%%% -*-BibTeX-*-
%%% ====================================================================
%%% BibTeX-file{
%%% author-1 = "Nelson H. F. Beebe",
%%% author-2 = "Stefano Foresti",
%%% version = "1.90",
%%% date = "23 September 2023",
%%% time = "14:20:15 MDT",
%%% filename = "golub-gene-h.bib",
%%% address-1 = "University of Utah
%%% Department of Mathematics, 110 LCB
%%% 155 S 1400 E RM 233
%%% Salt Lake City, UT 84112-0090
%%% USA",
%%% address-2 = "Center for High-Performance Computing
%%% University of Utah
%%% Salt Lake City, UT 84112
%%% USA",
%%% telephone-1 = "+1 801 581 5254",
%%% telephone-2 = "+1 801 581 3173",
%%% FAX-1 = "+1 801 581 4148",
%%% FAX-2 = "+1 801 585 5366",
%%% URL-1 = "https://www.math.utah.edu/~beebe",
%%% checksum = "02788 16383 75413 754159",
%%% email-1 = "beebe at math.utah.edu, beebe at acm.org,
%%% beebe at computer.org (Internet)",
%%% email-2 = "stefano at chpc.utah.edu (Internet)",
%%% codetable = "ISO/ASCII",
%%% keywords = "bibliography, linear algebra, numerical
%%% analysis, singular value decomposition, SVD",
%%% license = "public domain",
%%% supported = "yes",
%%% docstring = "This is a fairly complete bibliography of
%%% publications of the late Gene Howard Golub
%%% (February 29, 1932--November 16, 2007).
%%%
%%% Part 1 covers his publications, and Part 2
%%% covers publications about him by others.
%%%
%%% At version 1.88, the year coverage looked
%%% like this:
%%%
%%% 1959 ( 1) 1981 ( 4) 2003 ( 10)
%%% 1960 ( 0) 1982 ( 8) 2004 ( 12)
%%% 1961 ( 2) 1983 ( 8) 2005 ( 14)
%%% 1962 ( 2) 1984 ( 7) 2006 ( 13)
%%% 1963 ( 3) 1985 ( 5) 2007 ( 16)
%%% 1964 ( 1) 1986 ( 4) 2008 ( 11)
%%% 1965 ( 7) 1987 ( 14) 2009 ( 7)
%%% 1966 ( 1) 1988 ( 9) 2010 ( 2)
%%% 1967 ( 2) 1989 ( 14) 2011 ( 2)
%%% 1968 ( 3) 1990 ( 17) 2012 ( 0)
%%% 1969 ( 9) 1991 ( 22) 2013 ( 2)
%%% 1970 ( 7) 1992 ( 16) 2014 ( 0)
%%% 1971 ( 7) 1993 ( 13) 2015 ( 0)
%%% 1972 ( 3) 1994 ( 18) 2016 ( 3)
%%% 1973 ( 16) 1995 ( 8) 2017 ( 0)
%%% 1974 ( 8) 1996 ( 13) 2018 ( 1)
%%% 1975 ( 6) 1997 ( 19) 2019 ( 3)
%%% 1976 ( 13) 1998 ( 10) 2020 ( 1)
%%% 1977 ( 13) 1999 ( 16) 2021 ( 1)
%%% 1978 ( 12) 2000 ( 7) 2022 ( 1)
%%% 1979 ( 19) 2001 ( 9) 2023 ( 3)
%%% 1980 ( 8) 2002 ( 8)
%%%
%%% Article: 284
%%% Book: 28
%%% InBook: 1
%%% InCollection: 21
%%% InProceedings: 62
%%% Misc: 3
%%% PhdThesis: 1
%%% Proceedings: 61
%%% TechReport: 33
%%%
%%% Total entries: 494
%%%
%%% This bibliography was collected from
%%% multiple sources:
%%%
%%% * the authors' own files;
%%% * the TeX User Group bibliography
%%% collection on ftp.math.utah.edu in
%%% /pub/tex/bib;
%%% * the very large Computer Science
%%% bibliography collection on ftp.ira.uka.de
%%% in /pub/bibliography, to which many people
%%% have contributed;
%%% * the ACM Computing Archive CD ROM,
%%% covering literature of the 1980s;
%%% * the IEEE Inspec CD ROMs for 1989--1996;
%%% * Internet library catalogs, including
%%% University of California MELVYL, Stanford
%%% University RLIN, Library of Congress,
%%% OCLC;
%%% * the OCLC Contents1st and Article1st
%%% databases;
%%% * the AMS MathSciNet database;
%%% * Gene Golub's personal curriculum vita
%%% file.
%%%
%%% BibTeX citation tags are uniformly chosen
%%% as name:year:abbrev, where name is the
%%% family name of the first author or editor,
%%% year is a 4-digit number, and abbrev is a
%%% 3-letter condensation of important title
%%% words. Citation tags were automatically
%%% generated by software developed for the
%%% BibNet Project.
%%%
%%% In this bibliography, entries are sorted
%%% first by ascending year, and within each
%%% year, alphabetically by author or editor,
%%% and then, if necessary, by the 3-letter
%%% abbreviation at the end of the BibTeX
%%% citation tag, using the bibsort -byyear
%%% utility.
%%%
%%% The checksum field above contains a CRC-16
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%%% Solovay's checksum utility.",
%%% }
%%% ====================================================================
@Preamble{"\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi"}
%%% ====================================================================
%%% Acknowledgement abbreviations:
@String{ack-do = "Dianne O'Leary,
Department of Computer Science,
University of Maryland,
College Park, MD, USA,
email: \path|oleary@cs.umd.edu|"}
@String{ack-gg = "Grant Gustafson,
Department of Mathematics,
University of Utah,
Salt Lake City, UT 84112, USA,
Tel: +1 801 581 6879,
e-mail: Internet: \path|gustafso@math.utah.edu|"}
@String{ack-nhfb = "Nelson H. F. Beebe,
University of Utah,
Department of Mathematics, 110 LCB,
155 S 1400 E RM 233,
Salt Lake City, UT 84112-0090, USA,
Tel: +1 801 581 5254,
FAX: +1 801 581 4148,
e-mail: \path|beebe@math.utah.edu|,
\path|beebe@acm.org|,
\path|beebe@computer.org| (Internet),
URL: \path|https://www.math.utah.edu/~beebe/|"}
@String{ack-nj = "Norbert Juffa,
2445 Mission College Blvd.
Santa Clara, CA 95054
USA
email: \path=norbert@iit.com="}
@String{ack-sf = "Stefano Foresti,
Center for High-Performance Computing,
University of Utah,
Salt Lake City, UT 84112, USA,
Tel: +1 801 581 3173,
FAX: +1 801 585 5366,
e-mail: \path|stefano@chpc.utah.edu|"}
%%% ====================================================================
%%% Institutional abbreviations:
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@String{inst-ANL:adr = "9700 South Cass Avenue, Argonne, IL
60439-4801, USA"}
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@String{inst-U-MARYLAND-CS = "Department of Computer Science,
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@String{inst-U-MARYLAND-CS:adr = "College Park, MD, USA"}
%%% ====================================================================
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@String{pub-KLUWER:adr = "Norwell, MA, USA, and Dordrecht,
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@String{pub-LONGMAN:adr = "Essex, UK"}
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@String{pub-MATH-ASSOC-AMER:adr = "Washington, DC, USA"}
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@String{pub-NH:adr = "Amsterdam, The Netherlands"}
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@String{pub-OXFORD = "Oxford University Press"}
@String{pub-OXFORD:adr = "Walton Street, Oxford OX2 6DP, UK"}
@String{pub-PHYSICA = "Physica-Verlag"}
@String{pub-PHYSICA:adr = "Wien, Austria"}
@String{pub-PRINCETON = "Princeton University Press"}
@String{pub-PRINCETON:adr = "Princeton, NJ, USA"}
@String{pub-ROCQUENCOURT = "Rocquencourt"}
@String{pub-ROCQUENCOURT:adr = "Centre de Rocquencourt, France"}
@String{pub-SIAM = "Society for Industrial and Applied
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@String{pub-SIAM:adr = "Philadelphia, PA, USA"}
@String{pub-SPARTAN = "Spartan Books"}
@String{pub-SPARTAN:adr = "London, England"}
@String{pub-SV = "Spring{\-}er-Ver{\-}lag"}
@String{pub-SV:adr = "Berlin, Germany~/ Heidelberg,
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@String{pub-TEUBNER = "Teubner"}
@String{pub-TEUBNER:adr = "Stuttgart, Germany; Leipzig, Germany"}
@String{pub-U-ILLINOIS-PRESS = "University of Illinois Press"}
@String{pub-U-ILLINOIS-PRESS:adr = "Urbana, IL, USA"}
@String{pub-US-ARO = "U.S. Army Research Office"}
@String{pub-US-ARO:adr = "Research Triangle Park, NC, USA"}
@String{pub-WATERLOO = "University of Waterloo"}
@String{pub-WATERLOO:adr = "Waterloo, Ontario, Canada"}
@String{pub-WESTERN-PERIODICALS = "Western Periodicals Co.,"}
@String{pub-WESTERN-PERIODICALS:adr = "North Hollywood, CA"}
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@String{pub-WORLD-SCI:adr = "P. O. Box 128, Farrer Road,
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%%% ====================================================================
%%% Series abbreviations:
@String{ser-LNM = "Lecture Notes in Mathematics"}
%%% ====================================================================
%%%
%%% Part 1 (of 2): publications by Gene H. Golub
%%%
%%% Bibliography entries, sorted by year, and then by citation label
%%% (with ``bibsort -byyear''):
@PhdThesis{Golub:1959:UCM,
author = "Gene Howard Golub",
title = "The Use of {Chebyshev} Matrix Polynomials in the
Iterative Solution of Linear Equations Compared to the
Method of Successive Overrelaxation",
type = "Ph.D. Thesis in Mathematics",
school = "Department of Computer Science, University of Illinois
at Urbana-Champaign",
address = "Urbana, IL, USA",
pages = "vi + 134",
month = mar,
year = "1959",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/university-of-illinois-urbana-champagne.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Also published as Technical Report UIUC-DCS-R-59-85.
Abstracted in Dissertation Abstracts, v. 20 (1959), no.
5.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "numerical analysis; numerical calculations; relaxation
methods (mathematics)",
advisor = "Abraham Haskel Taub",
remark = "Gene Golub received a Master's degree with coursework,
but no thesis, in 1954 at UIUC \cite[page
13]{Haigh:2005:IGG}. In that interview, Golub expresses
hard feelings about his thesis advisor.",
}
@Article{Golub:1961:CSIa,
author = "Gene H. Golub and Richard S. Varga",
title = "{Chebyshev} Semi-Iterative Methods, Successive
Overrelaxation Iterative Methods, and Second Order
{Richardson} Iterative Methods. {I}",
journal = j-NUM-MATH,
volume = "3",
number = "1",
pages = "147--156",
month = dec,
year = "1961",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.35",
MRnumber = "26\#3207",
MRreviewer = "J. R. Cannon",
bibdate = "Sun Jan 14 10:09:19 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "nla, relaxation, iter, semi-iterative method,
Richardson's method",
}
@Article{Golub:1961:CSIb,
author = "Gene H. Golub and Richard S. Varga",
title = "{Chebyshev} Semi-Iterative Methods, Successive
Overrelaxation Iterative Methods, and Second Order
{Richardson} Iterative Methods. {II}",
journal = j-NUM-MATH,
volume = "3",
number = "1",
pages = "157--168",
month = dec,
year = "1961",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.35",
MRnumber = "26\#3208",
MRreviewer = "J. R. Cannon",
bibdate = "Sun Jan 14 10:09:24 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "nla, relaxation, iter, semi-iterative method,
Richardson's method",
}
@Article{Golub:1962:BET,
author = "Gene H. Golub",
title = "Bounds for Eigenvalues of Tridiagonal Symmetric
Matrices Computed by the {LR} Method",
journal = j-MATH-COMPUT,
volume = "16",
number = "80",
pages = "438--445",
month = oct,
year = "1962",
CODEN = "MCMPAF",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65.40",
MRnumber = "29 \#732",
MRreviewer = "P. Henrici",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2003134",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Golub:1962:BRE,
author = "Gene H. Golub",
title = "Bounds for the Round-Off Errors in the {Richardson}
Second Order Method",
journal = j-NORDISK-TIDSKR-INFORM-BEHAND,
volume = "2",
number = "4",
pages = "212--223",
month = dec,
year = "1962",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01940168",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65.35",
MRnumber = "29\#2958",
MRreviewer = "A. S. Householder",
bibdate = "Wed Jan 4 18:52:07 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=2&issue=4;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=2&issue=4&spage=212",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "floating-point arithmetic; rounding errors",
}
@Article{Golub:1963:CVM,
author = "Gene H. Golub",
title = "Comparison of the Variance of Minimum Variance and
Weighted Least Squares Regression Coefficients",
journal = j-ANN-MATH-STAT,
volume = "34",
number = "3",
pages = "984--991",
month = sep,
year = "1963",
CODEN = "AASTAD",
DOI = "https://doi.org/10.1214/aoms/1177704021",
ISSN = "0003-4851",
ISSN-L = "0003-4851",
MRclass = "62.55",
MRnumber = "27\#5336",
MRreviewer = "A. C. Cohen",
bibdate = "Sat May 31 09:11:02 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/annmathstat.bib",
URL = "http://projecteuclid.org/euclid.aoms/1177704021",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Annals of Mathematical Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aoms/",
}
@Article{Golub:1963:LBR,
author = "Gene H. Golub",
title = "On a Lower Bound for the Rank of a Partitioned Square
Matrix",
journal = j-MATH-COMPUT,
volume = "17",
number = "82",
pages = "186--188",
month = apr,
year = "1963",
CODEN = "MCMPAF",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "15.05",
MRnumber = "28\#1209",
MRreviewer = "Ky Fan",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2003639",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Golub:1963:RBG,
author = "Gene H. Golub",
title = "Review: {{\booktitle{A Guide to ALGOL Programming}},
by Daniel D. McCracken}",
journal = j-J-AM-STAT-ASSOC,
volume = "58",
number = "304",
pages = "1202--1202",
month = dec,
year = "1963",
CODEN = "JSTNAL",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
bibdate = "Wed Jan 25 08:05:37 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
http://www.jstor.org/journals/01621459.html;
http://www.jstor.org/stable/i314185;
https://www.math.utah.edu/pub/tex/bib/jamstatassoc1960.bib",
URL = "http://www.jstor.org/stable/2283384",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
}
@Article{Golub:1964:RPP,
author = "G. H. Golub",
title = "Recent Publications and Presentations: {{\em An
Introduction to Computational Methods}}, by {K. A.
