%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author-1 = "Nelson H. F. Beebe", %%% author-2 = "Stefano Foresti", %%% version = "1.54", %%% date = "06 June 2013", %%% time = "12:00:47 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 = "http://www.math.utah.edu/~beebe", %%% checksum = "25752 11836 50094 508299", %%% 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 1.54, the year coverage looked %%% like this: %%% %%% 1959 ( 1) 1977 ( 13) 1995 ( 8) %%% 1960 ( 0) 1978 ( 12) 1996 ( 13) %%% 1961 ( 2) 1979 ( 19) 1997 ( 16) %%% 1962 ( 2) 1980 ( 8) 1998 ( 9) %%% 1963 ( 3) 1981 ( 5) 1999 ( 16) %%% 1964 ( 1) 1982 ( 8) 2000 ( 8) %%% 1965 ( 7) 1983 ( 8) 2001 ( 9) %%% 1966 ( 1) 1984 ( 7) 2002 ( 8) %%% 1967 ( 2) 1985 ( 5) 2003 ( 10) %%% 1968 ( 3) 1986 ( 4) 2004 ( 12) %%% 1969 ( 9) 1987 ( 14) 2005 ( 13) %%% 1970 ( 8) 1988 ( 9) 2006 ( 12) %%% 1971 ( 5) 1989 ( 14) 2007 ( 17) %%% 1972 ( 3) 1990 ( 17) 2008 ( 9) %%% 1973 ( 16) 1991 ( 22) 2009 ( 7) %%% 1974 ( 8) 1992 ( 16) 2010 ( 2) %%% 1975 ( 6) 1993 ( 13) 2011 ( 2) %%% 1976 ( 12) 1994 ( 18) %%% %%% Article: 269 %%% Book: 30 %%% InBook: 1 %%% InCollection: 21 %%% InProceedings: 61 %%% Misc: 1 %%% PhdThesis: 1 %%% Proceedings: 57 %%% TechReport: 31 %%% %%% Total entries: 472 %%% %%% 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 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ==================================================================== @Preamble{"\ifx \undefined \booktitle \def \booktitle#1{{{\em #1}}} \fi"} %%% ==================================================================== %%% Acknowledgement abbreviations: @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|http://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: @String{inst-ANL = "Argonne National Laboratory"} @String{inst-ANL:adr = "9700 South Cass Avenue, Argonne, IL 60439-4801, USA"} @String{inst-CORNELL = "Cornell University"} @String{inst-CORNELL:adr = "Ithaca, NY, USA"} @String{inst-CSRD = "Center for Supercomputing Research and Development"} @String{inst-CSRD:adr = "University of Illinois at Urbana-Champaign, Urbana, IL, USA"} @String{inst-STANFORD-CS = "Department of Computer Science, Stanford University"} @String{inst-STANFORD-CS:adr = "Stanford, CA"} @String{inst-U-MARYLAND = "University of Maryland"} @String{inst-U-MARYLAND-CS = "Department of Computer Science, University of Maryland"} @String{inst-U-MARYLAND-CS:adr = "College Park, MD, USA"} %%% ==================================================================== %%% Journal abbreviations: @String{inst-U-MARYLAND:adr = "College Park, MD, USA"} @String{j-ACTA-NUMERICA = "Acta Numerica"} @String{j-AMER-MATH-MONTHLY = "American Mathematical Monthly"} @String{j-AMER-STAT = "The American Statistician"} @String{j-ANN-HIST-COMPUT = "Annals of the History of Computing"} @String{j-ANN-MATH-STAT = "Ann. Math. Statist."} @String{j-ANN-NUM-MATH = "Annals of Numerical Mathematics"} @String{j-ANN-STAT = "Annals of Statistics"} @String{j-APL-MAT = "Aplicace Mathematicky"} @String{j-APPL-MATH-OPTIM = "Appl. Math. Optim."} @String{j-APPL-NUM-MATH = "Applied Numerical Mathematics"} @String{j-BAMS-NS = "Bulletin (new series) of the American Mathematical Society"} @String{j-BIOINFORMATICS = "Bioinformatics"} @String{j-BIOMETRICS = "Biometrics"} @String{j-BIT = "BIT"} @String{j-BIT-NUM-MATH = "BIT Numerical Mathematics"} @String{j-BULL-AUSTRAL-MATH-SOC = "Bull. Austral. Math. Soc."} @String{j-CACM = "Communications of the Association for Computing Machinery"} @String{j-CALCOLO = "Calcolo"} @String{j-COMP-MATH-APPL = "Computers and Mathematics with Applications"} @String{j-COMP-METH-APPL-MECH-ENG = "Comp. Methods in Appl. Mech. and Engrg."} @String{j-COMP-PHYS = "J. Computational Physics"} @String{j-COMPUT-SYST-ENG = "Computing Systems in Engineering"} @String{j-COMPUTING = "Computing"} @String{j-DOKL-MATH = "Doklady Mathematics"} @String{j-ELECTRON-TRANS-NUMER-ANAL = "Electronic Transactions on Numerical Analysis"} @String{j-FOUND-COMPUT-MATH = "Foundations of Computational Mathematics"} @String{j-IEEE-ANN-HIST-COMPUT = "IEEE Annals of the History of Computing"} @String{j-IEEE-SIGNAL-PROCESS-LETT = "IEEE Signal Processing Letters"} @String{j-IEEE-TRANS-AUTOMAT-CONTR = "IEEE Transactions on Automatic Control"} @String{j-IEEE-TRANS-CIRC-SYS = "IEEE Trans. on Circuits and Systems"} @String{j-IEEE-TRANS-CIRCUITS-SYST-2 = "IEEE transactions on circuits and systems. 