation for a representative class
of problems and compare it with available alternatives
in Julia and MATLAB. Moreover, FdeSolver leverages the
power and flexibility of the Julia environment to offer
enhanced computational performance, and our development
emphasizes adherence to the best practices of open
research software. To highlight its practical utility,
we demonstrate its capability in simulating microbial
community dynamics and modeling the spread of COVID-19.
This latter application involves fitting the order of
derivatives grounded on real-world epidemiological
data. Overall, these results highlight the efficiency,
reliability, and practicality of the FdeSolver Julia
package.",
acknowledgement = ack-nhfb,
ajournal = "ACM Trans. Math. Softw.",
articleno = "22",
fjournal = "ACM Transactions on Mathematical Software (TOMS)",
journal-URL = "https://dl.acm.org/loi/toms",
}
@Article{Fuda:2024:ACC,
author = "Chiara Fuda and Kai Hormann",
title = "{Algorithm 1048}: a {C++} Class for Robust Linear
Barycentric Rational Interpolation",
journal = j-TOMS,
volume = "50",
number = "3",
pages = "23:1--23:??",
month = sep,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3681781",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Mon Oct 28 09:16:22 MDT 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3681781",
abstract = "Barycentric rational interpolation is a recent
interpolation method with several favourable
properties. In this article, we present the BRI class,
which features a new C++ class template that contains
all variables and functions related to linear
\ldots{}",
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{Gillette:2024:ADD,
author = "Andrew Gillette and Eugene Kur",
title = "{Algorithm 1049}: The {Delaunay} Density Diagnostic",
journal = j-TOMS,
volume = "50",
number = "4",
pages = "24:1--24:??",
month = dec,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3700134",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Dec 14 17:48:45 MST 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3700134",
abstract = "Accurate approximation of a real-valued function
depends on two aspects of the available data: the
density of inputs within the domain of interest and the
variation of the outputs over that domain. There are
few methods for assessing whether the density of inputs
is sufficient to identify the relevant variations in
outputs --- i.e., the ``geometric scale'' of the
function --- despite the fact that sampling density is
closely tied to the success or failure of an
approximation method. In this article, we introduce a
general purpose, computational approach to detecting
the geometric scale of real-valued functions over a
fixed domain using a deterministic interpolation
technique from computational geometry. The algorithm is
intended to work on scalar data in moderate dimensions
(2--10). Our algorithm is based on the observation that
a sequence of piecewise linear interpolants will
converge to a continuous function at a quadratic rate
(in norm) if and only if the data are sampled densely
enough to distinguish the feature from noise (assuming
sufficiently regular sampling). We present numerical
experiments demonstrating how our method can identify
feature scale, estimate uncertainty in feature scale,
and assess the sampling density for fixed (i.e.,
static) datasets of input--output pairs. We include
analytical results in support of our numerical findings
and have released lightweight code that can be adapted
for use in a variety of data science settings.",
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{Mejia-Domenzain:2024:ASC,
author = "Lorena Mejia-Domenzain and Jinhao Chen and Christopher
Lourenco and Erick Moreno-Centeno and Timothy A.
Davis",
title = "{Algorithm 1050}: {SPEX} {Cholesky}, {LDL}, and
{Backslash} for Exactly Solving Sparse Linear Systems",
journal = j-TOMS,
volume = "50",
number = "4",
pages = "25:1--25:??",
month = dec,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3700592",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Dec 14 17:48:45 MST 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3700592",
abstract = "SPEX Cholesky, SPEX LDL, and SPEX Backslash are
software packages for exactly solving sparse linear
systems, $ A \mathbf {x} = \mathbf {b} $. SPEX
Cholesky, used for symmetric positive definite (SPD)
systems, computes an integral Cholesky factorization to
solve the system in time proportional to arithmetic
work --- to date the only algorithm for SPD linear
systems with this property. SPEX LDL extends SPEX
Cholesky for symmetric negative definite and symmetric
indefinite matrices with exclusively non-zero leading
principal minors. SPEX Backslash is a general-purpose
exact solver that automatically determines the best
ordering and factorization to exactly solve the system.