Redish}",
journal = j-AMER-MATH-MONTHLY,
volume = "71",
number = "10",
pages = "1145--1145",
month = dec,
year = "1964",
CODEN = "AMMYAE",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Mon Jun 28 12:37:42 MDT 1999",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@Article{Businger:1965:LLS,
author = "Peter A. Businger and Gene H. Golub",
title = "Linear Least Squares Solutions by {Householder}
Transformations",
journal = j-NUM-MATH,
volume = "7",
number = "3",
pages = "269--276",
month = jun,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.20",
MRnumber = "31\#862",
bibdate = "Sun Jan 14 10:04:47 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "Also in \cite[pp. 111--118]{Wilkinson:1971:LA}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "Householder transformation; lsq; nla; qrd; software",
}
@Article{Forsythe:1965:SVS,
author = "George E. Forsythe and Gene H. Golub",
title = "On the Stationary Values of a Second-Degree Polynomial
on the Unit Sphere",
journal = j-SIAM,
volume = "13",
number = "4",
pages = "1050--1068",
month = dec,
year = "1965",
CODEN = "JSIMAV",
ISSN = "0368-4245 (print), 1095-712X (electronic)",
MRclass = "65.30",
MRnumber = "MR0195250 (33 \#3453)",
MRreviewer = "A. V. Balakrishnan",
bibdate = "Sun Jan 14 10:01:11 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/siam.bib; JSTOR
database",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
URL = "http://www.jstor.org/stable/2946425",
ZMnumber = "0168.03005",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "forms; linear algebra; nla; updating",
}
@Article{Golub:1965:CSV,
author = "G. H. Golub and W. Kahan",
title = "Calculating the Singular Values and Pseudo-Inverse of
a Matrix",
journal = j-SIAM-J-NUM-ANALYSIS-B,
volume = "2",
number = "2",
pages = "205--224",
month = "????",
year = "1965",
ISSN = "0887-459X (print), 1095-7170 (electronic)",
ISSN-L = "0887-459X",
MRclass = "65.35",
MRnumber = "32 \#587",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR
database",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of the Society for Industrial and Applied
Mathematics: Series B, Numerical Analysis",
journal-URL = "http://epubs.siam.org/loi/sjnaam.1",
keywords = "nla, svd, ginv",
}
@InProceedings{Golub:1965:IRL,
author = "G. H. Golub and J. H. Wilkinson",
title = "Iterative Refinement of Least Square Solution",
crossref = "Kalenich:1965:IPP",
pages = "606--607",
year = "1965",
bibdate = "Wed Apr 13 09:33:42 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, lsq, iterative refinement",
}
@Article{Golub:1965:NMSa,
author = "Gene H. Golub",
title = "Numerical methods for solving linear least squares
problems",
journal = j-APL-MAT,
volume = "10",
number = "??",
pages = "213--216",
month = "????",
year = "1965",
CODEN = "APMTAK",
ISSN = "0373-6725",
MRclass = "65.20",
MRnumber = "31\#5324",
MRreviewer = "W. J. Kotz{\'e}",
bibdate = "Sun Jan 14 10:03:53 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Aplikace Matematiky",
}
@Article{Golub:1965:NMSb,
author = "G. H. Golub",
title = "Numerical Methods for Solving Linear Least Squares
Problems",
journal = j-NUM-MATH,
volume = "7",
number = "3",
pages = "206--216",
month = jun,
year = "1965",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.20",
MRnumber = "31\#5323",
MRreviewer = "W. J. Kotz{\'e}",
bibdate = "Sun Jan 14 10:03:43 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "Householder transformation; lsq; nla; qrd; updating",
}
@Article{Golub:1966:NIR,
author = "G. H. Golub and J. H. Wilkinson",
title = "Note on the Iterative Refinement of Least Squares
Solution",
journal = j-NUM-MATH,
volume = "9",
number = "2",
pages = "139--148",
month = dec,
year = "1966",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.20",
MRnumber = "35 \#3849",
MRreviewer = "W. J. Kotz{\'e}",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "condition; iterative refinement; la; lsq; nla; pert",
}
@Article{Bjorck:1967:API,
author = "{\AA}ke Bj{\"o}rck and Gene H. Golub",
title = "{Algol} programming: Iterative Refinement of Linear
Least Squares Solutions by {Householder}
Transformation",
journal = j-BIT,
volume = "7",
number = "4",
pages = "322--337",
month = dec,
year = "1967",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01939326",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibdate = "Wed Jan 4 18:52:10 MST 2006",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/gvl.bib;
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=7&issue=4;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=7&issue=4&spage=322",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "nla, lsq, iterative refinement, Householder
transformation",
}
@Article{Golub:1967:GBA,
author = "G. H. Golub and T. N. Robertson",
title = "A generalized {Bairstow} algorithm",
journal = j-CACM,
volume = "10",
number = "6",
pages = "371--373",
month = jun,
year = "1967",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.50",
MRnumber = "39 \#2315",
bibdate = "Sat Nov 26 10:31:36 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Bartels:1968:ACS,
author = "Richard H. Bartels and Gene H. Golub",
title = "{Algorithm 328}: {Chebyshev} Solution to An
Overdetermined Linear System [{F4}]",
journal = j-CACM,
volume = "11",
number = "6",
pages = "428--430",
month = jun,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:20:20 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib",
note = "See certification \cite{Schryer:1969:CA}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
editorsnote = "The following algorithm by Barrels and Golub relates
to the paper by the same authors in the Numerical
Analysis department of this issue on pages 401--406
\cite{Bartels:1968:NAS}. This is the first instance of
this type of concurrent publication in Communications
under the policy announced by the Editors of the two
departments, J. G. Herriot and J. F. Traub, in the
March 1967 issue.",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Bartels:1968:NAS,
author = "Richard H. Bartels and Gene H. Golub",
title = "Numerical Analysis: Stable numerical methods for
obtaining the {Chebyshev} solution to an overdetermined
system of equations",
journal = j-CACM,
volume = "11",
number = "6",
pages = "401--406",
month = jun,
year = "1968",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65.35",
MRnumber = "39\#2302",
bibdate = "Thu Dec 08 06:16:41 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib",
note = "See algorithm \cite{Bartels:1968:ACS}.",
abstract = "An implementation of Stiefel's exchange algorithm for
determining a Chebyshev solution to an overdetermined
system of linear equations is presented, that uses
Gaussian LU decomposition with row interchanges. The
implementation is computationally more stable than
those usually given in the literature. A generalization
of Stiefel's algorithm is developed which permits the
occasional exchange of two equations simultaneously.",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "Chebyshev solutions; exchange algorithm; linear
equations; overdetermined linear systems",
}
@Article{Golub:1968:LSS,
author = "G. H. Golub",
title = "Least Squares, Singular Values, and Matrix
Approximations",
journal = j-APL-MAT,
volume = "13",
number = "??",
pages = "44--51",
month = "????",
year = "1968",
CODEN = "APMTAK",
ISSN = "0373-6725",
MRclass = "65.35",
MRnumber = "37 \#4944",
MRreviewer = "L. W. Ehrlich",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Aplikace Matematiky",
keywords = "nla, lsq, regr, svd, Schmidt-Mirsky theorem",
}
@Article{Bartels:1969:ASM,
author = "Richard H. Bartels and Gene H. Golub",
title = "{Algorithm 350}: simplex method procedure employing
{LU} decomposition [{H}]",
journal = j-CACM,
volume = "12",
number = "5",
pages = "275--278",
month = may,
year = "1969",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362946.362982",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Nov 26 10:31:36 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/cacm.bib",
note = "ACM Algorithm 350.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Bartels:1969:SML,
author = "Richard H. Bartels and Gene H. Golub",
title = "The Simplex Method of Linear Programming Using {LU}
Decomposition",
journal = j-CACM,
volume = "12",
number = "5",
pages = "266--268",
month = may,
year = "1969",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/362946.362974",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Nov 26 10:31:36 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/cacm.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "nla, nlop, lud, linear programming, updating",
}
@Article{Businger:1969:AAS,
author = "Peter A. Businger and Gene H. Golub",
title = "{Algorithm 358}: singular value decomposition of a
complex matrix [{F1}, 4, 5]",
journal = j-CACM,
volume = "12",
number = "10",
pages = "564--565",
month = oct,
year = "1969",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Sat Nov 26 10:31:36 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/cacm.bib",
note = "ACM Algorithm 358.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Golub:1969:CGQ,
author = "Gene H. Golub and John H. Welsch",
title = "Calculation of {Gauss} Quadrature Rules",
journal = j-MATH-COMPUT,
volume = "23",
number = "106",
pages = "221--230 + s1--s10",
month = apr,
year = "1969",
CODEN = "MCMPAF",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR
database; Theory/Matrix.bib",
note = "Loose microfiche suppl A1--A10. Reprinted in
\cite{Chan:2007:MMC}.",
URL = "http://www.jstor.org/stable/2004418",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "na, Gaussian quadrature",
}
@TechReport{Golub:1969:MDSa,
author = "G. H. Golub",
title = "Matrix Decompositions and Statistical Calculations",
type = "Technical Report",
number = "124",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
month = "????",
year = "1969",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "stat, nla, lsq, qrd, svd",
}
@InCollection{Golub:1969:MDSb,
author = "G. H. Golub",
title = "Matrix Decompositions and Statistical Computation",
crossref = "Milton:1969:CSC",
pages = "365--397",
year = "1969",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@TechReport{Golub:1969:SVR,
author = "G. H. Golub and R. Underwood",
title = "Stationary Values of the Ratio of Quadratic Forms
Subject to Linear Constraints",
type = "Technical Report",
number = "CS-142",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
month = "????",
year = "1969",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, geig, regularization",
}
@InCollection{Bartels:1970:NTM,
author = "R. H. Bartels and G. H. Golub and M. A. Saunders",
title = "Numerical Techniques in Mathematical Programming",
crossref = "Rosen:1970:SNP",
pages = "123--176",
year = "1970",
MRclass = "90.58 (65.00)",
MRnumber = "42 \#7277",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, qrd, rank determination",
}
@Article{Buzbee:1970:DMS,
author = "B. L. Buzbee and G. H. Golub and C. W. Nielson",
title = "On Direct Methods for Solving {Poisson}'s Equations",
journal = j-SIAM-J-NUMER-ANAL,
volume = "7",
number = "4",
pages = "627--656",
month = dec,
year = "1970",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65.66",
MRnumber = "44 \#4920",
MRreviewer = "G. T. McAllister",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR
database",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "nla, pde, direct Poisson solver, sparse",
}
@InProceedings{Golub:1970:LLS,
author = "G. H. Golub and M. A. Saunders",
title = "Linear Least Squares and Quadratic Programming",
crossref = "Abadie:1970:INP",
pages = "229--256",
year = "1970",
MRclass = "90C20",
MRnumber = "55 \#9983",
bibdate = "Fri Dec 20 16:55:01 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nlop, qrd, lsq, quadratic programming",
}
@Article{Golub:1970:SVD,
author = "G. H. Golub and C. Reinsch",
title = "Singular Value Decomposition and Least Squares
Solutions",
journal = j-NUM-MATH,
volume = "14",
number = "5",
pages = "403--420",
month = apr,
year = "1970",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "Also in \cite[pp. 134--151]{Wilkinson:1971:LA}.
Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Christian H. Reinsch (?? ?? 1932--8 October 2022);
Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "lsq; nla; rank determination; regularization;
software; svd",
}
@Article{Golub:1970:SVR,
author = "Gene H. Golub and Richard Underwood",
title = "Stationary Values of the Ratio of Quadratic Forms
Subject to Linear Constraints",
journal = j-Z-ANGE-MATH-PHYS,
volume = "21",
number = "??",
pages = "319--326 (or 318--326??)",
month = "????",
year = "1970",
MRclass = "65.40",
MRnumber = "42\#7056",
MRreviewer = "J. D. P. Donnelly",
bibdate = "Sun Jan 14 09:57:25 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Buzbee:1971:DSD,
author = "B. L. Buzbee and F. W. Dorr and J. A. George and G. H.
Golub",
title = "The Direct Solution of the Discrete {Poisson} Equation
on Irregular Regions",
journal = j-SIAM-J-NUMER-ANAL,
volume = "8",
number = "4",
pages = "722--736",
month = dec,
year = "1971",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65Q05",
MRnumber = "45 \#1403",
MRreviewer = "J. R. Kuttler",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR
database",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "nla, pde, direct Poisson solver, sparse",
}
@Article{Golub:1971:AAC,
author = "G. H. Golub and L. B. Smith",
title = "{ACM} Algorithm 414: {Chebyshev} Approximation of
Continuous Functions by a {Chebyshev} System of
Functions",
journal = j-CACM,
volume = "14",
number = "11",
pages = "737--746",
month = nov,
year = "1971",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Sep 20 19:46:04 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/cacm.bib",
note = "ACM Algorithm 414.",
acknowledgement = ack-nj,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@InCollection{Golub:1971:DMS,
author = "G. H. Golub",
title = "Direct methods for solving elliptic difference
equations",
crossref = "Morris:1971:STN",
pages = "1--19",
year = "1971",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1971:MMM,
author = "Gene Golub",
title = "Matrix methods in mathematical programming",
journal = j-LECT-NOTES-MATH,
volume = "193",
pages = "21--39",
year = "1971",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0060342",
ISBN = "3-540-05422-7 (print), 3-540-36538-9 (e-book)",
ISBN-13 = "978-3-540-05422-1 (print), 978-3-540-36538-9
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
bibdate = "Fri May 9 19:07:44 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1970.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0060342/",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
book-DOI = "https://doi.org/10.1007/BFb0060340",
book-URL = "http://www.springerlink.com/content/978-3-540-36538-9",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Golub:1971:SME,
author = "G. H. Golub",
title = "Some modified eigenvalue problems",
journal = j-LECT-NOTES-MATH,
volume = "228",
pages = "56--56",
year = "1971",
CODEN = "LNMAA2",
DOI = "https://doi.org/10.1007/BFb0069447",
ISBN = "3-540-05656-4 (print), 3-540-36976-7 (e-book)",
ISBN-13 = "978-3-540-05656-0 (print), 978-3-540-36976-9
(e-book)",
ISSN = "0075-8434 (print), 1617-9692 (electronic)",
ISSN-L = "0075-8434",
bibdate = "Fri May 9 19:07:43 MDT 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/lnm1970.bib",
URL = "http://link.springer.com/chapter/10.1007/BFb0069447",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
book-DOI = "https://doi.org/10.1007/BFb0069442",
book-URL = "http://www.springerlink.com/content/978-3-540-36976-9",
fjournal = "Lecture Notes in Mathematics",
journal-URL = "http://link.springer.com/bookseries/304",
}
@Article{Dahlquist:1972:BEL,
author = "Germund Dahlquist and Stanley C. Eisenstat and Gene H.
Golub",
title = "Bounds for the error of linear systems of equations
using the theory of moments",
journal = j-J-MATH-ANAL-APPL,
volume = "37",
number = "1",
pages = "151--166",
month = jan,
year = "1972",
CODEN = "JMANAK",
DOI = "https://doi.org/10.1016/0022-247X(72)90264-8",
ISSN = "0022-247X (print), 1096-0813 (electronic)",
ISSN-L = "0022-247X",
MRclass = "65F99",
MRnumber = "45 1368",
MRreviewer = "J. G. Herriot",
bibdate = "Sun Jan 14 09:56:10 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of Mathematical Analysis and Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/0022247X",
}
@TechReport{Golub:1972:LAS,
author = "G. H. Golub and R. Underwood and J. H. Wilkinson",
title = "The {Lanczos} Algorithm for the Symmetric {$ A x =
\lambda B x $} Problem",
type = "Technical Report",
number = "STAN-CS-72-270",
institution = "Computer Science, Stanford University",
address = "Stanford, CA",
pages = "24",
month = "????",
year = "1972",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, geig, Lanczos algorithm",
}
@Article{Bjorck:1973:NMC,
author = "{\AA}ke Bj{\"o}rck and Gene H. Golub",
title = "Numerical Methods for Computing Angles between Linear
Subspaces",
journal = j-MATH-COMPUT,
volume = "27",
number = "123",
pages = "579--594",
month = jul,
year = "1973",
CODEN = "MCMPAF",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F30",
MRnumber = "50 1485",
MRreviewer = "J. Legras",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database; Parallel/par.lin.alg.bib;
Theory/Matrix.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
URL = "http://www.jstor.org/stable/2005662",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classcodes = "B0240 (Probability and statistics); B0290H (Linear
algebra); C1140 (Probability and statistics); C4140
(Linear algebra)",
corpsource = "Link{\"o}ping Univ., Sweden",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "angles between linear; canonical; computing;
correlations; matrix algebra; numerical methods;
rectangular matrices; statistics; subspaces",
kwds = "math, nla, gsvd, canonical angles, subspace metric",
treatment = "T Theoretical or Mathematical",
}
@Article{Concus:1973:UFD,
author = "Paul Concus and Gene H. Golub",
title = "Use of Fast Direct Methods for the Efficient Numerical
Solution of Nonseparable Elliptic Equations",
journal = j-SIAM-J-NUMER-ANAL,
volume = "10",
number = "6",
pages = "1103--1120",
month = dec,
year = "1973",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65N05",
MRnumber = "49",
MRreviewer = "P. Laasonen",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/gvl.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2156207",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "nla, fast algorithm, elliptic pde, direct Poisson
solver",
}
@InCollection{Dantzig:1973:NSO,
author = "G. B. Dantzig and R. W. Cottle and B. C. Eaves and G.
H. Golub and F. S. Hillier and A. S. Manne and D. J.
Wilde and R. B. Wilson",
title = "On the need for a {Systems Optimization Laboratory}",
crossref = "Hu:1973:MPP",
pages = "1--32",
year = "1973",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
xxnote = "Is the cross-reference correct?? The original title
Mathematical Programming matches a great many library
catalog entries.",
}
@InProceedings{Golub:1973:CLI,
author = "G. H. Golub and W. Dent",
title = "Computation of the limited information maximum
likelihood estimator",
crossref = "Tarter:1973:PCS",
pages = "60--65",
year = "1973",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1973:CSD,
author = "G. H. Golub and E. Seneta",
title = "Computation of the stationary distribution of an
infinite {Markov} matrix",
journal = j-BULL-AUSTRAL-MATH-SOC,
volume = "8",
number = "??",
pages = "333--341",
month = "????",
year = "1973",
CODEN = "ALNBAB",
ISSN = "0004-9727 (print), 1755-1633 (electronic)",
ISSN-L = "0004-9727",
MRclass = "60J10 (68A10)",
MRnumber = "50 \#8710",
MRreviewer = "I. Vaduva",
bibdate = "Fri Dec 20 17:00:44 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Bulletin of the Australian Mathematical Society",
}
@Article{Golub:1973:DPI,
author = "G. H. Golub and V. Pereyra",
title = "The Differentiation of Pseudo-Inverses and Nonlinear
Least Squares Problems Whose Variables Separate",
journal = j-SIAM-J-NUMER-ANAL,
volume = "10",
number = "2",
pages = "413--432",
month = apr,
year = "1973",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F15",
MRnumber = "49 \#1753",
MRreviewer = "R. P. Tewarson",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR
database",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@InProceedings{Golub:1973:EPR,
author = "Gene H. Golub and Irwin Guttman and Rudolf Dutter",
title = "Examination of pseudo-residuals of outliers for
detecting spurosity in the general univariate linear
model",
crossref = "Kabe:1973:MSI",
pages = "63--108",
year = "1973",
MRclass = "62J05",
MRnumber = "51 9380",
MRreviewer = "Colin L. Mallows",
bibdate = "Sun Jan 14 09:51:59 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1973:NCU,
author = "Gene H. Golub and George P. H. Styan",
title = "Numerical computations for univariate linear models",
journal = j-J-STAT-COMPUT-SIMUL,
volume = "2",
number = "3",
pages = "253--274",
year = "1973",
CODEN = "JSCSAJ",
DOI = "https://doi.org/10.1080/00949657308810051",
ISSN = "0094-9655 (print), 1026-7778 (electronic), 1563-5163",
ISSN-L = "0094-9655",
MRclass = "62J05 (65F05)",
MRnumber = "51 11840",
MRreviewer = "Valery Fedorov",
bibdate = "Tue Apr 22 09:10:34 MDT 2014",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/jstatcomputsimul.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of Statistical Computation and Simulation",
journal-URL = "http://www.tandfonline.com/loi/gscs20",
keywords = "stat, nla, regr, lsq, qrd",
}
@InProceedings{Golub:1973:SAN,
author = "G. H. Golub and George P. H. Styan",
title = "Some aspects of numerical computations for linear
models",
crossref = "Kennedy:1973:PCS",
pages = "189--192",
year = "1973",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1973:SMM,
author = "Gene H. Golub",
title = "Some Modified Matrix Eigenvalue Problems",
journal = j-SIAM-REVIEW,
volume = "15",
number = "2",
pages = "318--334",
month = apr,
year = "1973",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1015032",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65F15",
MRnumber = "48 7569",
MRreviewer = "J. F. Traub",
bibdate = "Thu Mar 27 09:06:49 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/15/2;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available at
\verb=ftp://math.liu.se/pub/references=. Reprinted in
\cite{Chan:2007:MMC}.",
URL = "http://www.jstor.org/stable/2028604",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
error = "conflicting pages with your cv: 318-335",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "nla, eig, updating",
onlinedate = "April 1973",
xxpages = "318--344",
}
@InCollection{Golub:1973:SUL,
author = "G. H. Golub",
title = "Some uses of the {Lanczos} algorithm in numerical
algebra",
crossref = "Miller:1973:TNA",
pages = "173--184",
year = "1973",
MRclass = "65F15",
MRnumber = "50 \#11743",
MRreviewer = "F. Szidarovszky",
bibdate = "Fri Dec 20 17:46:23 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Fischer:1974:FTM,
author = "D. Fischer and G. Golub and O. Hald and C. Leiva and
O. Widlund",
title = "On {Fourier--Toeplitz} Methods for Separable Elliptic
Problems",
journal = j-MATH-COMPUT,
volume = "28",
number = "126",
pages = "349--368",
month = apr,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F05 (65N20)",
MRnumber = "54 \#4072",
MRreviewer = "R. H. Bartels",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classcodes = "B0290P (Differential equations); B0220 (Mathematical
analysis); C4170 (Differential equations)",
corpsource = "New York Univ., NY, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "differential equations; elliptic; fast; fast Fourier
transforms; Fourier Toeplitz method; Fourier transform;
numerical methods; separable elliptic problems;
Toeplitz factorizations",
treatment = "T Theoretical or Mathematical",
}
@Article{Gill:1974:MMM,
author = "P. E. Gill and G. H. Golub and W. Murray and M. A.