2, Analog and digital signal processing"} @String{j-IEEE-TRANS-CIRCUITS-SYST-VIDEO-TECH = "IEEE Transactions on Circuits and Systems for Video Technology"} @String{j-IEEE-TRANS-COMPUT = "IEEE Transactions on Computers"} @String{j-IEEE-TRANS-IMAGE-PROCESS = "IEEE Transactions on Image Processing"} @String{j-IEEE-TRANS-MED-IMAG = "IEEE Transactions on Medical Imaging"} @String{j-IEEE-TRANS-SIG-PROC = "IEEE Transactions on Signal Processing"} @String{j-IMA-J-NUMER-ANAL = "IMA Journal of Numerical Analysis"} @String{j-IMA-VOL-MATH-APPL = "The IMA volumes in mathematics and its applications"} @String{j-INT-J-NUMER-METHODS-ENG = "International Journal for Numerical Methods in Engineering"} @String{j-INT-J-NUMER-METHODS-FLUIDS = "International Journal for Numerical Methods in Fluids"} @String{j-INTERNET-MATH = "Internet Mathematics"} @String{j-INVERSE-PROBLEMS = "Inverse Problems"} @String{j-J-AM-STAT-ASSOC = "Journal of the American Statistical Association"} @String{j-J-COMP-APPL-MATH = "Journal of Computational and Applied Mathematics"} @String{j-J-COMPUT-GRAPH-STAT = "Journal of Computational and Graphical Statistics"} @String{j-J-ECONOMETRICS = "J. of Econometrics"} @String{j-LECT-NOTES-COMP-SCI = "Lecture Notes in Computer Science"} @String{j-LINEAR-ALGEBRA-APPL = "Linear Algebra and its Applications"} @String{j-MAA-STUD-MATH = "MAA studies in mathematics"} @String{j-MATH-ANAL-APPL = "J. Math. Anal. Appl."} @String{j-MATH-COMPUT = "Mathematics of Computation"} @String{j-MATH-PROG = "Mathematical Programming"} @String{j-MITT-MATH-GES-HAMBURG = "Mitteilungen der Mathematischen Gessellschaft in Hamburg"} @String{j-NORDISK-TIDSKR-INFORM-BEHAND = "Nordisk tidskrift for informationsbehandling"} @String{j-NUM-LIN-ALG-APPL = "Numerical Linear Algebra with Applications"} @String{j-NUM-MATH = "Numerische Mathematik"} @String{j-NUMER-ALGORITHMS = "Numerical Algorithms"} @String{j-PAMM = "Proceedings in Applied Mathematics and Mechanics"} @String{j-PROC-IEEE = "Proc. IEEE"} @String{j-PROC-NATL-ACAD-SCI-USA = "Proceedings of the National Academy of Sciences of the United States of America"} @String{j-PROC-SPIE = "Proceedings of the SPIE --- The International Society for Optical Engineering"} @String{j-ROCKY-MOUNTAIN-J-MATH = "Rocky Mountain J. of Math."} @String{j-SIAM = "Journal of the Society for Industrial and Applied Mathematics"} @String{j-SIAM-J-ALG-DISC-METH = "SIAM Journal of Algebraic Discrete Methods"} @String{j-SIAM-J-APPL-MATH = "SIAM Journal on Applied Mathematics"} @String{j-SIAM-J-MAT-ANA-APPL = "SIAM Journal on Matrix Analysis and Applications"} @String{j-SIAM-J-NUMER-ANAL = "SIAM Journal on Numerical Analysis"} @String{j-SIAM-J-NUM-ANALYSIS-B = "Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis"} @String{j-SIAM-J-SCI-COMP = "SIAM Journal on Scientific Computing"} @String{j-SIAM-J-SCI-STAT-COMP = "SIAM Journal on Scientific and Statistical Computing"} @String{j-SIAM-NEWS = "SIAM News"} @String{j-SIAM-REVIEW = "SIAM Review"} @String{j-SIGNUM = "ACM SIGNUM Newsletter"} @String{j-SIGPLAN = "ACM SIGPLAN Notices"} @String{j-STAT-COMPUT-SIMUL = "J. Stat. Comput. Simul."} @String{j-SYST-CONTROL = "Systems and Control"} @String{j-SYST-CONTROL-LETT = "Systems and Control Letters"} @String{j-TECHNOMETRICS = "Technometrics"} @String{j-TOMS = "ACM Transactions on Mathematical Software"} @String{j-Z-ANGE-MATH-MECH = "{Zeitschrift f{\"u}r Angewandte Mathematik und Mechanik}"} @String{j-ZEIT-ANGE-MATH-PHYS = "Z. Angew. Math. Phys"} %%% ==================================================================== %%% Miscellaneous abbreviations: @String{prep-latex = "Prepared with {\LaTeX}."} %%% ==================================================================== %%% Publishers and their addresses: @String{pub-ACADEMIC = "Academic Press"} @String{pub-ACADEMIC:adr = "New York, NY, USA"} @String{pub-ACM = "ACM Press"} @String{pub-ACM:adr = "New York, NY 10036, USA"} @String{pub-AMS = "American Mathematical Society"} @String{pub-AMS:adr = "Providence, RI, USA"} @String{pub-AP = "Academic Press"} @String{pub-AP:adr = "Boston, MA, USA"} @String{pub-BIRKHAUSER = "Birkh{\"a}user Verlag"} @String{pub-BIRKHAUSER:adr = "Basel, Switzerland"} @String{pub-CUP = "Cambridge University Press"} @String{pub-CUP:adr = "Cambridge, UK"} @String{pub-ELS = "Elsevier"} @String{pub-ELS:adr = "Amsterdam, The Netherlands"} @String{pub-ENH = "Elsevier North-Holland, Inc."} @String{pub-ENH:adr = "New York, NY, USA"} @String{pub-ESP = "Elsevier Science Publishers"} @String{pub-ESP:adr = "Amsterdam, The Netherlands"} @String{pub-EYROLLES = "Editions Eyrolles"} @String{pub-EYROLLES:adr = "Paris, France"} @String{pub-IEEE = "IEEE Computer Society Press"} @String{pub-IEEE:adr = "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} @String{pub-JH = "The Johns Hopkins University Press"} @String{pub-JH:adr = "Baltimore, MD, USA"} @String{pub-JHUP = "The Johns Hopkins University Press"} @String{pub-JHUP:adr = "Baltimore, MD, USA"} @String{pub-KLUWER = "Kluwer Academic Publishers Group"} @String{pub-KLUWER:adr = "Norwell, MA, USA, and Dordrecht, The Netherlands"} @String{pub-LONGMAN = "Longman Scientific and Technical"} @String{pub-LONGMAN:adr = "Essex, UK"} @String{pub-MATH-ASSOC-AMER = "Mathematical Association of America"} @String{pub-MATH-ASSOC-AMER:adr = "Washington, DC, USA"} @String{pub-NH = "North-Holland Publishing Co."} @String{pub-NH:adr = "Amsterdam, The Netherlands"} @String{pub-NORTH-OXFORD = "North Oxford Academic"} @String{pub-NORTH-OXFORD:adr = "Oxford, England"} @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 Mathematics"} @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, Germany~/ London, UK~/ etc."} @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"} @String{pub-WORLD-SCI = "World Scientific Publishing Co. Pte. Ltd."