Computationally, we test the accuracy of MATLAB sparse
backslash, the state-of-the-art collection of sparse
matrix solvers, revealing it is near perfect for 87\%
of the tested instances. In addition, we show that SPEX
Cholesky outperforms alternate exact solvers in
runtime; specifically, SPEX Cholesky outperforms the
exact solver Linbox and exact LU factorization on 70\%
and 92\% of tested instances, respectively. Each of
SPEX Cholesky, SPEX LDL, and SPEX Backslash is
implemented in C and is accompanied by easy-to-use
Python and MATLAB interfaces. They are distributed via
GitHub, as a component of the SPEX software package,
and as component of SuiteSparse.",
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{Lindquist:2024:GRB,
author = "Neil Lindquist and Piotr Luszczek and Jack Dongarra",
title = "Generalizing Random Butterfly Transforms to Arbitrary
Matrix Sizes",
journal = j-TOMS,
volume = "50",
number = "4",
pages = "26:1--26:??",
month = dec,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3699714",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Dec 14 17:48:45 MST 2024",
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 = "https://dl.acm.org/doi/10.1145/3699714",
abstract = "Parker and L{\^e} introduced random butterfly
transforms (RBTs) as a preprocessing technique to
replace pivoting in dense LU factorization.
Unfortunately, their FFT-like recursive structure
restricts the dimensions of the matrix. Furthermore, on
multinode systems, efficient management of the
communication overheads restricts the matrix's
distribution even more. To remove these limitations, we
have generalized the RBT to arbitrary matrix sizes by
truncating the dimensions of each layer in the
transform. We expanded Parker's theoretical analysis to
generalized RBT, specifically that in exact arithmetic,
Gaussian elimination with no pivoting will succeed with
probability 1 after transforming a matrix with
full-depth RBTs. Furthermore, we experimentally show
that these generalized transforms improve performance
over Parker's formulation by up to 62\% while retaining
the ability to replace pivoting. This generalized RBT
is available in the SLATE numerical software library.",
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{Toledo:2024:AUF,
author = "Sivan Toledo",
title = "{Algorithm 1051}: {UltimateKalman}, Flexible {Kalman}
Filtering and Smoothing Using Orthogonal
Transformations",
journal = j-TOMS,
volume = "50",
number = "4",
pages = "27:1--27:??",
month = dec,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3699958",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Dec 14 17:48:45 MST 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3699958",
abstract = "UltimateKalman is a flexible linear Kalman filter and
smoother implemented in three popular programming
languages: MATLAB, C, and Java. UltimateKalman is a
slight simplification and slight generalization of an
elegant Kalman filter and smoother that was proposed in
1977 by Paige and Saunders. Their algorithm appears to
be numerically superior and more flexible than other
Kalman filters and smoothers, but curiously has never
been implemented or used before. UltimateKalman is
flexible: it can easily handle time-dependent problems,
problems with state vectors whose dimensions vary from
step to step, problems with varying numbers of
observations in different steps (or no observations at
all in some steps), and problems in which the
expectation of the initial state is unknown. The
programming interface of UltimateKalman is broken into
simple building blocks that can be used to construct
filters, single or multi-step predictors, multi-step or
whole-track smoothers, and combinations. The article
describes the algorithm and its implementation as well
as a test suite of examples and tests.",
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{Bouillaguet:2024:AEB,
author = "Charles Bouillaguet",
title = "{Algorithm 1052}: Evaluating a {Boolean} Polynomial on
All Possible Inputs",
journal = j-TOMS,
volume = "50",
number = "4",
pages = "28:1--28:??",
month = dec,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3699957",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Dec 14 17:48:45 MST 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3699957",
abstract = "Evaluating a Boolean polynomial on all possible inputs
(i.e., building the truth table of the corresponding
Boolean function) is a simple computational problem
that sometimes appears inside broader applications, for
instance in cryptanalysis or in the implementation of
more sophisticated algorithms to solve Boolean
polynomial systems.\par