Saunders",
title = "Methods for Modifying Matrix Factorizations",
journal = j-MATH-COMPUT,
volume = "28",
number = "126",
pages = "505--535",
month = apr,
year = "1974",
CODEN = "MCMPAF",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F05",
MRnumber = "49 \#8299",
MRreviewer = "L. W. Ehrlich",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database; Theory/Matrix.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)",
corpsource = "Nat. Phys. Lab., Teddington, UK",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Cholesky factors; complete orthogonal factorisation;
matrix algebra; matrix factorizations; rank one
change",
kwds = "math, nla, qrd, lud, updating",
treatment = "T Theoretical or Mathematical",
}
@Article{Golub:1974:BMM,
author = "G. H. Golub",
title = "Bounds for matrix moments",
journal = j-ROCKY-MOUNTAIN-J-MATH,
volume = "4",
number = "2",
pages = "207--211",
month = "????",
year = "1974",
CODEN = "RMJMAE",
DOI = "https://doi.org/10.1216/RMJ-1974-4-2-207",
ISSN = "0035-7596 (print), 1945-3795 (electronic)",
ISSN-L = "0035-7596",
MRclass = "65F30",
MRnumber = "48 12803",
MRreviewer = "Walter Gautschi",
bibdate = "Sun Jan 14 09:54:42 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Proceedings of the International Conference on
Pad{\'e} Approximants, Continued Fractions and Related
Topics (Univ. Colorado, Boulder, Colo., 1972; dedicated
to the memory of H. S. Wall)",
URL = "http://projecteuclid.org/euclid.rmjm/1250130962",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Rocky Mountain Journal of Mathematics",
journal-URL = "http://projecteuclid.org/euclid.rmjm",
}
@Article{Golub:1974:CBS,
author = "G. H. Golub and J. M. Varah",
title = "On a Characterization of the Best $ l_2 $-Scaling of a
Matrix",
journal = j-SIAM-J-NUMER-ANAL,
volume = "11",
number = "3",
pages = "472--479",
month = jun,
year = "1974",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F35 (15A12)",
MRnumber = "55 \#9510",
MRreviewer = "H. Schwerdtfeger",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR
database",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "nla, condition, scaling",
}
@Article{Golub:1974:CSD,
author = "G. H. Golub and E. Seneta",
title = "Computation of the stationary distribution of an
infinite stochastic matrix of special form",
journal = j-BULL-AUSTRAL-MATH-SOC,
volume = "10",
number = "??",
pages = "255--261",
month = "????",
year = "1974",
CODEN = "ALNBAB",
ISSN = "0004-9727 (print), 1755-1633 (electronic)",
ISSN-L = "0004-9727",
MRclass = "60J10",
MRnumber = "51 \#9212",
MRreviewer = "Dean Isaacson",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Bulletin of the Australian Mathematical Society",
}
@InProceedings{Golub:1974:MCE,
author = "G. H. Golub",
title = "Methods for computing eigenvalues of sparse matrix
equations",
crossref = "Pereyra:1974:ADS",
pages = "127--148",
year = "1974",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Book{Miller:1974:TNA,
editor = "John J. H. Miller",
title = "Topics in Numerical Analysis {II}: Proceedings of the
Royal Irish Academy Conference on Numerical Analysis,
1974",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xiv + 266",
year = "1974",
ISBN = "0-12-496952-6",
ISBN-13 = "978-0-12-496952-0",
LCCN = "QA297.R69 1974",
bibdate = "Sat Oct 22 18:09:20 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Concus:1975:GCG,
author = "Paul Concus and Gene H. Golub",
title = "A generalized conjugate gradient method for
non-symmetric systems of linear equations",
crossref = "Glowinski:1975:CMA",
pages = "56--65",
year = "1975",
MRclass = "65F10",
MRnumber = "57 7968",
MRreviewer = "David R. Kincaid",
bibdate = "Sun Jan 14 09:49:28 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@TechReport{Golub:1975:ICE,
author = "G. H. Golub and J. H. Wilkinson",
title = "Ill-Conditioned Eigensystems and the Computation of
the {Jordan} Canonical Form",
type = "Technical Report",
number = "STAN-CS-75-478",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
year = "1975",
bibdate = "Wed Aug 24 16:47:40 2011",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Published as \cite{Golub:1976:ICE}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InCollection{Golub:1975:SMC,
author = "G. H. Golub",
title = "Sparse matrix computations: Eigenvalues and linear
equations",
crossref = "Anonymous:1975:SI",
pages = "117--140",
year = "1975",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1975:WPS,
author = "G. H. Golub and L. Jenning and W. H. Yang",
title = "Waves in periodically structured media",
journal = j-J-COMPUT-PHYS,
volume = "17",
number = "4",
pages = "349--357",
month = apr,
year = "1975",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(75)90039-X",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 09:15:17 MST 2012",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/jcomputphys1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/002199917590039X",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991/",
}
@InProceedings{Cline:1976:CNM,
author = "A. K. Cline and G. H. Golub and G. W. Platzman",
title = "Calculation of Normal Modes of Oceans Using a
{Lanczos} Method",
crossref = "Bunch:1976:SMC",
pages = "409--426",
year = "1976",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, eig, Lanczos algorithm",
}
@TechReport{Concus:1976:GCGa,
author = "P. Concus and G. H. Golub",
title = "A Generalized {Conjugate Gradient} Method for
Nonsymmetric Systems of Linear Equations",
type = "Technical Report",
number = "STAN-CS-76-535",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
month = "????",
year = "1976",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/par.lin.alg.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Concus:1976:GCGb,
author = "Paul Concus and Gene H. Golub and Dianne P. O'Leary",
title = "A Generalized Conjugate Gradient Method for the
Numerical Solution of Elliptic Partial Differential
Equations",
crossref = "Bunch:1976:SMC",
pages = "309--332",
year = "1976",
MRclass = "65F10 (65P05)",
MRnumber = "58",
MRreviewer = "M. R. Hestenes",
bibdate = "Sun Jan 14 09:48:20 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, conjugate gradients, elliptic pde",
}
@TechReport{Concus:1976:NSN,
author = "Paul Concus and Gene H. Golub and Dianne P. O'Leary",
title = "Numerical solutions of nonlinear elliptic partial
differential equations by a generalized conjugate
gradient method",
type = "Technical Report",
number = "STAN-CS-76-585",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "43",
month = "????",
year = "1976",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "differential equations, elliptic --- numerical
solutions",
}
@Article{Golub:1976:CVO,
author = "G. H. Golub and M. Heath and G. Wahba",
title = "Cross-Validation and Optimum Ridge Regression",
journal = j-SIAM-REVIEW,
volume = "18",
number = "4",
pages = "806--806",
month = "????",
year = "1976",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@InCollection{Golub:1976:DPI,
author = "G. H. Golub and V. Pereyra",
title = "Differentiation of Pseudo-Inverses, Separable
Nonlinear Least Squares Problems and Other Tales",
crossref = "Nashed:1976:GIA",
pages = "303--324",
year = "1976",
MRclass = "65F20 (15A09 65J05)",
MRnumber = "58 \#8200",
MRreviewer = "B. Levinger",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1976:ICE,
author = "G. H. Golub and J. H. Wilkinson",
title = "Ill-Conditioned Eigensystems and the Computation of
the {Jordan} Canonical Form",
journal = j-SIAM-REVIEW,
volume = "18",
number = "4",
pages = "578--619",
month = "????",
year = "1976",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1018113",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65F15 (15A21)",
MRnumber = "54 \#1570",
MRreviewer = "Robert Todd Gregory",
bibdate = "Fri Dec 20 17:05:12 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
keywords = "nla, eig, Jordan form, condition, pert,
ill-conditioned problem",
}
@TechReport{Golub:1976:RDLa,
author = "Gene H. Golub and Virginia Klema and G. W. Stewart",
title = "Rank Degeneracy and Least Squares Problems",
type = "Technical Report",
number = "TR-456",
institution = inst-U-MARYLAND,
address = inst-U-MARYLAND:adr,
pages = "????",
month = jun,
year = "1976",
bibdate = "Wed May 28 17:40:15 2014",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/university-of-maryland.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
note = "Also published as Stanford University Computer Science
Department Technical Report STAN-CS-76-559.",
abstract = "This paper is concerned with least squares problems
when the least squares matrix \$A\$ is near a matrix
that is not of full rank. A definition of numerical
rank is given. It is shown that under certain
conditions when \$A\$ has numerical rank \$r\$ there is
a distinguished \$r\$ dimensional subspace of the
column space of \$A\$ that is insensitive to how it is
approximated by \$r\$ independent columns of \$A\$. The
consequences of this fact for the least squares problem
are examined. Algorithms are described for
approximating the stable part of the column space of
\$A\$.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, svd, qrd, condition estimation, rank
determination, pert, variable selection",
xxnote = "Check: is this the same as Golub:1976:RDLb? If so,
which report number is correct??",
}
@TechReport{Golub:1976:RDLb,
author = "G. H. Golub and Virginia Klema and G. W. {Stewart
III}",
title = "Rank Degeneracy and Least Squares Problems",
type = "Report",
number = "TR-751",
institution = inst-CS-U-MARYLAND,
address = inst-CS-U-MARYLAND:adr,
pages = "????",
month = "????",
year = "1976",
bibdate = "Thu May 29 16:12:45 2014",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
gws-number = "N6",
xxnote = "Check: is this the same as Golub:1976:RDLa? If so,
which report number is correct??",
}
@InProceedings{Golub:1976:SVD,
author = "G. H. Golub and F. Luk",
title = "Singular value decomposition: applications and
computations",
crossref = "ARO:1976:PAN",
pages = "??--??",
year = "1976",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Bjorck:1977:EMA,
author = "{\AA}ke Bj{\"o}rck and Gene H. Golub",
title = "Eigenproblems for Matrices Associated with Periodic
Boundary Conditions",
journal = j-SIAM-REVIEW,
volume = "19",
number = "1",
pages = "5--16",
month = jan,
year = "1977",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1019002",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65F15",
MRnumber = "55 1716",
MRreviewer = "B. Levinger",
bibdate = "Sat Mar 29 09:52:39 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/19/1;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
URL = "http://www.jstor.org/stable/2029322",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "January 1977",
}
@TechReport{Boley:1977:IEPa,
author = "D. Boley and Gene H. Golub",
title = "Inverse eigenvalue problems for band matrices",
type = "Technical Report",
number = "STAN-CS-77-623",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "9",
month = "????",
year = "1977",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "eigenvalues; matrices",
}
@InCollection{Boley:1977:IEPb,
author = "D. Boley and G. H. Golub",
title = "Inverse eigenvalue problems for band matrices",
crossref = "Watson:1978:NAP",
pages = "??--??",
month = jun,
year = "1977",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InCollection{Buzbee:1977:VCS,
author = "B. Buzbee and G. Golub and J. Howell",
title = "Vectorizations for the {CRAY-1} of Some Methods for
Solving Elliptic Difference Equations",
crossref = "Kuck:1977:HSC",
pages = "255--271",
year = "1977",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/ovr.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@TechReport{deBoor:1977:NSR,
author = "Carl de Boor and Gene H. Golub",
title = "The numerically stable reconstruction of a {Jacobi}
matrix from spectral data",
type = "Technical Report",
number = "STAN-CS-77-602",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "18",
month = "????",
year = "1977",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "jacobi varieties; matrices",
}
@InCollection{Golub:1977:BLM,
author = "G. H. Golub and R. Underwood",
title = "The Block {Lanczos} Method for Computing Eigenvalues",
crossref = "Rice:1977:MSI",
pages = "364--377 (or 361--377??)",
year = "1977",
MRclass = "65F15",
MRnumber = "57 \#14376",
MRreviewer = "Colette Lebaud",
bibdate = "Fri Dec 20 17:48:35 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, block algorithm, Lanczos algorithm, eig",
}
@TechReport{Golub:1977:GCV,
author = "Gene H. Golub and Michael Heath and Grace Wahba",
title = "Generalized cross-validation as a method for choosing
a good ridge parameter",
type = "Technical Report",
number = "STAN-CS-77-622",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "24",
month = "????",
year = "1977",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Also issued as Dept. of Statistics Technical Report
no. 491, University of Wisconsin, Madison, WI.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "graphic methods; regression analysis",
}
@InProceedings{Golub:1977:TTC,
author = "Gene H. Golub and Franklin T. Luk",
title = "Singular value decomposition: applications and
computations",
crossref = "Army:1977:TTC",
pages = "577--605",
year = "1977",
MRclass = "65F30",
MRnumber = "58 31784",
bibdate = "Sun Jan 14 09:45:27 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Golub:1977:TTS,
author = "Gene H. Golub and Franklin T. Luk",
title = "Singular value decomposition: applications and
computations",
crossref = "Army:1977:TTC",
pages = "577--605",
year = "1977",
MRclass = "65F30",
MRnumber = "58 \#31784",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Boley:1978:IEP,
author = "D. Boley and G. H. Golub",
title = "Inverse eigenvalue problems for band matrices",
crossref = "Watson:1978:NAP",
pages = "23--31",
year = "1978",
MRclass = "65F15",
MRnumber = "57 \#14375",
MRreviewer = "H. Hochstadt",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@TechReport{Boley:1978:MIEa,
author = "D. Boley and Gene H. Golub",
title = "The Matrix Inverse Eigenvalue Problem for Periodic
{Jacobi} Matrices",
type = "Technical Report",
number = "STAN-CS-78-684",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "[5] + 14",
month = "????",
year = "1978",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "eigenvalues; matrices",
}
@InProceedings{Boley:1978:MIEb,
author = "D. L. Boley and G. H. Golub",
title = "The Matrix Inverse Eigenvalue Problem for Periodic
{Jacobi} Matrices",
crossref = "Marek:1978:PFS",
pages = "63--76",
year = "1978",
MRclass = "15A21 (58F07 65F15 65F30)",
MRnumber = "81e:15005",
MRreviewer = "J. S. Joel",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Concus:1978:NSN,
author = "P. Concus and G. H. Golub and D. P. O'Leary",
title = "Numerical Solution of Nonlinear Elliptic Partial
Differential Equations by a Generalized Conjugate
Gradient Method",
journal = j-COMPUTING,
volume = "19",
number = "4",
pages = "321--339",
month = "????",
year = "1978",
CODEN = "CMPTA2",
DOI = "https://doi.org/10.1007/BF02252030",
ISSN = "0010-485X (print), 1436-5057 (electronic)",
ISSN-L = "0010-485X",
MRclass = "65H10 (65N99)",
MRnumber = "58 \#31799",
MRreviewer = "L. Hageman",
bibdate = "Fri Dec 20 17:41:37 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Computing: Archiv f{\"u}r informatik und numerik",
journal-URL = "http://link.springer.com/journal/607",
keywords = "nla, conjugate gradients",
}
@Article{Cottle:1978:SLS,
author = "Richard W. Cottle and Gene H. Golub and Richard S.