} @String{pub-WORLD-SCI:adr = "P. O. Box 128, Farrer Road, Singapore 9128, and River Edge, NJ, USA"} %%% ==================================================================== %%% %%% 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; http://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, keywords = "numerical analysis; numerical calculations; relaxation methods (mathematics)", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; JSTOR database", URL = "http://www.jstor.org/stable/2003134", acknowledgement = ack-nhfb, } @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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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; http://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, 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 coefficient", journal = j-ANN-MATH-STAT, volume = "34", number = "3", pages = "984--991", month = sep, year = "1963", CODEN = "AASTAD", DOI = "http://dx.doi.org/10.1214/aoms/1177704021", ISSN = "0003-4851", MRclass = "62.55", MRnumber = "27\#5336", MRreviewer = "A. C. Cohen", bibdate = "Sun Jan 14 10:07:20 1996", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://projecteuclid.org/euclid.aoms/1177704021", acknowledgement = ack-nhfb # " and " # ack-sf, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; JSTOR database", URL = "http://www.jstor.org/stable/2003639", acknowledgement = ack-nhfb, } @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 = "ftp://ftp.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.jstor.org/journals/01621459.html; http://www.jstor.org/stable/i314185; http://www.math.utah.edu/pub/tex/bib/jamstatassoc1960.bib", URL = "http://www.jstor.org/stable/2283384", acknowledgement = ack-nhfb, fjournal = "Journal of the American Statistical Association", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; JSTOR database", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", note = "Also in \cite[pp. 111--118]{Wilkinson:1971:LA}.", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib; http://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, 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)", MRclass = "65.35", MRnumber = "32 \#587", bibdate = "Fri Oct 16 06:57:22 MDT 1998", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR database", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, 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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, 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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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; http://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, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, } @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/; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/cacm1960.bib", note = "See certification \cite{Schryer:1969:CA}.", acknowledgement = ack-nhfb, 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.", } @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/; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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, 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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Sat Nov 26 10:31:36 2005", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/cacm.bib", note = "ACM Algorithm 350.", acknowledgement = ack-nhfb, } @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", ISSN = "0001-0782 (print), 1557-7317 (electronic)", ISSN-L = "0001-0782", bibdate = "Sat Nov 26 10:31:36 2005", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/cacm.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/cacm.bib", note = "ACM Algorithm 358.", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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, 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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, } @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; http://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, 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; http://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, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR database", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, 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 = "Adadie: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; http://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, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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, 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-ZEIT-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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR database", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/cacm.bib", note = "ACM Algorithm 414.", acknowledgement = ack-nj, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, } @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-MATH-ANAL-APPL, volume = "37", number = "??", pages = "151--166", month = "????", year = "1972", MRclass = "65F99", MRnumber = "45 1368", MRreviewer = "J. G. Herriot", bibdate = "Sun Jan 14 09:56:10 1996", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb # " and " # ack-sf, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, 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 = "http://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, classcodes = "B0240 (Probability and statistics); B0290H (Linear algebra); C1140 (Probability and statistics); C4140 (Linear algebra)", corpsource = "Link{\"o}ping Univ., Sweden", 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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; JSTOR database", URL = "http://www.jstor.org/stable/2156207", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, } @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", ISSN-L = "0004-9727", MRclass = "60J10 (68A10)", MRnumber = "50 \#8710", MRreviewer = "I. Vaduva", bibdate = "Fri Dec 20 17:00:44 1996", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR database", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb # " and " # ack-sf, } @Article{Golub:1973:NCU, author = "Gene H. Golub and George P. Styan", title = "Numerical Computations for Univariate Linear Models", journal = j-STAT-COMPUT-SIMUL, volume = "2", number = "??", pages = "253--274", month = "????", year = "1973", MRclass = "62J05 (65F05)", MRnumber = "51 11840", MRreviewer = "Valery Fedorov", bibdate = "Sun Jan 14 09:50:51 1996", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Theory/Matrix.bib; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, } @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", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "65F15", MRnumber = "48 7569", MRreviewer = "J. F. Traub", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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/2028604", acknowledgement = ack-nhfb, error = "conflicting pages with your cv: 318-335", keywords = "nla, eig, updating", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; JSTOR database", acknowledgement = ack-nhfb, classcodes = "B0290P (Differential equations); B0220 (Mathematical analysis); C4170 (Differential equations)", corpsource = "New York Univ., NY, USA", 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 = "http://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, classcodes = "B0290H (Linear algebra); C4140 (Linear algebra)", corpsource = "Nat. Phys. Lab., Teddington, UK", 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 = "http://dx.doi.org/10.1216/RMJ-1974-4-2-207", ISSN = "0035-7596", ISSN-L = "0035-7596", MRclass = "65F30", MRnumber = "48 12803", MRreviewer = "Walter Gautschi", bibdate = "Sun Jan 14 09:54:42 1996", bibsource = "http://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, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib; JSTOR database", acknowledgement = ack-nhfb, 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", ISSN-L = "0004-9727", MRclass = "60J10", MRnumber = "51 \#9212", MRreviewer = "Dean Isaacson", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, } @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-AP, address = pub-AP: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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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:SIS", 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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib", note = "Published as \cite{Golub:1976:ICE}.", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, } @Article{Golub:1975:WPS, author = "G. H. Golub and L. Jennings and W. Yang", title = "Waves in periodically structured media", journal = j-COMP-PHYS, volume = "17", number = "4", pages = "349--357", month = "????", year = "1975", CODEN = "JCTPAH", DOI = "http://dx.doi.org/10.1016/0021-9991(75)90039-X", ISSN = "0021-9991", ISSN-L = "0021-9991", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, fjournal = "Journal of Computational Physics", } @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:SSM", pages = "409--426", year = "1976", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, 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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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:SSM", pages = "309--332", year = "1976", MRclass = "65F10 (65P05)", MRnumber = "58", MRreviewer = "M. R. Hestenes", bibdate = "Sun Jan 14 09:48:20 1996", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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", ISSN-L = "0036-1445", bibdate = "Thu Jun 6 10:13:11 MDT 2013", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, } @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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, keywords = "nla, eig, Jordan form, condition, pert, ill-conditioned problem", } @TechReport{Golub:1976:RDL, author = "G. H. Golub and V. 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, month = "????", year = "1976", bibsource = "ftp://ftp.ira.uka.de/pub/bibliography/Techreports/university-of-maryland.bib; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.