Two techniques share the crown to perform this task:
the Fast Exhaustive Search (FES) algorithm from 2010
(which is based on Gray Codes) and the space-efficient
Moebius transform from 2021 (which is reminiscent of
the FFT). Both require operations for a degree-$d$
Boolean polynomial on variables and operate mostly
in-place, but have other slightly different
characteristics. They both provide an efficient
iterator over the full truth table.\par
This article describes BoolEAN POLynomial Evaluation
(BeanPolE), a concise and flexible C library that
implements both algorithms, as well as many other
functions to deal with Boolean multivariate polynomials
in dense representation.",
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{Ge:2024:ASD,
author = "Dongdong Ge and Jinsong Liu and Tianhao Liu and Jiyuan
Tan and Yinyu Ye",
title = "{Algorithm 1053}: {SOLNP+}: a Derivative-Free Solver
for Constrained Nonlinear Optimization",
journal = j-TOMS,
volume = "50",
number = "4",
pages = "29:1--29:??",
month = dec,
year = "2024",
CODEN = "ACMSCU",
DOI = "https://doi.org/10.1145/3699956",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Dec 14 17:48:45 MST 2024",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
URL = "https://dl.acm.org/doi/10.1145/3699956",
abstract = "SOLNP+ is a derivative-free solver for constrained
nonlinear optimization. It starts from SOLve Nonlinear
Programming (SOLNP) proposed in 1989 by Ye. The main
ideas are to use finite difference to approximate the
gradient of the objective function and constraints, and
use augmented Lagrangian method and sequential
quadratic programming to deal with nonlinear
constraints. We incorporate the techniques of implicit
filtering, a new restart mechanism, and a modern
quadratic programming solver into this new version with
an ANSI C implementation. The algorithm exhibits a
great advantage in running time and robustness under
noise compared with the old version implemented in
MATLAB. The numerical experiments show that SOLNP is
comparable with two widely used solvers, COBYLA and
NOMAD. SOLNP is available at
\url{https://github.com/COPT-Public/SOLNP_plus}.",
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",
}
@TechReport{Learmonth:1973:NPS,
author = "G. P. Learmonth and P. A. W. Lewis",
title = "{Naval Postgraduate School} Random Number Generator
Package {LLRANDOM}",
type = "Report",
number = "NP555LW73061A",
institution = "Naval Postgraduate School",
address = "Monterey, CA, USA",
year = "1973",
bibdate = "Thu Jan 05 14:33:09 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "The shuffling algorithm proposed in this report does
{\em not\/} lengthen the period, and only marginally
reduces the lattice structure of linear congruential
generators, despite the apparently tiny difference with
the \cite{Bays:1976:IPR} algorithm: see
\cite{Bays:1990:CIR} for a comparison, both
mathematical, and graphical.",
acknowledgement = ack-nhfb,
}
@Article{Hanson:1981:APE,
author = "David R. Hanson",
title = "{Algorithm 568}: {PDS}\emdash a Portable Directory
System",
journal = j-TOPLAS,
volume = "3",
number = "2",
pages = "162--167",
month = apr,
year = "1981",
CODEN = "ATPSDT",
DOI = "https://doi.org/10.1145/357133.357137",
ISSN = "0164-0925 (print), 1558-4593 (electronic)",
ISSN-L = "0164-0925",
bibdate = "Fri Sep 9 14:11:06 1994",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
acknowledgement = ack-nhfb,
fjournal = "ACM Transactions on Programming Languages and
Systems",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J783",
}
@Article{Bays:1990:CIR,
author = "Carter Bays",
title = "{C364}. {Improving} a random number generator: a
comparison between two shuffling methods",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "36",
number = "1",
pages = "57--59",
month = may,
year = "1990",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949659008811264",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
bibdate = "Tue Feb 7 06:50:18 2012",
bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See \cite{Learmonth:1973:NPS,Bays:1976:IPR} for the
two nearly-identical shuffling algorithms. This paper
explains why the first does not lengthen the generator
period, or much reduce the lattice structure of linear
congruential generators, but the second improves both
dramatically.",
URL = "http://www.tandfonline.com/doi/abs/10.1080/00949659008811264",
acknowledgement = ack-nhfb,
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
keywords = "random number; shuffling",
onlinedate = "20 Mar 2007",
}
@Misc{ACM:2002:CSE,
author = "ACM",
title = "{CALGO} Special Edition {CD}",