Sacher",
title = "On the solution of large structured linear
complementarity problems: the block partitioned case",
journal = j-APPL-MATH-OPTIM,
volume = "4",
number = "4",
pages = "347--363",
month = "????",
year = "1978",
CODEN = "AMOMBN",
ISSN = "0095-4616 (print), 1432-0606 (electronic)",
ISSN-L = "0095-4616",
MRclass = "90C30 (90C05)",
MRnumber = "80a:90120",
bibdate = "Mon Jan 15 09:15:16 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Applied Mathematics and Optimization",
journal-URL = "http://link.springer.com/journal/245",
}
@Article{deBoor:1978:NSR,
author = "C. de Boor and G. H. Golub",
title = "The numerically stable reconstruction of a {Jacobi}
matrix from spectral data",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "21",
number = "3",
pages = "245--260",
month = sep,
year = "1978",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A18 (15A57)",
MRnumber = "80i:15007",
MRreviewer = "O. Pokorn{\'a}",
bibdate = "Tue Feb 16 18:50:27 MST 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/linala1970.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
URL = "http://www.sciencedirect.com/science/article/pii/0024379578900861",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@TechReport{Golub:1978:SHM,
author = "G. H. Golub and S. Nash and C. {Van Loan}",
title = "A {Schur-Hessenberg} Method for the Problem {$ {Ax +
xB = C} $}",
type = "Technical Report",
number = "TR 78-354",
institution = inst-CORNELL,
address = inst-CORNELL:adr,
month = oct,
year = "1978",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/cornell-university.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "mailto::lmc@cs.cornell.edu",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@TechReport{Golub:1978:UPD,
author = "G. H. Golub and C. {Van Loan}",
title = "Unsymmetric Positive Definite Linear Systems",
type = "Technical Report",
number = "TR 78-352",
institution = inst-CORNELL,
address = inst-CORNELL:adr,
month = sep,
year = "1978",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/cornell-university.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "mailto::lmc@cs.cornell.edu",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{VanLoan:1978:SUP,
author = "C. {Van Loan} and G. H. Golub",
title = "Solving Unsymmetric Positive Definite Linear Systems",
journal = j-SIAM-REVIEW,
volume = "20",
number = "3",
pages = "636--636",
month = "????",
year = "1978",
CODEN = "SIREAD",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Fri Jun 21 11:25:02 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Bauer:1979:ES,
author = "F. L. Bauer and G. H. Golub and A. S. Householder and
K. Samelson",
title = "{Eduard L. Stiefel}: 4/21/1909--11/27/1978",
journal = j-NUM-MATH,
volume = "32",
number = "4",
pages = "480--481",
month = dec,
year = "1979",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "01A70",
MRnumber = "82e:01083",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "With a German translation.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@InProceedings{Dahlquist:1979:BEL,
author = "Germund Dahlquist and Gene H. Golub and Stephen G.
Nash",
title = "Bounds for the error in linear systems",
crossref = "Hettich:1979:SIP",
pages = "154--172",
year = "1979",
MRclass = "65F10 (90C05)",
MRnumber = "154--172",
MRreviewer = "Jacques Dubois",
bibdate = "Sun Jan 14 09:41:57 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Dahlquist:1979:SIP,
author = "Germund Dahlquist and Gene H. Golub and Stephen G.
Nash",
title = "Bounds for the error in linear systems",
crossref = "Hettich:1979:SIP",
pages = "154--172",
year = "1979",
MRclass = "65F10 (90C05)",
MRnumber = "81b:65028",
MRreviewer = "Jacques Dubois",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Golub:1979:CMA,
author = "Gene H. Golub and Robert J. Plemmons",
title = "Sparse least squares problems",
crossref = "Glowinski:1979:CMA",
pages = "489--496",
year = "1979",
MRclass = "65F05",
MRnumber = "82a:65025",
MRreviewer = "D. S. Henderson",
bibdate = "Sun Jan 14 08:25:42 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1979:DSE,
author = "G. H. Golub and W. Langlois",
title = "Direct solution of the equation for the {Stokes}
stream function",
journal = j-COMPUT-METH-APPL-MECH-ENG,
volume = "19",
number = "3",
pages = "391--399",
month = sep,
year = "1979",
CODEN = "CMMECC",
DOI = "https://doi.org/10.1016/0045-7825(79)90066-5",
ISSN = "0045-7825 (print), 1879-2138 (electronic)",
ISSN-L = "0045-7825",
MRclass = "76D05 (65P05)",
MRnumber = "82c:76029",
MRreviewer = "C. Taylor",
bibdate = "Fri Dec 20 17:07:23 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
ajournal = "Comp. Methods in Appl. Mech. and Engrg.",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Computer Methods in Applied Mechanics and
Engineering",
journal-URL = "http://www.sciencedirect.com/science/journal/00457825",
}
@InProceedings{Golub:1979:EUV,
author = "Gene H. Golub and Randall J. LeVeque",
title = "Extensions and Uses of the Variable Projection
Algorithm for Solving Nonlinear Least Squares
Problems",
crossref = "ARO:1979:PAN",
pages = "1--12",
year = "1979",
MRclass = "65F20",
MRnumber = "81b:65036",
bibdate = "Sun Jan 14 09:40:39 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nlop, nllsq",
}
@Article{Golub:1979:GCV,
author = "Gene H. Golub and Michael T. Heath and Grace Wahba",
title = "Generalized Cross-Validation as a Method for Choosing
a Good Ridge Parameter",
journal = j-TECHNOMETRICS,
volume = "21",
number = "2",
pages = "215--223",
month = may,
year = "1979",
CODEN = "TCMTA2",
DOI = "https://doi.org/10.1080/00401706.1979.10489751",
ISSN = "0040-1706 (print), 1537-2723 (electronic)",
ISSN-L = "0040-1706",
MRclass = "62J07",
MRnumber = "81e:62079",
MRreviewer = "Colin L. Mallows",
bibdate = "Sun Jan 14 09:39:58 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available at
\verb=ftp://math.liu.se/pub/references=. Reprinted in
\cite{Chan:2007:MMC}.",
URL = "http://www.jstor.org/stable/1268518",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Technometrics",
journal-URL = "http://www.jstor.org/journals/00401706.html;
http://www.tandfonline.com/loi/utch20",
keywords = "nla, stat, ridge regression, cross validation,
regularization",
}
@TechReport{Golub:1979:HSMa,
author = "Gene H. Golub and Stephen Nash and Charles F. {Van
Loan}",
title = "A {Hessenberg--Schur} method for the problem {$ {AX +
XB = C} $}",
type = "Technical Report",
number = "STAN-CS-79-713",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "50",
month = "????",
year = "1979",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "matrix mechanics; numerical analysis",
}
@Article{Golub:1979:HSMb,
author = "G. H. Golub and S. Nash and C. {Van Loan}",
title = "A {Hessenberg--Schur} Method for the Matrix Problem {$
A X + X B = C $}",
journal = j-IEEE-TRANS-AUTOMAT-CONTR,
volume = "24",
number = "6",
pages = "909--913",
month = "????",
year = "1979",
CODEN = "IETAA9",
DOI = "https://doi.org/10.1109/TAC.1979.1102170",
ISSN = "0018-9286 (print), 1558-2523 (electronic)",
ISSN-L = "0018-9286",
MRclass = "65F30 (93C05)",
MRnumber = "81a:65046",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "IEEE Transactions on Automatic Control",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9",
keywords = "nla, Sylvester equation, Hessenberg matrix, Schur
form, Lyapunov equation, matrix equation",
}
@InProceedings{Golub:1979:LSL,
author = "G. H. Golub and F. Luk and M. Pagano",
title = "A large sparse least squares problem in
photogrammetry",
crossref = "Gentleman:1979:PCS",
pages = "??--??",
year = "1979",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Golub:1979:SLS,
author = "G. H. Golub and R. Plemmons",
title = "Sparse least squares problems",
crossref = "ISCMASE:1979:PIF",
pages = "??--??",
year = "1979",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InProceedings{Golub:1979:TLS,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Total least squares",
crossref = "Gasser:1979:STC",
pages = "69--76",
year = "1979",
MRclass = "65D10 (65U05)",
MRnumber = "82a:65013",
MRreviewer = "Valery Fedorov",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "nla, svd, total least squares",
}
@Article{Golub:1979:UPD,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Unsymmetric Positive Definite Linear Systems",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "28",
number = "??",
pages = "85--97",
month = dec,
year = "1979",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(79)90122-8",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A23 (65F05)",
MRnumber = "80k:15016",
MRreviewer = "Colette Lebaud",
bibdate = "Tue Feb 16 18:50:44 MST 2016",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/linala1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0024379579901228",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
keywords = "nla, linear system, positive definite matrix,
nonsymmetric matrix",
}
@TechReport{Golub:1980:ATLa,
author = "G. H. Golub and C. F. {Van Loan}",
title = "An Analysis of the Total Least Squares Problem",
type = "Technical Report",
number = "80-411",
institution = inst-CORNELL,
address = inst-CORNELL:adr,
month = feb,
year = "1980",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/cornell-university.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "mailto::lmc@cs.cornell.edu",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1980:ATLb,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "An Analysis of the Total Least Squares Problem",
journal = j-SIAM-J-NUMER-ANAL,
volume = "17",
number = "6",
pages = "883--893",
month = dec,
year = "1980",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0717073",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65D10",
MRnumber = "83g:65020",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR
database",
note = "Reprinted in \cite{Chan:2007:MMC}.",
URL = "http://www.jstor.org/stable/2156807",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "statistics, least squares, math, nla, lsq, svd, deriv,
total least squares",
}
@Article{Golub:1980:LSG,
author = "Gene H. Golub and Robert J. Plemmons",
title = "Large-Scale Geodetic Least-Squares Adjustment by
Dissection and Orthogonal Decomposition",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "34",
pages = "3--28",
month = dec,
year = "1980",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(80)90156-1",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "86A30 (15A23 65F10)",
MRnumber = "81k:86010",
MRreviewer = "K. R. Koch",
bibdate = "Sun Jan 14 09:38:35 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
keywords = "nla, lsq, sparse, geodesy, qrd",
}
@Book{Golub:1980:NA,
editor = "Gene H. Golub and Joseph Oliger",
booktitle = "Numerical Analysis",
title = "Numerical Analysis",
volume = "22",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "viii + 135",
year = "1980",
DOI = "https://doi.org/10.1090/psapm/022",
ISBN = "0-8218-0122-8, 0-8218-9237-1 (e-book)",
ISBN-13 = "978-0-8218-0122-2, 978-0-8218-9237-4 (e-book)",
LCCN = "QA1 .S93 v.22",
MRclass = "65-06",
MRnumber = "80c:65007",
bibdate = "Sun Jan 14 09:43:24 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/m/moler-cleve-b.bib",
series = "Proceedings of symposia in applied mathematics",
acknowledgement = ack-nhfb,
annote = "Reprinted with corrections, 1980. Lecture notes
prepared for the American Mathematical Society Short
Course on Numerical Analysis, held in Atlanta, Georgia,
January 3--4, 1978.",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "Numerical analysis.",
tableofcontents = "Preface / vii \\
Three research problems in numerical linear algebra /
Cleve B. Moler / 1 \\
A brief introduction to quasi-Newton methods / J. E.
Dennis / 19 \\
The approximation of functions and linear functionals:
Best vs. good approximation / Carl de Boor / 53 \\
Numerical methods for the solution of ordinary
differential equations / James M. Varah / 71 \\
Methods for time dependent partial differential
equations / Joseph E. Oliger / 87 \\
Variational methods for elliptic boundary value
problems / George J. Fix / 109",
}
@Article{Golub:1980:RSD,
author = "G. Golub and V. Klema and S. C. Peters",
title = "Rules and Software for Detecting Rank Degeneracy",
journal = j-J-ECONOMETRICS,
volume = "12",
number = "1",
pages = "41--48",
month = "????",
year = "1980",
CODEN = "JECMB6",
DOI = "https://doi.org/10.1016/0304-4076(80)90051-2",
ISSN = "0304-4076 (print), 1872-6895 (electronic)",
ISSN-L = "0304-4076",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of Econometrics",
journal-URL = "http://www.sciencedirect.com/science/journal/03044076",
}
@InProceedings{Golub:1980:SLS,
author = "Gene H. Golub and Robert J. Plemmons",
title = "Sparse least squares problems",
crossref = "Glowinski:1980:CMA",
pages = "489--496",
year = "1980",
MRclass = "65F05",
MRnumber = "82a:65025",
MRreviewer = "D. S. Henderson",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Ward:1980:NLA,
author = "Robert C. Ward and Gene H. Golub",
title = "Numerical linear algebra",
journal = j-SIGNUM,
volume = "15",
number = "3",
pages = "9--26",
month = sep,
year = "1980",
CODEN = "SNEWD6",
ISSN = "0163-5778 (print), 1558-0237 (electronic)",
ISSN-L = "0163-5778",
bibdate = "Tue Apr 12 07:50:09 MDT 2005",
bibsource = "http://portal.acm.org/;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "ACM SIGNUM Newsletter",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J690",
}
@Article{Bjorck:1981:EMA,
author = "{\AA}ke Bj{\"o}rck and Gene H. Golub",
title = "Eigenproblems for matrices associated with periodic
boundary conditions. ({Chinese})",
journal = "Yingyong Shuxue yu Jisuan Shuxue",
volume = "1",
number = "??",
pages = "10--18",
month = "????",
year = "1981",
MRclass = "65F15",
MRnumber = "83d:65110",
bibdate = "Sun Jan 14 09:34:26 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Translated from the English by Cheng Ming Huang",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1981:BDV,
author = "G. H. Golub and W. P. Tang",
title = "The Block Decomposition of a {Vandermonde} Matrix and
Its Applications",
journal = j-BIT,
volume = "21",
number = "??",
pages = "505--517",
year = "1981",
CODEN = "BITTEL",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "nla, block algorithm, Vandermonde matrix",
}
@Article{Golub:1981:BLM,
author = "Gene H. Golub and Franklin T. Luk and Michael L.
Overton",
title = "A Block {Lanczos} Method for Computing the Singular
Values and 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 = "Sun Jan 14 09:28:55 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/toms.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
keywords = "nla, svd, Lanczos algorithm, block Lanczos method,
singular values, singular vectors, large sparse matrix,
singular-value decomposition, upper-triangular band
matrix, nla, svd, Lanczos algorithm",
}
@Article{Tang:1981:BDV,
author = "W. P. Tang and G. H. Golub",
title = "The Block Decomposition of a {Vandermonde} Matrix and
Its Applications",
journal = j-BIT,
volume = "21",
number = "4",
pages = "505--517",
month = dec,
year = "1981",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01932847",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65F30 (15A06)",
MRnumber = "83e:65077",
MRreviewer = "V. Syamala Devi",
bibdate = "Wed Jan 4 18:52:17 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=21&issue=4;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=21&issue=4&spage=505",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
keywords = "nla, block algorithm, Vandermonde matrix",
}
@TechReport{Chan:1982:ACS,
author = "T. F. Chan and G. H. Golub and R. J. Le Veque",
title = "Algorithms for Computing the Sample Variance: Analysis
and Recommendations",
type = "??",
number = "222",
institution = "Department of Computer Science, Yale University",
address = "??",
month = "????",
year = "1982",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "stat, na, variance, standard deviation",
}
@InProceedings{Chan:1982:UFP,
author = "T. F. Chan and G. H. Golub and R. J. LeVeque",
title = "Updating formulae and a pairwise algorithm for
computing sample variances",
crossref = "Caussinus:1982:CSH",
pages = "30--41",
year = "1982",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
descriptors = "Simulation; statistics; numeric calculation",
}
@InProceedings{Golub:1982:CTS,
author = "Gene H. Golub and Michael L. Overton",
title = "Convergence of a two-stage {Richardson} iterative
procedure for solving systems of linear equations",
crossref = "Watson:1982:NAP",
pages = "125--139",
year = "1982",
DOI = "https://doi.org/10.1007/BFb0093153",
MRclass = "65F10",
MRnumber = "83f:65045",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1982:NAV,
author = "Gene H. Golub and Stephen G. Nash",
title = "Nonorthogonal Analysis of Variance using a Generalized
Conjugate-Gradient Algorithm",
journal = j-J-AM-STAT-ASSOC,
volume = "77",
number = "377",
pages = "109--116",
month = mar,
year = "1982",
CODEN = "JSTNAL",
DOI = "https://doi.org/10.2307/2287776",
ISSN = "0162-1459 (print), 1537-274X (electronic)",
ISSN-L = "0162-1459",
MRclass = "62J10 (65U05)",
MRnumber = "83i:62135",
MRreviewer = "Walter Schlee",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
URL = "http://www.jstor.org/stable/2287776",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
error = "in Gene's cv is Statistical Computing, but we found
this reference: The American Statistician",
fjournal = "Journal of the American Statistical Association",
journal-URL = "http://www.tandfonline.com/loi/uasa20",
keywords = "stat, anova, conjugate gradients",
}
@Article{Paige:1982:LAS,
author = "C. C. Paige and M. 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",
ISSN = "0098-3500 (print), 1557-7295 (electronic)",
ISSN-L = "0098-3500",
bibdate = "Sat Oct 22 16:35:44 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "ACM Transactions on Mathematical Software",
journal-URL = "http://portal.acm.org/toc.cfm?idx=J782",
keywords = "algorithms; measurement",
review = "ACM CR 39252",
subject = "G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Sparse and very large systems
\\ G.1.6 Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Least squares methods G Mathematics of
Computing, MATHEMATICAL SOFTWARE",
}
@Article{Chan:1983:ACS,
author = "Tony F. Chan and Gene H. Golub and Randall J.