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, keywords = "nla, svd, qrd, condition estimation, rank determination, pert, variable selection", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, } @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", ISSN = "0036-1445 (print), 1095-7200 (electronic)", ISSN-L = "0036-1445", MRclass = "65F15", MRnumber = "55 1716", MRreviewer = "B. Levinger", bibdate = "Sun Jan 14 09:50:11 1996", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://www.jstor.org/stable/2029322", acknowledgement = ack-nhfb # " and " # ack-sf, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/ovr.bib", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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:MSS", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-sf, 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 = "http://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, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-sf, } @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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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", ISSN-L = "0095-4616", MRclass = "90C30 (90C05)", MRnumber = "80a:90120", bibdate = "Mon Jan 15 09:15:16 1996", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb # " and " # ack-sf, fjournal = "Applied Mathematics and Optimization", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb # " and " # ack-sf, } @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", pages = "245--260", 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 = "Sat Apr 16 17:44:41 2005", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-sf, fjournal = "Linear Algebra and its Applications", } @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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "mailto::lmc@cs.cornell.edu", acknowledgement = ack-nhfb, } @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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "mailto::lmc@cs.cornell.edu", acknowledgement = ack-nhfb, } @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", ISSN-L = "0036-1445", bibdate = "Thu Jun 6 10:13:11 MDT 2013", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Review", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "With a German translation.", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @Article{Golub:1979:DSE, author = "G. H. Golub and W. Langlois", title = "Direct solution of the equation for the {Stokes} stream function", journal = j-COMP-METH-APPL-MECH-ENG, volume = "19", number = "3", pages = "391--399", month = "????", year = "1979", CODEN = "CMMECC", DOI = "http://dx.doi.org/10.1016/0045-7825(79)90066-5", ISSN = "0045-7825", ISSN-L = "0045-7825", MRclass = "76D05 (65P05)", MRnumber = "82c:76029", MRreviewer = "C. Taylor", bibdate = "Fri Dec 20 17:07:23 1996", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, fjournal = "Computer Methods in Applied Mechanics and Engineering", } @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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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, fjournal = "Technometrics", 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} $}", type = "Technical Report", number = "STAN-CS-79-713", institution = inst-STANFORD-CS, address = inst-STANFORD-CS:adr, pages = "50", month = "????", year = "1979", bibdate = "Mon Oct 24 10:35:29 MDT 1994", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, keywords = "matrix mechanics; numerical analysis", } @Article{Golub:1979:HSMb, author = "G. H. Golub and S. Nash and C. {Van Loan}", title = "A {Hessenberg--Schur} Method for the Matrix Problem {$ A X + X B = C $}", journal = j-IEEE-TRANS-AUTOMAT-CONTR, volume = "24", number = "6", pages = "909--913", month = "????", year = "1979", CODEN = "IETAA9", DOI = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-sf, fjournal = "IEEE Transactions on Automatic Control", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, } @InProceedings{Golub:1979:SLS, author = "G. H. Golub and R. Plemmons", title = "Sparse least squares problems", crossref = "ISCMASE:1979:PIF", pages = "??--??", year = "1979", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, } @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; http://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, keywords = "nla, svd, total least squares", } @Article{Golub:1979:UPD, author = "G. H. Golub and C. F. {Van Loan}", title = "Unsymmetric Positive Definite Linear Systems", journal = j-LINEAR-ALGEBRA-APPL, volume = "28", pages = "85--97", year = "1979", CODEN = "LAAPAW", DOI = "http://dx.