howpublished = "CD-ROM organized as a Web site.",
year = "2002",
ISBN = "1-58113-333-2",
ISBN-13 = "978-1-58113-333-2",
bibdate = "Thu Jan 31 05:49:15 2002",
bibsource = "https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "ACM order number 201001.",
price = "US\$99.95 (member), US\$159.95 (nonmember), US\$199.95
(library)",
acknowledgement = ack-nhfb,
}
@Article{Brent:2008:SCC,
author = "Richard P. Brent",
title = "Some Comments on {C. S. Wallace}'s Random Number
Generators",
journal = j-COMP-J,
volume = "51",
number = "5",
pages = "579--584",
month = feb,
year = "2008",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/bxm122",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Sun Apr 26 12:52:31 2009",
bibsource = "https://www.math.utah.edu/pub/tex/bib/prng.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See \cite{Wallace:1996:FPG}.",
abstract = "We outline some of Chris Wallace's contributions to
pseudo-random number generation. In particular, we
consider his recent idea for generating normally
distributed variates without relying on a source of
uniform random numbers and compare it with more
conventional methods for generating normal random
numbers. Implementations of Wallace's idea can be very
fast (approximately as fast as good uniform
generators). We discuss the statistical quality of the
output, and mention how certain pitfalls can be
avoided.",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "Gaussian distribution; maximum-entropy distributions;
normal distribution; orthogonal transformations; random
number generation; Wallace algorithm",
remark = "Wallace's generators produce normal and exponential
distributions directly, without first generation
numbers from a uniform distribution.",
}
@Article{Nakatsukasa:2013:SES,
author = "Yuji Nakatsukasa and Nicholas J. Higham",
title = "Stable and Efficient Spectral Divide and Conquer
Algorithms for the Symmetric Eigenvalue Decomposition
and the {SVD}",
journal = j-SIAM-J-SCI-COMP,
volume = "35",
number = "3",
pages = "A1325--A1349",
month = "????",
year = "2013",
CODEN = "SJOCE3",
DOI = "https://doi.org/10.1137/120876605",
ISSN = "1064-8275 (print), 1095-7197 (electronic)",
ISSN-L = "1064-8275",
MRclass = "65F15",
MRnumber = "3054594",
MRreviewer = "Fatemeh Panjeh Ali Beik",
bibdate = "Fri Jul 19 07:43:53 MDT 2013",
bibsource = "http://epubs.siam.org/sam-bin/dbq/toc/SISC/35/3;
https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "See \cite{Sukkari:2019:QBS}.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Scientific Computing",
journal-URL = "http://epubs.siam.org/sisc",
onlinedate = "January 2013",
}
@Article{Dumas:2014:NRI,
author = "Jean-Guillaume Dumas",
title = "On {Newton--Raphson} Iteration for Multiplicative
Inverses Modulo Prime Powers",
journal = j-IEEE-TRANS-COMPUT,
volume = "63",
number = "8",
pages = "2106--2109",
month = aug,
year = "2014",
CODEN = "ITCOB4",
DOI = "https://doi.org/10.1109/TC.2013.94",
ISSN = "0018-9340 (print), 1557-9956 (electronic)",
ISSN-L = "0018-9340",
bibdate = "Mon Aug 25 08:24:32 2014",
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",
note = "See corrections \cite{Walther:2019:VNR}.",
acknowledgement = ack-nhfb,
fjournal = "IEEE Transactions on Computers",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}
@Article{Du:2021:IES,
author = "Yusong Du and Baoying Fan and Baodian Wei",
title = "An improved exact sampling algorithm for the standard
normal distribution",
journal = j-COMP-STAT,
volume = "37",
number = "??",
pages = "721--737",
month = jul,
year = "2021",
CODEN = "CSTAEB",
DOI = "https://doi.org/10.1007/s00180-021-01136-w",
ISSN = "0943-4062 (print), 1613-9658 (electronic)",
ISSN-L = "0943-4062",
bibdate = "Mon Jan 24 15:06:17 MST 2022",
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 \cite{Karney:2016:SEN}.",
abstract = "In 2016, Karney [\cite{Karney:2016:SEN}] proposed an
exact sampling algorithm for the standard normal
distribution. In this paper, we study the computational
complexity of this algorithm under the random deviate
model. Specifically, Karney's algorithm requires the
access to an infinite sequence of independently and
uniformly random deviates over the range $ (0, 1) $. We
give a theoretical estimate of the expected number of
uniform deviates used by this algorithm until it
completes, and present an improved algorithm with lower
uniform deviate consumption. The experimental results
also shows that our improved algorithm has better
performance than Karney's algorithm.",
acknowledgement = ack-nhfb,
fjournal = "Computational Statistics",
journal-URL = "https://www.springer.com/journal/180",
}