LeVeque",
title = "Algorithms for computing the sample variance: Analysis
and recommendations",
journal = j-AMER-STAT,
volume = "37",
number = "3",
pages = "242--247",
month = aug,
year = "1983",
CODEN = "ASTAAJ",
DOI = "https://doi.org/10.2307/2683386",
ISSN = "0003-1305 (print), 1537-2731 (electronic)",
ISSN-L = "0003-1305",
MRclass = "62-04",
MRnumber = "84k:62003",
bibdate = "Mon May 5 09:19:29 MDT 1997",
bibsource = "Distributed/QLD.bib; Distributed/QLD/1983.bib;
ftp://ftp.ira.uka.de/pub/bibliography/Distributed/QLD.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://www.jstor.org/stable/2683386",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
country = "USA",
date = "13/05/93",
descriptors = "Simulation; statistics; numeric calculation",
enum = "7109",
fjournal = "The American Statistician",
journal-URL = "http://www.tandfonline.com/loi/utas20",
location = "SEL: Wi",
references = "0",
revision = "16/01/94",
}
@Article{Golub:1983:CGQ,
author = "G. H. Golub and J. Kautsk{\'y}",
title = "Calculation of {Gauss} quadratures with multiple free
and fixed knots",
journal = j-NUM-MATH,
volume = "41",
number = "2",
pages = "147--163",
month = jun,
year = "1983",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01390210",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65D32 (65F15)",
MRnumber = "84i:65030",
bibdate = "Sat Oct 22 16:35:44 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290M (Numerical integration and differentiation);
C4160 (Numerical integration and differentiation)",
corpsource = "Dept. of Computer Sci., Stanford Univ., Stanford, CA,
USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "algorithms; fixed knots; Gauss knots; Gauss
quadratures; integration; Jacobi matrix; quadratic
convergence; theory",
subject = "G.1.4 Mathematics of Computing, NUMERICAL ANALYSIS,
Quadrature and Numerical Differentiation, Gaussian
quadrature",
treatment = "T Theoretical or Mathematical",
}
@Book{Golub:1983:MC,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Matrix Computations",
publisher = pub-JOHNS-HOPKINS # " and " # pub-NORTH-OXFORD,
address = pub-JOHNS-HOPKINS:adr # " and " # pub-NORTH-OXFORD:adr,
pages = "xvi + 476",
year = "1983",
ISBN = "0-8018-3010-9 (hardcover), 0-8018-3011-7 (paperback),
0-946536-00-7, 0-946536-05-8 (paperback)",
ISBN-13 = "978-0-8018-3010-5 (hardcover), 978-0-8018-3011-2
(paperback), 978-0-946536-00-9, 978-0-946536-05-4
(paperback)",
LCCN = "QA188 .G65 1983",
MRclass = "65Fxx (65-02)",
MRnumber = "85h:65063",
MRreviewer = "C. Ilioi",
bibdate = "Sun Jan 14 09:27:53 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib",
series = "Johns Hopkins Series in the Mathematical Sciences",
URL = "http://www.jstor.org/stable/2008107;
http://www.jstor.org/stable/2030489;
http://www.jstor.org/stable/3616959",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "algebra --- matrices --- computation by digital
computer systems; matrices --- data processing",
remark = "See review by James W. Demmel in SIAM Review, Vol. 28,
No. 2 (Jul., 1986), pp. 252-255, review by David F.
Mayers, Mathematics of Computation, Vol. 47, No. 175
(Jul., 1986), pp. 376-377, and review by T. J. Randall,
The Mathematical Gazette, Vol. 69, No. 448 (Jun.,
1985), p. 152.",
tableofcontents = "Preface to the Third Edition \\
Software \\
Selected References \\
Matrix Multiplication Problems / 1 \\
Matrix Analysis / 48 \\
General Linear Systems / 87 \\
Special Linear Systems / 133 \\
Orthogonalization and Least Squares / 206 \\
Parallel Matrix Computations / 275 \\
The Unsymmetric Eigenvalue Problem / 308 \\
The Symmetric Eigenvalue Problem / 391 \\
Lanczos Methods / 470 \\
Iterative Methods for Linear Systems / 508 \\
Functions of Matrices / 555 \\
Special Topics / 579 \\
Bibliography / 637 \\
Index / 687",
}
@Book{Golub:1983:RNG,
author = "Gene H. Golub and G{\'e}rard A. Meurant",
title = "{R}{\'e}solution Num{\'e}rique des Grands Syst{\`e}mes
Lin{\'e}aires (English: Numerical solution of large
linear systems)",
volume = "49",
publisher = pub-EYROLLES,
address = pub-EYROLLES:adr,
pages = "x + 329",
year = "1983",
ISBN = "??",
ISBN-13 = "??",
LCCN = "??",
MRclass = "65-01 (65F10 65F20 65N20)",
MRnumber = "86b:65002",
MRreviewer = "G. Maess",
bibdate = "Sun Jan 14 09:26:25 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
series = "Collection de la Direction des Etudes et Recherches de
l'Electricit\'e de France",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "book, nla, linear system, sparse",
}
@InProceedings{Golub:1983:UPI,
author = "G. Golub and D. Mayers",
title = "The Use of Preconditioning Over Irregular Regions",
crossref = "Blackburn:1983:SIC",
pages = "??--??",
year = "1983",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/ovr.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Kautsky:1983:CJM,
author = "J. Kautsk{\'y} and G. H. Golub",
title = "On the Calculation of {Jacobi} Matrices",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "52/53",
pages = "439--456",
year = "1983",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(83)90028-9",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F30 (15A99 33A65)",
MRnumber = "84g:65050",
MRreviewer = "Walter Gautschi",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
keywords = "nla, Jacobi matrix",
}
@Article{Boley:1984:LAA,
author = "D. L. Boley and G. H. Golub",
title = "The {Lanczos--Arnoldi} Algorithm and controllability",
journal = j-SYST-CONTROL-LETT,
volume = "4",
number = "6",
pages = "317--324",
month = sep,
year = "1984",
CODEN = "SCLEDC",
DOI = "https://doi.org/10.1016/S0167-6911(84)80072-9",
ISSN = "0167-6911 (print), 1872-7956 (electronic)",
ISSN-L = "0167-6911",
MRclass = "93B40 (93B05)",
MRnumber = "86a:93044",
bibdate = "Fri Dec 20 17:12:57 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Systems and Control Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01676911",
keywords = "nla, controllability, Lanczos algorithm, Arnoldi's
method, algorithms",
subject = "G.1 Mathematics of Computing, NUMERICAL ANALYSIS,
Miscellaneous",
}
@Article{Boley:1984:MMR,
author = "Daniel Boley and Gene H. Golub",
title = "A modified method for reconstructing periodic {Jacobi}
matrices",
journal = j-MATH-COMPUT,
volume = "42",
number = "165",
pages = "143--150",
month = jan,
year = "1984",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2007564",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F15 (15A18)",
MRnumber = "85h:65078",
MRreviewer = "Alan L. Andrew",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2007564",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classcodes = "B0210 (Algebra); C1110 (Algebra)",
corpsource = "Computer Sci. Dept., Univ. of Minnesota, Minneapolis,
MN, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "algorithm; initial data items; matrix algebra;
numerically stable; periodic Jacobi matrices; spectral
data",
treatment = "T Theoretical or Mathematical",
}
@Article{Concus:1984:GCG,
author = "Paul Concus and Gene H. Golub and Dianne P. O'Leary",
title = "A generalized conjugate gradient method for the
numerical solution of elliptic partial differential
equations",
journal = j-MAA-STUD-MATH,
volume = "24",
number = "??",
pages = "178--198",
month = "????",
year = "1984",
CODEN = "MSTMBI",
ISSN = "0081-8208",
MRclass = "65N20 (65F10 65F15)",
MRnumber = "925 214",
bibdate = "Sun Jan 14 08:25:42 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Reprinted in \cite{Chan:2007:MMC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "MAA studies in mathematics",
}
@Article{Gallant:1984:ICR,
author = "A. Ronald Gallant and Gene H. Golub",
title = "Imposing curvature restrictions on flexible functional
forms",
journal = j-J-ECONOMETRICS,
volume = "26",
number = "3",
pages = "295--321",
month = dec,
year = "1984",
CODEN = "JECMB6",
DOI = "https://doi.org/10.1016/0304-4076(84)90024-1",
ISSN = "0304-4076 (print), 1872-6895 (electronic)",
ISSN-L = "0304-4076",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Journal of Econometrics",
journal-URL = "http://www.sciencedirect.com/science/journal/03044076",
}
@InCollection{Golub:1984:UPI,
author = "Gene H. Golub and David Mayers",
title = "The use of preconditioning over irregular regions",
crossref = "Glowinski:1983:CMA",
pages = "3--14",
year = "1984",
MRclass = "65F10 (65F35)",
MRnumber = "87h:65059",
bibdate = "Sun Jan 14 09:23:24 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Parallel/Multi.grid.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Concus:1985:BPC,
author = "P. Concus and G. H. Golub and G. A. Meurant",
title = "Block Preconditioning for the Conjugate Gradient
Method",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "6",
number = "??",
pages = "220--252",
month = "????",
year = "1985",
CODEN = "SIJCD4",
DOI = "https://doi.org/10.1137/0906018",
ISSN = "0196-5204",
MRclass = "65F10 (65N20)",
MRnumber = "87c:65035a",
MRreviewer = "Ian Gladwell",
bibdate = "Thu Apr 09 15:41:33 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
note = "See corrigendum \cite{Concus:1985:CBP}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
keywords = "nla, block algorithm, preconditioning, conjugate
gradients",
}
@Article{Concus:1985:CBP,
author = "P. Concus and G. H. Golub and G. Meurant",
title = "Corrigendum: {``Block preconditioning for the
conjugate gradient method''}",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "6",
number = "3",
pages = "791--791",
month = "????",
year = "1985",
CODEN = "SIJCD4",
ISSN = "0196-5204",
MRclass = "65F10 (65N20)",
MRnumber = "87c:65035b",
MRreviewer = "Ian Gladwell",
bibdate = "Thu Apr 09 15:41:30 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "See \cite{Concus:1985:BPC}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
}
@Article{Golub:1985:SLS,
author = "G. H. Golub",
title = "Solution of Large Sparse Structured Least-Squares
Problem",
journal = j-BIOMETRICS,
volume = "41",
number = "3",
pages = "799--799",
month = "????",
year = "1985",
CODEN = "BIOMB6",
ISSN = "0006-341X (print), 1541-0420 (electronic)",
ISSN-L = "0006-341X",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/biometrics1980.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Biometrics",
journal-URL = "http://www.jstor.org/journal/biometrics",
}
@Article{Golub:1986:CBS,
author = "G. H. Golub and P. Manneback and Ph. L. Toint",
title = "A Comparison Between some Direct and Iterative Methods
for Large Scale Geodetic Least Squares Problems",
journal = j-SIAM-J-SCI-STAT-COMP,
volume = "7",
number = "3",
pages = "799--816",
month = jul,
year = "1986",
CODEN = "SIJCD4",
DOI = "https://doi.org/10.1137/0907053",
ISSN = "0196-5204",
MRclass = "65F50 (65U05)",
MRnumber = "87g:65063",
bibdate = "Sat Oct 22 16:35:44 MDT 1994",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Scientific and Statistical Computing",
journal-URL = "http://epubs.siam.org/loi/sijcd4",
keywords = "algorithms; conjugate gradients; geodesy; iter; lsq;
nested dissection; nla; sparse; theory; verification",
subject = "G.1.6 Mathematics of Computing, NUMERICAL ANALYSIS,
Optimization, Least squares methods \\ J.2 Computer
Applications, PHYSICAL SCIENCES AND ENGINEERING,
Physics",
}
@Article{Golub:1986:CTS,
author = "Gene H. Golub and R. Kannan",
title = "Convergence of a two-stage {Richardson} process for
nonlinear equations",
journal = j-BIT,
volume = "26",
number = "2",
pages = "209--216",
month = jun,
year = "1986",
CODEN = "BITTEL, NBITAB",
DOI = "https://doi.org/10.1007/BF01933747",
ISSN = "0006-3835 (print), 1572-9125 (electronic)",
ISSN-L = "0006-3835",
MRclass = "65H10 (47H17 65F10)",
MRnumber = "87f:65064",
MRreviewer = "V. Pereyra",
bibdate = "Wed Jan 4 18:52:19 MST 2006",
bibsource = "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=26&issue=2;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=26&issue=2&spage=209",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "BIT (Nordisk tidskrift for informationsbehandling)",
journal-URL = "http://link.springer.com/journal/10543",
}
@TechReport{Golub:1986:PBS,
author = "Gene H. Golub and Robert J. Plemmons and Ahmed Sameh",
title = "Parallel Block Schemes for Large Scale Least Squares
Computations",
type = "Technical Report",
number = "574",
institution = inst-CSRD,
address = inst-CSRD:adr,
pages = "20",
month = apr,
year = "1986",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/ovr.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "matrices; parallel processing (electronic computers)",
}
@Article{Golub:1986:UFG,
author = "Gene H. Golub and Carl D. {Meyer, Jr.}",
title = "Using the {$ {QR} $} Factorization and Group Inversion
to Compute, Differentiate, and estimate the Sensitivity
of Stationary Probabilities for {Markov} Chains",
journal = j-SIAM-J-ALG-DISC-METH,
volume = "7",
number = "2",
pages = "273--281",
month = apr,
year = "1986",
CODEN = "SJAMDU",
DOI = "https://doi.org/10.1137/0607031",
ISSN = "0196-5212 (print), 2168-345X (electronic)",
ISSN-L = "0196-5212",
MRclass = "60J10 (65F05)",
MRnumber = "87i:60073",
MRreviewer = "M. F. Neuts",
bibdate = "Sun Jan 14 09:22:16 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Algebraic and Discrete Methods",
journal-URL = "http://epubs.siam.org/loi/sjamdu",
keywords = "eig; ginv; Markov chain; nla; qrd; theory;
verification",
subject = "F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices \\ G.2.1 Mathematics
of Computing, DISCRETE MATHEMATICS, Combinatorics",
}
@TechReport{Arbenz:1987:SDH,
author = "P. Arbenz and G. H. Golub",
title = "On the Spectral Decomposition of {Hermitian} Matrices
Subject to Indefinite Low Rank Perturbations with
Applications",
type = "??",
number = "NA 87-07",
institution = "Computer Science, Stanford University",
address = "Stanford, CA",
month = "????",
year = "1987",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Boley:1987:SMI,
author = "Daniel Boley and Gene H. Golub",
title = "A survey of matrix inverse eigenvalue problems",
journal = j-INVERSE-PROBLEMS,
volume = "3",
number = "4",
pages = "595--622",
month = "????",
year = "1987",
CODEN = "INPEEY",
DOI = "https://doi.org/10.1088/0266-5611/3/4/010",
ISSN = "0266-5611 (print), 1361-6420 (electronic)",
ISSN-L = "0266-5611",
MRclass = "65F15",
MRnumber = "89m:65036",
bibdate = "Sat Apr 16 17:44:41 2005",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Inverse Problems",
journal-URL = "http://iopscience.iop.org/0266-5611/",
}
@InProceedings{Ferziger:1987:BSA,
author = "J. H. Ferziger and G. H. Golub and M. C. Thompson",
title = "Block {SOR} applied to the cyclically-reduced
equations as an efficient solution technique for
convection-diffusion equations",
crossref = "Noye:1987:CTA",
pages = "??--??",
year = "1987",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1987:D,
author = "Gene H. Golub and Iain Duff and Cleve Moler",
title = "Dedication",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "88/89",
pages = "1--12",
year = "1987",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "01A70",
MRnumber = "88e:01060",
bibdate = "Mon Jan 15 17:54:33 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@Article{Golub:1987:GEY,
author = "G. H. Golub and Alan Hoffman and G. W. Stewart",
title = "A generalization of the {Eckart--Young--Mirsky} matrix
approximation theorem",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "88/89",
pages = "317--327",
year = "1987",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(87)90114-5",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "41A45 (15A60 62J05 65F99)",
MRnumber = "88f:41039",
MRreviewer = "R. A. Lorentz",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@Article{Golub:1987:JW,
author = "Gene H. Golub and Miki Neumann and James W. Demmel and
Paul Saylor and James M. Boyle and Iain Duff and Jack
Dongarra",
title = "{James Wilkinson} (1919--1986)",
journal = j-ANN-HIST-COMPUT,
volume = "9",
number = "2",
pages = "205--210",
month = apr # "\slash " # jun,
year = "1987",
CODEN = "AHCOE5",
ISSN = "0164-1239",
bibdate = "Sat Jul 14 18:11:40 2001",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Math/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "From the introduction: ``A series of lightly edited
extracts from messages that were sent over various
computer networks during the period October 5,
1986--February 13, 1987''.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Annals of the History of Computing",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5488650",
keywords = "obituary",
}
@Article{Golub:1987:LAA,
author = "G. H. Golub and C. Moler",
title = "Linear Algebra and its Applications --- in Memory of
{James H. Wilkinson}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "88--89",
pages = "1--3",
month = apr,
year = "1987",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(87)90098-X",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@InProceedings{Golub:1987:LSL,
author = "G. H. Golub",
title = "Large scale least squares problems",
crossref = "Heiberger:1987:CSS",
pages = "3",
month = "????",
year = "1987",
bibdate = "Mon Sep 9 12:13:04 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "Summary form only given as follows. With the advent of
satellites, it is possible to collect large sets of
data which are frequently analysed through least
squares methods. These problems can have over a million
observations and several hundred thousand unknowns.