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 = "Sun Jan 14 09:43:05 1996", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", 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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "mailto::lmc@cs.cornell.edu", acknowledgement = ack-sf, } @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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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, 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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", keywords = "nla, lsq, sparse, geodesy, qrd", } @Book{Golub:1980:NA, author = "Gene H. Golub and Joseph Oliger", title = "Numerical analysis", volume = "22", publisher = pub-AMS, address = pub-AMS:adr, pages = "viii + 135", year = "1980", ISBN = "0-8218-0122-8", ISBN-13 = "978-0-8218-0122-2", LCCN = "QA1 .S93 v.22", MRclass = "65-06", MRnumber = "80c:65007", bibdate = "Sun Jan 14 09:43:24 1996", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.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.", keywords = "Numerical analysis.", } @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 = "http://dx.doi.org/10.1016/0304-4076(80)90051-2", ISSN = "0304-4076", ISSN-L = "0304-4076", bibdate = "Thu Jun 6 10:13:11 MDT 2013", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Econometrics", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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/; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Translated from the English by Cheng Ming Huang", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, 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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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, 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", } @InProceedings{Golub:1981: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 = "1981", MRclass = "65F10", MRnumber = "83f:65045", bibdate = "Sun Jan 14 09:32:52 1996", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb # " and " # ack-sf, } @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 = "http://www.springerlink.com/openurl.asp?genre=article&id=doi: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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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, 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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, descriptors = "Simulation; statistics; numeric calculation;", } @InCollection{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", MRclass = "65F10", MRnumber = "83f:65045", bibdate = "Fri Dec 20 16:39:55 MST 1996", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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 = "http://dx.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; http://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, error = "in Gene's cv is Statistical Computing, but we found this reference: The American Statistician", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", URL = "http://www.jstor.org/stable/2683386", acknowledgement = ack-nhfb, country = "USA", date = "13/05/93", descriptors = "Simulation; statistics; numeric calculation;", enum = "7109", fjournal = "The American Statistician", 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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, classification = "B0290M (Numerical integration and differentiation); C4160 (Numerical integration and differentiation)", corpsource = "Dept. of Computer Sci., Stanford Univ., Stanford, CA, USA", 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-JH # " and " # pub-NORTH-OXFORD, address = pub-JH: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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.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, 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.", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/ovr.bib", acknowledgement = ack-nhfb, } @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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", 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 = "http://dx.doi.org/10.1016/S0167-6911(84)80072-9", ISSN = "0167-6911", 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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; JSTOR database", URL = "http://www.jstor.org/stable/2007564", acknowledgement = ack-nhfb, classcodes = "B0210 (Algebra); C1110 (Algebra)", corpsource = "Computer Sci. Dept., Univ. of Minnesota, Minneapolis, MN, USA", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Reprinted in \cite{Chan:2007:MMC}.", acknowledgement = ack-nhfb, } @Article{Gallant:1984:ICR, author = "R. Gallant and G. H. Golub", title = "Imposing curvature restrictions on flexible functional forms", journal = j-J-ECONOMETRICS, volume = "26", number = "??", pages = "295--321", month = "????", year = "1984", CODEN = "JECMB6", DOI = "http://dx.doi.org/10.1016/0304-4076(84)90024-1", ISSN = "0304-4076", ISSN-L = "0304-4076", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, } @Book{Golub:1984:SNA, editor = "Gene H. Golub", title = "Studies in Numerical Analysis", volume = "24", publisher = pub-MATH-ASSOC-AMER, address = pub-MATH-ASSOC-AMER:adr, pages = "x + 415", year = "1984", ISBN = "0-88385-126-1 (v. 1), 0-88385-100-8 (set)", ISBN-13 = "978-0-88385-126-5 (v. 1), 978-0-88385-100-5 (set)", LCCN = "QA297 .S83 1984", MRclass = "65-06", MRnumber = "88i:65007", bibdate = "Sat Oct 22 17:16:36 1994", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", series = "Studies in mathematics", acknowledgement = ack-nhfb, keywords = "numerical analysis", } @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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", note = "See corrigendum \cite{Concus:1985:CBP}.", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "See \cite{Concus:1985:BPC}.", acknowledgement = ack-nhfb, } @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", ISSN-L = "0006-341X", bibdate = "Thu Jun 6 10:13:11 MDT 2013", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, fjournal = "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 = "http://dx.