Fortunately, the data is highly structured so that one
can combine direct and iterative methods for solving
the associated least squares problem. Furthermore, it
is possible to decompose the problem in such a way that
the computation can be performed in parallel. The
author discusses this computation and points out its
connection to other large scale least squares
problems.",
acknowledgement = ack-nhfb,
affiliation = "Stanford Univ., CA, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "C4130 (Interpolation and function approximation);
C7310 (Mathematics)",
keywords = "Associated least squares problem; Highly structured;
Iterative methods; Large scale least squares problems;
Least squares methods; Observations; Parallel;
Satellites; Unknowns",
thesaurus = "Least squares approximations; Mathematics computing",
}
@TechReport{Golub:1987:SHC,
author = "Gene H. Golub and Dianne P. O'Leary",
title = "Some history of the conjugate gradient and {Lanczos}
algorithms: 1948--1976",
type = "Technical Report",
number = "TR-1859, UMIACS-TR-87-20",
institution = inst-U-MARYLAND-CS,
address = inst-U-MARYLAND-CS:adr,
pages = "51",
month = "????",
year = "1987",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "Algorithms --- Bibliography",
}
@Article{Arbenz:1988:RRM,
author = "Peter Arbenz and Walter Gander and Gene H. Golub",
title = "Restricted Rank Modification of the Symmetric
Eigenvalue Problem: Theoretical Considerations",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "104",
pages = "75--95",
year = "1988",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(88)90309-6",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (15A18)",
MRnumber = "89h:65052",
MRreviewer = "V. S. Zaja{\v{c}}kovski",
bibdate = "Sun Jan 14 09:18:09 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
keywords = "nla, eig, symmetric matrix, updating",
}
@Article{Arbenz:1988:SDH,
author = "Peter Arbenz and Gene H. Golub",
title = "On the Spectral Decomposition of {Hermitian} Matrices
Modified by Low Rank Perturbations with Applications",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "9",
number = "1",
pages = "40--58",
month = "????",
year = "1988",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/0609004",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A57 (15A18 65F15)",
MRnumber = "89c:15028",
MRreviewer = "Moody T. Chu",
bibdate = "Tue Jan 21 07:54:58 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib;
https://www.math.utah.edu/pub/tex/bib/siamjmatanaappl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "algorithms; eig; indefinite matrix; nla; symmetric
matrix; theory; updating",
subject = "F.2.1 Theory of Computation, ANALYSIS OF ALGORITHMS
AND PROBLEM COMPLEXITY, Numerical Algorithms and
Problems, Computations on matrices \\ I.1.1 Computing
Methodologies, ALGEBRAIC MANIPULATION, Expressions and
Their Representation, Simplification of expressions \\
G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS,
General, Stability (and instability) \\ G.1.3
Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
Linear Algebra, Error analysis",
}
@InProceedings{Gander:1988:CEP,
author = "Walter Gander and Gene H. Golub and Urs {von Matt}",
title = "A constrained eigenvalue problem",
crossref = "Golub:1991:NLA",
pages = "677--686",
year = "1988",
MRclass = "65F15",
MRnumber = "92k:65067",
bibdate = "Sun Jan 14 08:57:55 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "Variants of this problem occur in many applications.
The authors show how to eliminate the linear
constraint. Three different methods are presented for
the solution of the resulting Lagrange equations.",
acknowledgement = ack-nhfb,
affiliation = "Inst. fur Inf., ETH, Zurich, Switzerland",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0210 (Algebra); C1110 (Algebra)",
keywords = "Constrained eigenvalue problem; Lagrange equations;
Linear constraint",
thesaurus = "Eigenvalues and eigenfunctions; Matrix algebra",
}
@Article{Golub:1988:CIC,
author = "Gene H. Golub and Michael L. Overton",
title = "The Convergence of Inexact {Chebyshev} and
{Richardson} Iterative Methods for Solving Linear
Systems",
journal = j-NUM-MATH,
volume = "53",
number = "5",
pages = "571--593",
month = aug,
year = "1988",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01397553",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F10",
MRnumber = "90b:65054",
bibdate = "Sat Oct 22 16:35:44 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290H (Linear algebra); C4140 (Linear algebra)",
corpsource = "Dept. of Comput. Sci., Stanford Univ., CA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "Chebyshev approximation; convergence; convergence of
numerical methods; error analysis; error bound;
experimentation; inexactness; iter; iterative methods;
linear algebra; linear system; linear systems;
measurement; nla; nonsymmetric inexact Chebyshev
iteration; numerical experiments; performance;
preconditioned iteration; Richardson iterative methods;
skew-symmetric iteration; spectral radius; theory;
verification",
subject = "G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Linear systems (direct and
iterative methods)",
treatment = "T Theoretical or Mathematical",
xxtitle = "The Convergence of Inexact {Tschebyscheff} and
{Richardson} Iterative Methods for Solving
Linear-Systems",
}
@Article{Golub:1988:GEY,
author = "G. H. Golub and A. Hoffman and G. W. Stewart",
title = "A Generalization of the {Eckart--Young--Mirsky}
Approximation Theorem",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "88/89",
pages = "317--328",
year = "1988",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/tex/bib/gvl.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@Article{Golub:1988:OPH,
author = "Gene H. Golub and Richard S. Varga",
title = "Obituary to {Peter Henrici (13. September 1923--13.
March 1987)}",
journal = j-NUM-MATH,
volume = "52",
number = "5",
pages = "481--482",
month = may,
year = "1988",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01400886",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "01A70",
MRnumber = "89i:01077",
bibdate = "Sun Jan 14 09:17:43 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/h/henrici-peter.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
subject-dates = "Peter Karl Henrici (13 September 1923--13 March
1987)",
}
@InCollection{Golub:1988:PBS,
author = "Gene H. Golub and Robert J. Plemmons and Ahmed Sameh",
title = "Parallel Block Schemes for Large-Scale Least-Squares
Computations",
crossref = "Wilhelmson:1988:HSC",
pages = "171--179",
year = "1988",
bibdate = "Sat Oct 22 16:35:44 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
price = "US\$29.95",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "algorithms; design; theory",
subject = "J.2 Computer Applications, PHYSICAL SCIENCES AND
ENGINEERING, Engineering \\ F.2.1 Theory of
Computation, ANALYSIS OF ALGORITHMS AND PROBLEM
COMPLEXITY, Numerical Algorithms and Problems,
Computations on matrices \\ G.1.0 Mathematics of
Computing, NUMERICAL ANALYSIS, General, Parallel
algorithms \\ G.1.6 Mathematics of Computing, NUMERICAL
ANALYSIS, Optimization, Least squares methods",
}
@TechReport{Elhay:1989:UDO,
author = "Sylvan Elhay and Gene H. Golub and Jaroslav
Kautsk{\'y}",
title = "Updating and downdating of orthogonal polynomials with
data fitting applications",
type = "Technical Report",
number = "STAN-CS-89-04, NA-89-04",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "32",
month = "????",
year = "1989",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "least squares; orthogonal polynomials",
}
@TechReport{Elman:1989:IMC,
author = "Howard C. Elman and Gene H. Golub",
title = "Iterative methods for cyclically reduced
non-self-adjoint linear systems {II}",
type = "Technical Report",
number = "STAN CS-TR-2238, UMIACS-TR-89-45",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "26",
month = "????",
year = "1989",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "iterative methods (mathematics); linear systems",
}
@InProceedings{Elman:1989:LIM,
author = "Howard C. Elman and Gene H. Golub",
title = "Line iterative methods for cyclically reduced
non-self-adjoint elliptic problems",
crossref = "ARO:1990:TSA",
pages = "457--466",
year = "1989",
MRclass = "65F10 (65N20)",
MRnumber = "057 847",
bibdate = "Sun Jan 14 10:11:05 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Gander:1989:CEP,
author = "Walter Gander and Gene H. Golub and Urs {von Matt}",
title = "A constrained eigenvalue problem",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "114/115",
pages = "815--839",
year = "1989",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(89)90494-1",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A18 (15A23)",
MRnumber = "90e:15008",
MRreviewer = "Lajos L{\'a}szl{\'o}",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@Article{Gander:1989:DLS,
author = "Walter Gander and Gene H. Golub",
title = "Discussion: Linear Smoothers and Additive Models",
journal = j-ANN-STAT,
volume = "17",
number = "2",
pages = "529--532",
month = jun,
year = "1989",
CODEN = "ASTSC7",
DOI = "https://doi.org/10.1214/aos/1176347120",
ISSN = "0090-5364 (print), 2168-8966 (electronic)",
ISSN-L = "0090-5364",
bibdate = "Tue May 18 17:06:23 2010",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://projecteuclid.org/euclid.aos/1176347120;
http://www.jstor.org/stable/2241565",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Annals of Statistics",
journal-URL = "http://projecteuclid.org/all/euclid.aos/",
}
@InCollection{Gander:1989:SLE,
author = "Walter Gander and Gene H. Golub and Dominik Gruntz",
title = "Solving linear equations by extrapolation",
crossref = "Kowalik:1989:S",
pages = "279--293",
year = "1989",
MRclass = "65F10",
MRnumber = "91j:65060",
MRreviewer = "R. P. Tewarson",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1989:CEP,
author = "Walter Gander and Gene H. Golub and Urs {von Matt}",
title = "A Constrained Eigenvalue Problem",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "114/115",
pages = "815--839",
year = "1989",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A18 (15A23)",
MRnumber = "90e:15008",
MRreviewer = "Lajos L{\'a}szl{\'o}",
bibdate = "Sun Jan 14 09:13:37 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
keywords = "nla, eig, constrained eigenvalue problem",
}
@Article{Golub:1989:EEI,
author = "Gene H. Golub and Mark D. Kent",
title = "Estimates of Eigenvalues for Iterative Methods",
journal = j-MATH-COMPUT,
volume = "53",
number = "188",
pages = "619--626",
month = oct,
year = "1989",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2008724",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F10 (65F15)",
MRnumber = "90e:65043",
MRreviewer = "Vasile I. Ionescu",
bibdate = "Tue Oct 13 08:06:19 MDT 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database",
URL = "http://www.jstor.org/stable/2008724",
abstract = "Describes a procedure for determining estimates of the
eigenvalues of operators used in various iterative
methods for the solution of linear systems of
equations. The authors show how to determine upper and
lower bounds for the error in the approximate solution
of linear equations, using essentially the same
information as that needed for the eigenvalue
calculations. The methods described depend strongly
upon the theory of moments and Gauss quadrature.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Comp. Sci., Stanford Univ., CA, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classcodes = "C4140 (Linear algebra); C4130 (Interpolation and
function approximation); C4160 (Numerical integration
and differentiation)",
corpsource = "Dept. of Comp. Sci., Stanford Univ., CA, USA",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "approximate solution; approximation theory;
eigenvalues; eigenvalues and eigenfunctions; error;
estimates; Gauss quadrature; integration; iterative
methods; linear equations; linear systems; lower
bounds; theory of moments; upper bounds",
thesaurus = "Approximation theory; Eigenvalues and eigenfunctions;
Integration; Iterative methods",
treatment = "T Theoretical or Mathematical",
}
@Book{Golub:1989:MC,
author = "Gene H. Golub and Charles F. {Van Loan}",
title = "Matrix Computations",
volume = "3",
publisher = pub-JOHNS-HOPKINS,
address = pub-JOHNS-HOPKINS:adr,
edition = "Second",
pages = "xix + 642",
year = "1989",
ISBN = "0-8018-3772-3 (hardcover), 0-8018-3739-1 (paperback)",
ISBN-13 = "978-0-8018-3772-2 (hardcover), 978-0-8018-3739-5
(paperback)",
LCCN = "QA188 .G65 1989",
MRclass = "65Fxx (65-02)",
MRnumber = "90d:65055",
MRreviewer = "Perry Smith",
bibdate = "Mon Oct 26 07:31:01 1998",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
https://www.math.utah.edu/pub/bibnet/subjects/domain-decomp.bib;
https://www.math.utah.edu/pub/tex/bib/master.bib;
https://www.math.utah.edu/pub/tex/bib/matlab.bib;
https://www.math.utah.edu/pub/tex/bib/texbook2.bib",
price = "US\$14.50",
series = "Johns Hopkins Series in the Mathematical Sciences",
ZMnumber = "0733.65016",
abstract = "Thoroughly revised, updated, and expanded by more than
one third, this new edition of Golub and Van Loan's
landmark book in scientific computing provides the
vital mathematical background and algorithmic skills
required for the production of numerical software. New
chapters on high performance computing use matrix
multiplication to show how to organize a calculation
for vector processors as well as for computers with
shared or distributed memories. Also new are
discussions of parallel vector methods for linear
equations, least squares, and eigenvalue problems.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "book; math; matrices --- data processing; matrices ---
informatique; na; nla",
libnote = "Not yet in my library.",
remark = "See review by G. W. Steward in Mathematics of
Computation, Vol. 56, No. 193 (Jan., 1991),
pp. 380--381.",
shorttableofcontents = "Preface to the Third Edition \\
Software \\
Selected References \\
Matrix Multiplication Problems / 1 \\
Matrix Analysis / 48 \\
General Linear Systems / 87 \\
Special Linear Systems / 133 \\
Orthogonalization and Least Squares / 206 \\
Parallel Matrix Computations / 275 \\
The Unsymmetric Eigenvalue Problem / 308 \\
The Symmetric Eigenvalue Problem / 391 \\
Lanczos Methods / 470 \\
Iterative Methods for Linear Systems / 508 \\
Functions of Matrices / 555 \\
Special Topics / 579 \\
Bibliography / 637 \\
Index / 687",
tableofcontents = "Preface to the First Edition / xi \\
Preface to the Second Edition / xv \\
Using the Book / xvii \\
1: Matrix Multiplication Problems / 1 \\
1.1 Basic Algorithms and Notations / 2 \\
1.2 Exploiting Structure / 16 \\
1.3 Block Matrices and Algorithms / 25 \\
1.4 Aspects of Vector Pipeline Computing / 35 \\
2: Matrix Analysis / 49 \\
2.1 Basic Ideas from Linear Algebra / 49 \\
2.2 Vector Norms / 53 \\
2.3 Matrix Norms / 55 \\
2.4 Finite Precision Matrix Computations / 60 \\
2.5 Orthogonality and the SVD / 70 \\
2.6 Projections and the CS Decomposition / 75 \\
2.7 The Sensitivity of Square Linear Systems / 79 \\
3: General Linear Systems / 86 \\
3.1 Triangular Systems / 86 \\
3.2 Computing the LU Factorization / 92 \\
3.3 Roundoff Analysis of Gaussian Elimination / 104 \\
3.4 Pivoting / 108 \\
3.5 Improving and Estimating Accuracy / 123 \\
4: Special Linear Systems / 133 \\
4.1 The $LDM^T$ and $LDL^T$ Factorizations / 134 \\
4.2 Positive Definite Systems / 139 \\
4.3 Banded Systems / 149 \\
4.4 Symmetric Indefinite Systems / 159 \\
4.5 Block Tridiagonal Systems / 170 \\
4.6 Vandermonde Systems / 178 \\
4.7 Toeplitz Systems / 183 \\
5: Orthogonalization and Least Squares / 193 \\
5.1 Householder and Givens Transformations / 194 \\
5.2 The $Q R$ Factorization / 211 \\
5.3 The Full Rank Least Squares Problem / 221 \\
5.4 Other Orthogonal Factorizations / 233 \\
5.5 The Rank Deficient Least Squares Problem / 241 \\
5.6 Weighting and Iterative Improvement / 250 \\
5.7 A Note on Square and Underdetermined Systems / 256
\\
6: Parallel Matrix Computations / 260 \\
6.1 Distributed Memory Gaxpy / 261 \\
6.2 Shared Memory Gaxpy / 276 \\
6.3 Parallel Matrix Multiplication / 288 \\
6.4 Ring Factorization Procedures / 301 \\
6.5 Mesh Factorization Procedures / 310 \\
6.6 Shared Memory Factorization Methods / 321 \\
7: The Unsymmetric Eigenvalue Problem / 331 \\
7.1 Properties and Decompositions / 332 \\
7.2 Perturbation Theory / 341 \\
7.3 Power Iterations / 351 \\
7.4 Hessenberg and Real Schur Forms / 361 \\
7.5 The Practical $Q R$ Algorithm / 373 \\
7.6 Invariant Subspace Computations / 382 \\
7.7 The $QZ$ Method for $A x = \lambda B x$ / 394 \\
8: The Symmetric Eigenvalue Problem / 409 \\
8.1 Properties, Decompositions, Perturbation Theory /
410 \\
8.2 The Symmetric $Q R$ Algorithm / 418 \\
8.3 Computing the SVD / 427 \\
8.4 Some Special Methods / 437 \\
8.5 Jacobi Methods / 444 \\
8.6 A Divide and Conquer Method / 459 \\
8.7 More Generalized Eigenvalue Problems / 466 \\
9: Lanczos Methods / 475 \\
9.1 Derivation and Convergence Properties / 476 \\
9.2 Practical Lanczos Procedures / 484 \\
9.3 Applications and Extensions / 494 \\
10: Iterative Methods for Linear Systems / 505 \\
10.1 The Standard Iterations / 506 \\
10.2 The Conjugate Gradient Method / 516 \\
10.3 Preconditioned Conjugate Gradient Methods / 527
\\
11: Functions of Matrices / 539 \\
11.1 Eigenvalue Methods / 540 \\
11.2 Approximation Methods / 546 \\
11.3 The Matrix Exponential / 555 \\
12: Special Topics / 561 \\
12.1 Some Constrained Least Squares Problems / 561 \\
12.2 Subset Selection Using the SVD / 571 \\
12.3 Total Least Squares / 576 \\
12.4 Comparing Subspaces Using the SVD / 581 \\
12.5 Some Modified Eigenvalue Problems / 587 \\
12.6 Updating the $Q R$ Factorization / 592 \\
Bibliography / 601 \\
Index / 635",
}
@TechReport{Golub:1989:MMI,
author = "Gene H. Golub and Martin H. Gutknecht",
title = "Modified moments for indefinite weight functions",
type = "Technical Report",
number = "STAN-CS-89-08, NA-89-08",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "19",
month = "????",
year = "1989",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "orthogonal polynomials",
}
@Article{Golub:1989:SHC,
author = "Gene H. Golub and Dianne P. O'Leary",
title = "Some History of the Conjugate Gradient and {Lanczos}
Algorithms: 1948--1976",
journal = j-SIAM-REVIEW,
volume = "31",
number = "1",
pages = "50--102",
month = mar,
year = "1989",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1031003",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65-03 (00A15 01A60 65-00 65Fxx 90-03)",
MRnumber = "90b:65003",
bibdate = "Mon Jan 20 10:31:25 MST 1997",
bibsource = "Compendex database;
ftp://ftp.ira.uka.de/pub/bibliography/Parallel/par.lin.alg.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
URL = "http://www.jstor.org/stable/2030847",
abstract = "The conjugate gradient and Lanczos algorithms for
solving linear systems of equations and eigenproblems
represent very important computational innovations of
the early 1950s. These methods came into wide use only
in the mid-1970s. Shortly thereafter, vector computers
and massive computer memories made it possible to use
these methods to solve problems which could not be
solved in any other way. Since that time, the
algorithms have been further refined and have become a
basic tool for solving a wide variety of problems on a
wide variety of computer architectures. The conjugate
gradient algorithm has also been extended to solve
nonlinear systems of equations and optimization
problems, and this has had tremendous impact on the
computation of unconstrained and constrained
optimization problems. This paper gives some of the
history of the conjugate gradient and Lanczos
algorithms and an annotated bibliography for the period
1948--1976.",
acknowledgement = ack-nhfb,
affiliation = "Stanford Univ",
affiliationaddress = "Stanford, CA, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "723; 921",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
journalabr = "SIAM Rev",
keywords = "Algorithms; Computer Programming--Algorithms;
Conjugate Gradient Algorithm; Lanczos Algorithm;
Mathematical Techniques; Optimization--Theory; Variable
Metric Algorithms",
mynote = "June 1987 Maryland TR-1859",
subject = "G.1.3 Mathematics of Computing, NUMERICAL ANALYSIS,
Numerical Linear Algebra, Linear systems (direct and
iterative methods) \\ G.1.3 Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra,
Eigenvalues \\ G.1.3 Mathematics of Computing,
NUMERICAL ANALYSIS, Numerical Linear Algebra, Matrix
inversion",
}
@TechReport{Moor:1989:GSV,
author = "Bart L. R. De Moor and Gene H. Golub",
title = "Generalized singular value decompositions: a proposal
for a standardized nomenclature",
type = "Technical Report",
number = "STAN-CS-TR-2002",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "12",
month = "????",
year = "1989",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "decomposition (mathematics)",
}
@TechReport{Moor:1989:RSV,
author = "Bart L. R. De Moor and Gene H. Golub",
title = "The restricted singular value decomposition:
properties and applications",
type = "Technical Report",
number = "STAN-CS-TR-2001",
institution = inst-STANFORD-CS,
address = inst-STANFORD-CS:adr,
pages = "69",
month = "????",
year = "1989",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "decomposition (mathematics)",
}
@Article{Comon:1990:TFE,
author = "Pierre Comon and Gene H. Golub",
title = "Tracking a Few Extreme Singular Values and Vectors in
Signal Processing",
journal = j-PROC-IEEE,
volume = "78",
number = "8",
pages = "1327--1343",
month = aug,
year = "1990",
CODEN = "IEEPAD",
DOI = "https://doi.org/10.1109/5.58320",
ISSN = "0018-9219 (print), 1558-2256 (electronic)",
ISSN-L = "0018-9219",
bibdate = "Mon Sep 9 11:37:15 MDT 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=58320",
abstract = "In various applications it is necessary to keep track
of a low-rank approximation of a covariance matrix,
R(t), slowly varying with time. It is convenient to
track the left singular vectors associated with the
largest singular values of the triangular factor, L(t),
of its Cholesky factorization. These algorithms are
referred to as square-root. The drawback of the
eigenvalue decomposition (EVD) or the singular value
decompositions (SVD) is usually the volume of the
computations. Various numerical methods for carrying
out this task are surveyed, and it is shown why this
heavy computational burden is questionable in numerous
situations and should be revised. Indeed, the
complexity per eigenpair is generally a quadratic
function of the problem size, but there exist faster
algorithms with linear complexity. Finally, in order to
make a choice among the large and fuzzy set of
available techniques, comparisons based on computer
simulations in a relevant signal processing context are
made.",
acknowledgement = ack-nhfb,
affiliation = "Thomson-Sintra, Cagnes-sur-Mer, France",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290 (Numerical analysis); B6140 (Signal processing
and detection); C1260 (Information theory); C4100
(Numerical analysis)",
fjournal = "Proceedings of the IEEE",
journal-URL = "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
keywords = "Adaptive algorithms; Cholesky factorization; Computer
simulations; Covariance matrix; Eigenvalue
decomposition; Extreme singular values; Extreme
singular vectors; Linear complexity; Low-rank
approximation; nla, signal processing, Lanczos
algorithm, rank determination; Numerical methods;
Signal processing; Singular value decompositions;
Square root algorithms; Tracking; Triangular factor",
thesaurus = "Computational complexity; Eigenvalues and
eigenfunctions; Matrix algebra; Numerical methods;
Signal processing",
}
@Article{Elman:1990:IMC,
author = "Howard C. Elman and Gene H. Golub",
title = "Iterative methods for cyclically reduced
non-self-adjoint linear systems",
journal = j-MATH-COMPUT,
volume = "54",
number = "190",
pages = "671--700",
month = apr,
year = "1990",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2008506",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F10 (65N22)",
MRnumber = "91b:65036",
MRreviewer = "Harry Yserentant",
bibdate = "Mon Sep 09 12:10:35 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.jstor.org/stable/2008506",
abstract = "The authors study iterative methods for solving linear
systems of the type arising from two-cyclic
discretizations of non-self-adjoint two-dimensional
elliptic partial differential equations. A prototype is
the convection-diffusion equation. The methods consist
of applying one step of cyclic reduction, resulting in
a `reduced system' of half the order of the original
discrete problem, combined with a reordering and a
block iterative technique for solving the reduced
system. For constant-coefficient problems, they present
analytic bounds on the spectral radii of the iteration
matrices in terms of cell Reynolds numbers that show
the methods to be rapidly-convergent. In addition, they
describe numerical experiments that supplement the
analysis and that indicate that the methods compare
favourably with methods for solving the `unreduced'
system.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Comput. Sci., Maryland Univ., College Park,
MD, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290P (Differential equations); C4170 (Differential
equations)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Analytic bounds; Block iterative technique; Cell
Reynolds numbers; Convection-diffusion equation;
Cyclically reduced non-self-adjoint linear systems;
Elliptic partial differential equations; Iterative
methods; Linear systems; Numerical experiments;
Rapidly-convergent; Reordering; Spectral radii",
thesaurus = "Convergence of numerical methods; Iterative methods;
Partial differential equations",
}
@InProceedings{Elman:1990:IML,
author = "Howard C. Elman and Gene H. Golub",
title = "Block iterative methods for cyclically reduced
nonselfadjoint elliptic problems",
crossref = "Kincaid:1990:IML",
pages = "91--105",
year = "1990",
MRclass = "65F10",
MRnumber = "1 038 090",
bibdate = "Fri Dec 20 17:21:26 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@TechReport{Elman:1990:LIMa,
author = "Howard C. Elman and Gene H. Golub",
title = "Line Iterative Methods for Cyclically Reduced Discrete
Convection-Diffusion Problems",
type = "Technical Report",
number = "CS-TR-2403, UMIACS-TR-90-16",
institution = inst-U-MARYLAND-CS,
address = inst-U-MARYLAND-CS:adr,
pages = "29",
month = "????",
year = "1990",
bibdate = "Mon Oct 24 10:35:29 MDT 1994",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "We perform an analytic and empirical study of line
iterative methods for solving the discrete
convection-diffusion equation. The methodology consists
of performing one step of the cyclic reduction method,
followed by iteration on the resulting cyclic reduction
method, followed by iteration on the resulting reduced
system using line orderings of the reduced grid. Two
classes of iterative methods are considered: block
stationary methods, such as the block Gauss--Seidel and
SOR methods, and preconditioned generalized minimum
residual methods with incomplete LU preconditioners.
New analysis extends convergence bounds for constant
coefficient problems to problems with separable
variable coefficients. In addition, analytic results
show that iterative methods based on incomplete LU
preconditioners have faster convergence rates on
incomplete LU preconditioners have faster convergence
rates than block Jacobi relaxation methods. Numerical
experiments examine additional properties of the two
classes of methods, including the effects of flow,
discretization, and grid ordering on performance.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
keywords = "Iterative methods (Mathematics); Numerical analysis",
}
@InProceedings{Elman:1990:LIMb,
author = "Howard C. Elman and Gene H. Golub",
title = "Line iterative methods for cyclically reduced
nonselfadjoint elliptic problems",
crossref = "ARO:1990:TSA",
pages = "457--466",
year = "1990",
MRclass = "65F10 (65N20)",
MRnumber = "1 057 847",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Ferng:1990:ALM,
author = "W. R. Ferng and G. H. Golub and R. J. Plemmons",
title = "Adaptive {Lanczos} methods for recursive condition
estimation",
journal = j-PROC-SPIE,
volume = "1348",
pages = "326--337",
month = "????",
year = "1990",
CODEN = "PSISDG",
ISSN = "0277-786X (print), 1996-756X (electronic)",
ISSN-L = "0277-786X",
bibdate = "Mon Sep 9 11:37:15 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "This paper proposes an adaptive Lanczos Estimator
scheme for tracking the condition number of the
modified matrix over time. Applications to recursive
least squares computations using the covariance method
with sliding data windows are considered. Comparisons
are made with other adaptive and non-adaptive condition
estimators for recursive least squares problems.
Numerical experiments are reported.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Math., North Carolina State Univ., Raleigh,
NC, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290H (Linear algebra); B6140 (Signal processing
and detection); C1240 (Adaptive system theory); C1260
(Information theory); C4140 (Linear algebra)",
fjournal = "Proceedings of the SPIE --- The International Society
for Optical Engineering",
keywords = "Adaptive Lanczos Estimator; Covariance method;
Modified matrix; Recursive condition estimation;
Recursive least squares computations; RLS method;
Signal processing; Sliding data windows",
thesaurus = "Adaptive filters; Least squares approximations; Matrix
algebra; Parameter estimation; Signal processing;
Variational techniques",
}
@InProceedings{Gander:1990:SLE,
author = "Walter Gander and G. H. Golub and Dominik Gruntz",
title = "Solving linear equations by extrapolation",
crossref = "Kowalik:1990:SNA",
pages = "279--293",
year = "1990",
MRclass = "65F10",
MRnumber = "91j:65060",
MRreviewer = "R. P. Tewarson",
bibdate = "Sun Jan 14 09:09:38 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1990:DVK,
author = "Gene Golub and Bo K{\aa}gstr{\"o}m and Axel Ruhe and
Paul {Van Dooren}",
title = "Dedication to {Vera N. Kublanovskaya} on her 70th
Birthday",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "11",
number = "4",
pages = "vii--ix",
month = oct,
year = "1990",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/0611033",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "01A70",
MRnumber = "91j:01043",
bibdate = "Fri Oct 17 06:15:04 2003",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InProceedings{Golub:1990:IML,
author = "Gene H. Golub and John E. de Pillis",
title = "Toward an effective two-parameter {SOR} method",
crossref = "Kincaid:1990:IML",
pages = "107--119",
year = "1990",
MRclass = "65F10",
MRnumber = "038 091",
bibdate = "Sun Jan 14 10:13:28 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1990:MMI,
author = "Gene H. Golub and Martin H. Gutknecht",
title = "Modified Moments for Indefinite Weight Functions",
journal = j-NUM-MATH,
volume = "57",
number = "6\slash 7",
pages = "607--624",
month = jul,
year = "1990",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "30E05 (41A10 65F99)",
MRnumber = "91i:30034",
MRreviewer = "Jia Rong Yu",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Paper presented at the Conference on Approximation
Theory and Numerical Linear Algebra, 30 March -- 1
April, 1989, Kent, Ohio.",
abstract = "The problem of generating the recurrence coefficients
of orthogonal polynomials from the moments or from
modified moments of the weight function is well
understood for positive weight distributions. The
authors extend this theory and the basic algorithms to
the case of an indefinite weight function. While the
generic indefinite case is formally not much different
from the positive definite case, there exist nongeneric
degenerate situations, and these require a different
more complicated treatment. The understanding of these
degenerate situations makes it possible to construct a
stable approximate solution of an ill-conditioned
problem. The application to adaptive iterative methods
for linear systems of equations is anticipated.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Comput. Sci., Stanford Univ., CA, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "C4140 (Linear algebra)",
corpsource = "Dept. of Comput. Sci., Stanford Univ., CA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "adaptive iterative methods; Adaptive iterative
methods; degenerate situations; Degenerate situations;
ill-conditioned problem; Ill-conditioned problem;
indefinite weight functions; Indefinite weight
functions; iterative methods; linear algebra; linear
systems; Linear systems; orthogonal polynomials;
Orthogonal polynomials; polynomials",
thesaurus = "Iterative methods; Linear algebra; Polynomials",
treatment = "T Theoretical or Mathematical",
}
@InCollection{Golub:1990:PRJ,
author = "Gene Golub",
title = "Prologue. Reflections on {Jim Wilkinson}",
crossref = "Cox:1990:RNC",
pages = "1--5",
year = "1990",
MRclass = "01A70",
MRnumber = "92b:01057a",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Berry:1991:ELS,
author = "Michael Berry and Gene Golub",
title = "Estimating the Largest Singular Values of Large Sparse
Matrices via Modified Moments",
journal = j-NUMER-ALGORITHMS,
volume = "1",
number = "4",
pages = "353--374 (or 353--373??)",
month = nov,
year = "1991",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F15 (65D32 65F50 65Y05)",
MRnumber = "93a:65046",
MRreviewer = "Cs. J. Heged{\H{u}}s",
bibdate = "Mon Sep 9 11:25:40 MDT 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Cited in {\AA}ke Bj{\"o}rck's bibliography on least
squares, which is available by anonymous ftp from {\tt
math.liu.se} in {\tt pub/references}.",
abstract = "The authors describe a procedure for determining a few
of the largest singular values of a large sparse
matrix. The method by Golub and Kent (1989) which uses
the method of modified moments for estimating the
eigenvalues of operators used in iterative methods for
the solution of linear systems of equations is
appropriately modified in order to generate a sequence
of bidiagonal matrices whose singular values
approximate those of the original sparse matrix. A
simple Lanczos recursion is proposed for determining
the corresponding left and right singular vectors. The
potential asynchronous computation of the bidiagonal
matrices using modified moments with the iterations of
an adapted Chebyshev semi-iterative (CSI) method is an
attractive feature for parallel computers. Comparisons
in efficiency and accuracy with an appropriate Lanczos
algorithm (with selective re-orthogonalization) are
presented on large sparse (rectangular) matrices
arising from applications such as information retrieval
and seismic reflection tomography. This procedure is
essentially motivated by the theory of moments and
Gauss quadrature.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Tennessee Univ., Knoxville, TN,
USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290F (Interpolation and function approximation);
B0290H (Linear algebra); C4130 (Interpolation and
function approximation); C4140 (Linear algebra)",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Adaptive Chebyshev semi-iterative method; Asynchronous
computation; Eigenvalues; Gauss quadrature; Information
retrieval; Iterative methods; Lanczos recursion; Large
sparse matrices; Largest singular values estimation;
Linear systems of equations; Modified moments; nla,
sparse, svd; Parallel computers; Seismic reflection
tomography; Singular vectors",
pubcountry = "Switzerland",
thesaurus = "Chebyshev approximation; Eigenvalues and
eigenfunctions; Iterative methods; Matrix algebra",
}
@InProceedings{Boley:1991:MNL,
author = "D. Boley and G. H. Golub",
title = "A modified non-symmetric {Lanczos} algorithm and
applications",
crossref = "Vaccaro:1991:SSP",
pages = "189--196",
month = "????",
year = "1991",
bibdate = "Mon Sep 9 11:37:15 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "Gives a brief description of a non-symmetric Lanczos
algorithm that does not require strict bi-orthogonality
among the generated vectors. Several applications are
mentioned. For example, it is shown how the vectors
generated are algebraically related to `controllable
space' and `observable space' for a related linear
dynamical system. The algorithm described is
particularly appropriate for large sparse problems.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Minnesota, Univ., Minneapolis,
MN, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290H (Linear algebra); C4140 (Linear algebra)",
keywords = "Controllable space; Large sparse problems; Linear
dynamical system; Matrix eigenvalue computation;
Modified nonsymmetric Lanczos algorithm; Observable
space",
thesaurus = "Eigenvalues and eigenfunctions; Matrix algebra",
}
@Article{Boley:1991:NLA,
author = "Daniel Boley and Gene Golub",
title = "The nonsymmetric {Lanczos} algorithm and
controllability",
journal = j-SYST-CONTROL-LETT,
volume = "16",
number = "2",
pages = "97--105",
month = feb,
year = "1991",
CODEN = "SCLEDC",
ISSN = "0167-6911 (print), 1872-7956 (electronic)",
ISSN-L = "0167-6911",
MRclass = "93B05 (93B40)",
MRnumber = "92e:93004",
MRreviewer = "Alexander N. Shoshitaishvili",
bibdate = "Fri Dec 20 17:23:54 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "Gives a brief description of a nonsymmetric Lanczos
algorithm that does not require strict bi-orthogonality
among the generated vectors. The authors show how the
vectors generated are algebraically related to
reachable space and observable space for a related
linear dynamical system. The algorithm described is
particularly appropriate for large sparse systems.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Comput. Sci. Dept., Minnesota Univ., Minneapolis, MN,
USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "C1110 (Algebra); C1120 (Analysis); C1310 (Analysis
and synthesis methods); C1320 (Stability)",
fjournal = "Systems and Control Letters",
journal-URL = "http://www.sciencedirect.com/science/journal/01676911",
keywords = "Controllability; Large sparse systems; Linear
dynamical system; Nonsymmetric Lanczos algorithm;
Observability; Observable space; Reachable space;
Vectors",
pubcountry = "Netherlands",
thesaurus = "Algebra; Controllability; Linear systems;
Observability; Vectors",
}
@Article{Boley:1991:NLF,
author = "Daniel L. Boley and Sylvan Elhay and Gene H. Golub and
Martin H. Gutknecht",
title = "Nonsymmetric {Lanczos} and finding orthogonal
polynomials associated with indefinite weights",
journal = j-NUMER-ALGORITHMS,
volume = "1",
number = "1",
pages = "21--43",
month = "????",
year = "1991",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F15 (65F30 65F50 65G05)",
MRnumber = "93f:65033",
MRreviewer = "Alexander S. Babanin",
bibdate = "Sun Jan 14 08:49:25 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "The nonsymmetric Lanczos algorithm reduces a general
matrix to tridiagonal by generating two sequences of
vectors which satisfy a mutual bi-orthogonality
property. The process can proceed as long as the two
vectors generated at each stage are not mutually
orthogonal, otherwise the process breaks down. The
authors propose a variant that does not break down by
grouping the vectors into clusters and enforcing the
bi-orthogonality property only between different
clusters, but relaxing the property within clusters.