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; http://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, 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 = "http://dx.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; http://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, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/ovr.bib", acknowledgement = ack-nhfb, 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 = "http://dx.doi.org/10.1137/0607031", ISSN = "0196-5212", MRclass = "60J10 (65F05)", MRnumber = "87i:60073", MRreviewer = "M. F. Neuts", bibdate = "Sun Jan 14 09:22:16 1996", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, } @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 = "http://dx.doi.org/10.1088/0266-5611/3/4/010", ISSN = "0266-5611", ISSN-L = "0266-5611", MRclass = "65F15", MRnumber = "89m:65036", bibdate = "Sat Apr 16 17:44:41 2005", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb # " and " # ack-sf, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", } @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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", } @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; http://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, 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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://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", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", 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 = jan, year = "1988", CODEN = "SJMAEL", DOI = "http://dx.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 = "Sun Jan 14 09:20:14 1996", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, 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 = "http://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", 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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, classification = "B0290H (Linear algebra); C4140 (Linear algebra)", corpsource = "Dept. of Comput. Sci., Stanford Univ., CA, USA", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/gvl.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", } @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", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", price = "US\$29.95", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb # " and " # ack-sf, } @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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", } @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 = "http://dx.doi.org/10.1214/aos/1176347120", ISSN = "0090-5364", bibdate = "Tue May 18 17:06:23 2010", bibsource = "http://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, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, fjournal = "Linear Algebra and its Applications", 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 = "http://dx.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 = "http://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", classcodes = "C4140 (Linear algebra); C4130 (Interpolation and function approximation); C4160 (Numerical integration and differentiation)", corpsource = "Dept. of Comp. Sci., Stanford Univ., CA, USA", 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-JHUP, address = pub-JHUP: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 = "Sun Jan 14 09:14:13 1996", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/tex/bib/texbook2.bib", note = "Second edition", series = "Johns Hopkins Series in the Mathematical Sciences", URL = "http://www.jstor.org/stable/2008552", acknowledgement = ack-nhfb, keywords = "book; math; matrices --- data processing; matrices --- informatique; na; nla", remark = "See review by G. W. S. in Mathematics of Computation, Vol. 56, No. 193 (Jan., 1991), pp. 380-381.", } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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", classification = "723; 921", fjournal = "SIAM Review", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://dx.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; http://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", 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 = "http://dx.