They show how this variant of the matrix Lanczos
algorithm applies directly to a problem of computing a
set of orthogonal polynomials and associated indefinite
weights with respect to an indefinite inner product,
given the associated moments. The authors discuss the
close relationship between the modified Lanczos
algorithm and the modified Chebyshev algorithm. They
further show the connection between this last problem
and checksum-based error correction schemes for
fault-tolerant computing.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Comput. Sci., Minnesota Univ., Minneapolis,
MN, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290H (Linear algebra); B6120B (Codes); C4140
(Linear algebra)",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Checksum-based error correction; Fault-tolerant
computing; Indefinite inner product; Indefinite
weights; Matrix Lanczos algorithm; Modified Chebyshev
algorithm; Modified Lanczos algorithm; Mutual
bi-orthogonality property; Nonsymmetric Lanczos
algorithm; Orthogonal polynomials; Tridiagonal matrix",
pubcountry = "Switzerland",
thesaurus = "Error correction codes; Matrix algebra; Polynomials",
}
@Article{DeMoor:1991:RSV,
author = "Bart L. R. De Moor and Gene H. Golub",
title = "The Restricted Singular Value Decomposition:
Properties and Applications",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "12",
number = "3",
pages = "401--425",
month = jul,
year = "1991",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/0612029",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Sun Jan 14 08:07:16 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "nla, gsvd",
}
@InProceedings{Elhay:1991:UDOa,
author = "Sylvan Elhay and G. H. Golub and Jaroslav
Kautsk{\'y}",
title = "Updating and downdating of orthogonal polynomials with
data fitting applications",
crossref = "Golub:1991:NLA",
pages = "149--172",
year = "1991",
MRclass = "65D15 (65F30)",
MRnumber = "92j:65017",
bibdate = "Sun Jan 14 09:02:43 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "Derives and assesses new methods for updating and
downdating least squares polynomial fits to discrete
data using polynomials orthogonal on all the data
points being used. Rather than fixing on one basis
throughout, the methods adaptively update and downdate
both the least squares fit and the polynomial basis.
This is achieved by performing similarity
transformations on the tridiagonal Jacobi matrices
representing the basis.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Comput. Sci., Adelaide Univ., SA, Australia",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B6140 (Signal processing and detection); C1260
(Information theory)",
keywords = "Data fitting applications; Data points; Downdating;
Least squares polynomial fits; Orthogonal polynomials;
Similarity transformations; Tridiagonal Jacobi
matrices; Updating",
thesaurus = "Data compression; Least squares approximations; Matrix
algebra; Polynomials",
}
@Article{Elhay:1991:UDOb,
author = "Sylvan Elhay and Gene H. Golub and Jaroslav
Kautsk{\'y}",
title = "Updating and downdating of orthogonal polynomials with
data fitting applications",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "12",
number = "2",
pages = "327--353",
month = apr,
year = "1991",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/0612024",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65D20 (65F05)",
MRnumber = "91m:65054",
bibdate = "Sun Jan 14 09:07:02 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Elman:1991:IMC,
author = "Howard C. Elman and Gene H. Golub",
title = "Iterative methods for cyclically reduced
nonselfadjoint linear systems. {II}",
journal = j-MATH-COMPUT,
volume = "56",
number = "193",
pages = "215--242",
month = jan,
year = "1991",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2008538",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "65F10 (65N22)",
MRnumber = "91e:65051",
MRreviewer = "Harry Yserentant",
bibdate = "Sun Jan 14 09:10:54 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
JSTOR database",
abstract = "For pt.~I see ibid., vol.~54, p.~671--700 (1990). The
authors perform an analytic and experimental study of
line iterative methods for solving linear systems
arising from finite difference discretizations of
nonself-adjoint elliptic partial differential equations
on two-dimensional domains. The methods consist of
performing one step of cyclic reduction, followed by
solution of the resulting reduced system by line
relaxation. They augment previous analyses of one-line
methods, and derive a new convergence analysis for
two-line methods, showing that both classes of methods
are highly effective for solving the
convection-diffusion equation. In addition, they
compare the experimental performance of several
variants of these methods, and show that the methods
can be implemented efficiently on parallel
architectures.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Comput. Sci., Maryland Univ., College Park,
MD, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290P (Differential equations); C4170 (Differential
equations)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "2D domains; Convection-diffusion equation; Convergence
analysis; Finite difference discretizations; Line
iterative methods; Line relaxation; Linear systems;
Nonself-adjoint elliptic partial differential
equations; Parallel architectures",
thesaurus = "Convergence of numerical methods; Iterative methods;
Parallel algorithms; Partial differential equations",
}
@Article{Ferng:1991:ALM,
author = "William R. Ferng and Gene H. Golub and Robert J.
Plemmons",
title = "Adaptive {Lanczos} methods for recursive condition
estimation",
journal = j-NUMER-ALGORITHMS,
volume = "1",
number = "1",
pages = "1--20",
month = "????",
year = "1991",
CODEN = "NUALEG",
ISSN = "1017-1398 (print), 1572-9265 (electronic)",
ISSN-L = "1017-1398",
MRclass = "65F10 (65F20 65F35 93E10 94A12)",
MRnumber = "92h:65053",
MRreviewer = "De Hui Chen",
bibdate = "Fri Nov 6 18:06:29 MST 1998",
bibsource = "http://www.math.psu.edu/dna/contents/na.html;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
abstract = "Estimates for the condition number of a matrix are
useful in many areas of scientific computing,
including: recursive least squares computations,
optimization, eigenanalysis, and general nonlinear
problems solved by linearization techniques where
matrix modification techniques are used. The purpose of
this paper is to propose an adaptive Lanczos estimator
scheme, which the authors call ale, for tracking the
condition number of the modified matrix over time.
Applications to recursive least squares (RLS)
computations using the covariance method with sliding
data windows are considered. ale is fast for relatively
small n-parameter problems arising in RLS methods in
control and signal processing, and is adaptive over
time, i.e., estimates at time t are used to produce
estimates at time t+1. Comparisons are made with other
adaptive and non-adaptive condition estimators for
recursive least squares problems. Numerical experiments
are reported indicating that ale yields a very accurate
recursive condition estimator.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Dept. of Math., North Carolina State Univ., Raleigh,
NC, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290F (Interpolation and function approximation);
B0290H (Linear algebra); B6140 (Signal processing and
detection); C1260 (Information theory); C4130
(Interpolation and function approximation); C4140
(Linear algebra)",
corpsource = "Dept. of Math., North Carolina State Univ., Raleigh,
NC, USA",
fjournal = "Numerical Algorithms",
journal-URL = "http://link.springer.com/journal/11075",
keywords = "Adaptive Lanczos estimator; adaptive Lanczos
estimator; Adaptive Lanczos methods; adaptive Lanczos
methods; Covariance method; covariance method; least
squares approximations; matrix algebra; Matrix
condition number; matrix condition number; Matrix
modification; matrix modification; numerical methods;
Recursive condition estimation; recursive condition
estimation; Recursive least squares computations;
recursive least squares computations; signal
processing; Sliding data windows; sliding data
windows",
pubcountry = "Switzerland",
thesaurus = "Least squares approximations; Matrix algebra;
Numerical methods; Signal processing",
treatment = "T Theoretical or Mathematical",
xxpages = "1--19",
}
@Article{Fischer:1991:GPW,
author = "Bernd Fischer and Gene H. Golub",
title = "On generating polynomials which are orthogonal over
several intervals",
journal = j-MATH-COMPUT,
volume = "56",
number = "194",
pages = "711--730",
month = apr,
year = "1991",
CODEN = "MCMPAF",
DOI = "https://doi.org/10.2307/2008403",
ISSN = "0025-5718 (paper), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
MRclass = "33C45",
MRnumber = "92d:33015",
MRreviewer = "J. Prasad",
bibdate = "Sun Jan 14 09:06:36 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
URL = "http://www.jstor.org/stable/2008403",
abstract = "The authors consider the problem of generating the
recursion coefficients of orthogonal polynomials for a
given weight function. The weight function is assumed
to be the weighted sum of weight functions, each
supported on its own interval. Some of these intervals
may coincide, overlap or are contiguous. They discuss
three algorithms. Two of them are based on modified
moments, whereas the other is based on an explicit
expression for the desired coefficients. Several
examples, illustrating the numerical performance of the
various methods, are presented.",
acknowledgement = ack-nhfb # " and " # ack-sf,
affiliation = "Inst. fur Angewandte Math., Hamburg Univ., Germany",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "B0290F (Interpolation and function approximation);
C4130 (Interpolation and function approximation)",
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
keywords = "Explicit expression; Generating polynomials; Modified
moments; Numerical performance; Recursion coefficients;
Weight function; Weighted sum",
thesaurus = "Polynomials",
}
@TechReport{Freund:1991:ISLa,
author = "Roland W. Freund and Gene H. Golub and No{\"e}l M.
Nachtigal",
title = "Iterative Solution of Linear Systems",
type = "Technical Report",
number = "NA-91-05",
institution = "Computer Science Department, Stanford University",
address = "Stanford, CA, USA",
month = "????",
year = "1991",
bibdate = "Sun Jan 14 08:46:41 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@InCollection{Gander:1991:CEP,
author = "Walter Gander and Gene H. Golub and Urs {von Matt}",
title = "A constrained eigenvalue problem",
crossref = "Golub:1991:NLA",
pages = "677--686",
year = "1991",
MRclass = "65F15",
MRnumber = "92k:65067",
bibdate = "Fri Dec 20 16:39:55 MST 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1991:DJW,
author = "G. Golub and B. Parlett",
title = "Dedication to {J. Wallace Givens}",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "12",
number = "1",
pages = "U1--U1",
month = jan,
year = "1991",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
bibdate = "Thu Jun 6 10:13:11 MDT 2013",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Golub:1991:HMN,
author = "Gene H. Golub",
title = "A history of modern numerical linear algebra",
journal = j-MITT-MATH-GES-HAMBURG,
volume = "12",
number = "4",
pages = "949--960",
year = "1991/1992",
CODEN = "MNGBAK",
ISSN = "0340-4358",
MRclass = "65-03 (01A60 65Fxx)",
MRnumber = "93c:65002",
bibdate = "Sun Jan 14 08:25:42 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Mathematische Wissenschaften gestern und heute. 300
Jahre Mathematische Gesellschaft in Hamburg, Teil 4
(Hamburg, 1990).",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "Mitteilungen der Mathematischen Gesellschaft in
Hamburg",
}
@InProceedings{Golub:1991:IMC,
author = "G. H. Golub and R. S. Tuminaro",
title = "Iterative Methods for Cyclically Reduced
Non-Self-Adjoint Linear Systems",
crossref = "Anonymous:1991:PIS",
pages = "7--8",
year = "1991",
bibdate = "Mon Aug 26 10:38:41 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Golub:1991:QCL,
author = "Gene H. Golub and Urs {von Matt}",
title = "Quadratically Constrained Least Squares and Quadratic
Problems",
journal = j-NUM-MATH,
volume = "59",
number = "6",
pages = "561--580",
month = sep,
year = "1991",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01385796",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F20 (65F50 65K10)",
MRnumber = "92f:65049",
MRreviewer = "R. P. Tewarson",
bibdate = "Sun Jan 14 09:05:23 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "The article considers the following problem: Compute a
vector x such that //Ax-b///sub 2/-min, subject to the
constraint //x///sub 2/= alpha. A new approach to this
problem based on Gauss quadrature is given. The method
is especially well suited when the dimensions of A are
large and the matrix is sparse. It is also possible to
extend this technique to a constrained quadratic form:
For a symmetric matrix A it considers the minimization
of x/sup T/Ax-2b/sup T/x subject to the constraint
//x///sub 2/= alpha. Some numerical examples are
given.",
acknowledgement = ack-nhfb,
affiliation = "Dept. of Comput. Sci., Stanford Univ., CA, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "C1110 (Algebra); C1180 (Optimisation techniques);
C4140 (Linear algebra)",
corpsource = "Dept. of Comput. Sci., Stanford Univ., CA, USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "constraints; Gauss quadrature; lsq; matrix algebra;
minimisation; Minimization; minimization; nla; nllsq;
nlop; Quadratically constrained least squares problems;
quadratically constrained least squares problems;
Quadratically constrained quadratic problems;
quadratically constrained quadratic problems; Sparse
matrix; sparse matrix; Symmetric matrix; symmetric
matrix; Vector; vector",
thesaurus = "Matrix algebra; Minimisation",
treatment = "T Theoretical or Mathematical",
}
@Article{Moor:1991:RSV,
author = "Bart L. R. De Moor and Gene H. Golub",
title = "The restricted singular value decomposition:
properties and applications",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "12",
number = "3",
pages = "401--425",
month = "????",
year = "1991",
CODEN = "SJMAEL",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "15A09 (15A18 15A21 15A24 47A99)",
MRnumber = "92k:15012",
MRreviewer = "Zdzislaw W. Trzaska",
bibdate = "Sun Jan 14 08:25:42 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Book{VanHuffel:1991:TLS,
author = "Sabine {Van Huffel} and Joos Vandewalle",
title = "The total least squares problem. Computational aspects
and analysis",
publisher = pub-SIAM,
address = pub-SIAM:adr,
pages = "xiv + 300",
year = "1991",
ISBN = "0-89871-275-0",
ISBN-13 = "978-0-89871-275-9",
LCCN = "QA275.H84 1991",
MRclass = "65-00 (00A69 65-01)",
MRnumber = "93b:65001",
MRreviewer = "R. P. Tewarson",
bibdate = "Sun Jan 14 08:25:42 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
note = "Foreword by Gene H. Golub.",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
}
@Article{Arbenz:1992:LAS,
author = "Peter Arbenz and Gene H. Golub",
title = "{$ Q R $}-Like Algorithms for Symmetric Arrow
Matrices",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "2",
pages = "655--658",
month = apr,
year = "1992",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/0613039",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15",
MRnumber = "92k:65064",
bibdate = "Sun Jan 14 08:58:46 1996",
bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib;
https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
acknowledgement = ack-nhfb,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
keywords = "nla, arrowhead matrix, QR algorithm, eig",
}
@Article{Bojanczyk:1992:PSD,
author = "A. Bojanczyk and G. Golub and P. {Van Dooren}",
title = "The periodic {Schur} decomposition: algorithms and
applications",
journal = j-PROC-SPIE,
volume = "1770",
pages = "31--42",
month = "????",
year = "1992",
CODEN = "PSISDG",
ISSN = "0277-786X (print), 1996-756X (electronic)",
ISSN-L = "0277-786X",
bibdate = "Mon Sep 9 11:06:23 MDT 1996",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "The authors derive a unitary eigendecomposition for a
sequence of matrices which they call the periodic Schur
decomposition. They prove its existence and discuss its
application to the solution of periodic difference
arising in control. It is shown how the classical QR
algorithm can be extended to provide a stable algorithm
for computing this generalized decomposition. The
decomposition is also applied to cyclic matrices and
two-point boundary value problems.",
acknowledgement = ack-nhfb,
affiliation = "Dept. Electr. Eng., Cornell Univ., Ithaca, NY, USA",
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
classification = "C1110 (Algebra); C1120 (Analysis); C1340G
(Time-varying systems); C4140 (Linear algebra); C4170
(Differential equations)",
fjournal = "Proceedings of the SPIE --- The International Society
for Optical Engineering",
keywords = "Cyclic matrices; Matrix sequence; Periodic difference;
Periodic Schur decomposition; QR algorithm; Stable
algorithm; Time-varying control systems; Two-point
boundary value problems; Unitary eigendecomposition",
thesaurus = "Boundary-value problems; Difference equations;
Eigenvalues and eigenfunctions; Matrix algebra;
Time-varying systems",
}
@Article{Boley:1992:AFT,
author = "Daniel L. Boley and Richard P. Brent and Gene H. Golub
and Franklin T. Luk",
title = "Algorithmic Fault Tolerance Using the {Lanczos}
Method",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "1",
pages = "312--332",
month = jan,
year = "1992",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/0613023",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15 (94B05)",
MRnumber = "93f:65034",
MRreviewer = "Herbert J. Bernstein",
bibdate = "Tue Jan 21 08:54:30 MST 1997",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib",
acknowledgement = ack-nhfb # " and " # ack-sf,
author-dates = "Gene Howard Golub (February 29, 1932--November 16,
2007)",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@Article{Carey:1992:NAS,
author = "Cheryl Carey and Hsin-Chu Chen and G. H. Golub and
Ahmed Sameh",
title = "A new approach for solving symmetric eigenvalue
problems",
journal = j-COMPUT-SYST-ENG,
volume = "3",
number = "6",
pages = "671--679",
month = dec,
year = "1992",
CODEN = "COSEEO",
ISSN = "0956-0521 (print), 1873-6211 (electronic)",
ISSN-L = "0956-0521",
bibsource = "https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib",
abstract = "Presents a new approach for the solution to a series
of slightly perturbed symmetric eigenvalue problems
(A+BS/sub i/B/sup T/)x= lambda x, 0