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 = "http://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", classification = "B0290P (Differential equations); C4170 (Differential equations)", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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 = "http://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, 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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", classification = "B0290H (Linear algebra); B6140 (Signal processing and detection); C1240 (Adaptive system theory); C1260 (Information theory); C4140 (Linear algebra)", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-sf, } @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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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 = "http://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", classification = "C4140 (Linear algebra)", corpsource = "Dept. of Comput. Sci., Stanford Univ., CA, USA", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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; http://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", classification = "B0290F (Interpolation and function approximation); B0290H (Linear algebra); C4130 (Interpolation and function approximation); C4140 (Linear algebra)", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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", 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", ISSN-L = "0167-6911", MRclass = "93B05 (93B40)", MRnumber = "92e:93004", MRreviewer = "Alexander N. Shoshitaishvili", bibdate = "Fri Dec 20 17:23:54 1996", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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", classification = "C1110 (Algebra); C1120 (Analysis); C1310 (Analysis and synthesis methods); C1320 (Stability)", 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 = "http://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", classification = "B0290H (Linear algebra); B6120B (Codes); C4140 (Linear algebra)", 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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://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", 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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb # " and " # ack-sf, } @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 = "http://dx.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 = "http://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", classification = "B0290P (Differential equations); C4170 (Differential equations)", 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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://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", 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", 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 = "http://dx.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 = "http://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", classification = "B0290F (Interpolation and function approximation); C4130 (Interpolation and function approximation)", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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", ISSN-L = "0895-4798", bibdate = "Thu Jun 6 10:13:11 MDT 2013", bibsource = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib", acknowledgement = ack-nhfb, fjournal = "SIAM Journal on Matrix Analysis and Applications", } @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 = "http://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, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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 = "http://dx.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; http://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", classification = "C1110 (Algebra); C1180 (Optimisation techniques); C4140 (Linear algebra)", corpsource = "Dept. of Comput. Sci., Stanford Univ., CA, USA", 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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, } @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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", note = "Foreword by Gene H. Golub.", acknowledgement = ack-nhfb, } @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 = "http://dx.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; http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib", acknowledgement = ack-nhfb, 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 = "http://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", classification = "C1110 (Algebra); C1120 (Analysis); C1340G (Time-varying systems); C4140 (Linear algebra); C4170 (Differential equations)", 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 = "http://dx.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 = "http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib", acknowledgement = ack-nhfb # " and " # ack-sf, fjournal = "SIAM Journal on Matrix Analysis and Applications", } @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", ISSN-L = "0956-0521", bibsource = "http://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