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%%% date = "28 August 2020",
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%%% docstring = "This is a bibliography of publications of the
%%% late James H. Wilkinson (27 September 1919--5
%%% October 1986). The companion LaTeX file
%%% wilkinson-james-hardy.ltx can be used to
%%% typeset this bibliography.
%%%
%%% See
%%%
%%% http://www-history.mcs.st-and.ac.uk/Biographies/Wilkinson.html
%%%
%%% and entry Fox:1987:JHW for biographies of
%%% James H. Wilkinson.
%%%
%%% At version 1.65, the year coverage looked
%%% like this:
%%%
%%% 1948 ( 5) 1972 ( 5) 1996 ( 0)
%%% 1950 ( 0) 1974 ( 13) 1998 ( 0)
%%% 1951 ( 3) 1975 ( 6) 1999 ( 0)
%%% 1952 ( 1) 1976 ( 6) 2000 ( 0)
%%% 1953 ( 0) 1977 ( 4) 2001 ( 0)
%%% 1954 ( 3) 1978 ( 8) 2002 ( 1)
%%% 1955 ( 4) 1979 ( 3) 2003 ( 1)
%%% 1956 ( 0) 1980 ( 6) 2004 ( 0)
%%% 1957 ( 8) 1981 ( 4) 2005 ( 3)
%%% 1958 ( 4) 1982 ( 3) 2006 ( 0)
%%% 1959 ( 4) 1983 ( 1) 2007 ( 0)
%%% 1960 ( 4) 1984 ( 6) 2008 ( 0)
%%% 1961 ( 7) 1985 ( 2) 2009 ( 0)
%%% 1962 ( 9) 1986 ( 3) 2010 ( 0)
%%% 1963 ( 5) 1987 ( 9) 2011 ( 1)
%%% 1964 ( 1) 1988 ( 1) 2012 ( 2)
%%% 1965 ( 10) 1989 ( 1) 2013 ( 0)
%%% 1966 ( 8) 1990 ( 4) 2014 ( 0)
%%% 1967 ( 8) 1991 ( 0) 2015 ( 0)
%%% 1968 ( 11) 1992 ( 1) 2016 ( 0)
%%% 1969 ( 3) 1993 ( 0) 2017 ( 0)
%%% 1970 ( 11) 1994 ( 1) 2018 ( 0)
%%% 1971 ( 25) 1995 ( 0) 2019 ( 3)
%%%
%%% Article: 108
%%% Book: 13
%%% InBook: 1
%%% InCollection: 35
%%% InProceedings: 24
%%% Misc: 4
%%% Proceedings: 15
%%% TechReport: 27
%%% Unpublished: 5
%%%
%%% Total entries: 232
%%%
%%% This file is available as part of the BibNet
%%% Project. The master copy is available for
%%% public access on ftp.math.utah.edu in the
%%% directory tree /pub/bibnet/authors. It is
%%% mirrored to netlib.bell-labs.com in the directory
%%% tree /netlib/bibnet/authors, from which it is
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%%% service.
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%%% ====================================================================
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%%% ====================================================================
%%% Part 1 (of 2) --- James H. Wilkinson and his works
%%%
%%% Bibliography entries, sorted by ascending year and then by citation
%%% label:
@Article{Fox:1948:NSA,
author = "L. Fox and H. D. Huskey and J. H. Wilkinson",
title = "Notes on the solution of algebraic linear simultaneous
equations",
journal = j-QUART-J-MECH-APPLIED-MATH,
volume = "1",
pages = "149--173",
year = "1948",
CODEN = "QJMMAV",
DOI = "https://doi.org/10.1093/qjmam/1.1.149",
ISSN = "0033-5614 (print), 1464-3855 (electronic)",
ISSN-L = "0033-5614",
MRclass = "65.0X",
MRnumber = "MR0026421 (10,152i)",
MRreviewer = "E. Bodewig",
bibdate = "Fri May 14 17:18:08 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
abstract = "In this paper four methods of solving simultaneous
equations and inverting matrices are described from the
viewpoint of the practical computer. The first three
methods can be performed on ordinary desk calculating
machines; the fourth uses Hollerith punched card
equipment. The desk methods considered are the method
of elimination or pivotal condensation, the method of
orthogonal vectors, and the method of Choleski. The
elimination method is, with slight variants, the simple
method taught at school, used in such a way that
solutions are obtained with the maximum possible speed
and accuracy. In the method of orthogonal vectors,
applicable only to symmetric matrices, a new set of
variables is chosen in such a way that the matrix is
transformed to a diagonal form, from which the solution
of equations or the inverse of the matrix is
immediately obtainable. The Choleski method, applied
here again only to symmetric matrices, expresses the
square matrix as the product of two triangular
matrices, the reciprocation of which is a relatively
simple operation. This method is quicker and more
accurate than the others and can be used, with slight
modifications, in the case of unsymmetric matrices. The
procedure used with punched card equipment is
essentially a mechanization of the elimination method,
with a considerable advantage in speed over the
corresponding desk method.",
acknowledgement = ack-nhfb,
fjournal = "The Quarterly Journal of Mechanics and Applied
Mathematics",
journal-URL = "http://qjmam.oxfordjournals.org/content/by/year",
}
@TechReport{Fox:1948:SAL,
author = "L. Fox and H. D. Huskey and J. H. Wilkinson",
title = "The Solution of Algebraic Linear Simultaneous
Equations by Punched Card Methods",
type = "Maths",
institution = inst-NPL,
address = inst-NPL:adr,
year = "1948",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@Article{Hartree:1948:DCM,
author = "D. R. Hartree and M. H. A. Newman and M. V. Wilkes and
F. C. Williams and J. H. Wilkinson and A. D. Booth",
title = "A discussion on computing machines",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "195",
number = "1042",
pages = "265--287 (2 plates)",
day = "22",
month = dec,
year = "1948",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.1948.0118",
ISSN = "0080-4630",
MRclass = "65.0X",
MRnumber = "MR0028103 (10,405f)",
bibdate = "Fri May 14 17:18:08 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
URL = "http://www.jstor.org/stable/98328",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical, Physical and Engineering Sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/content/current",
}
@TechReport{Wilkinson:1948:PRA,
author = "J. H. Wilkinson",
title = "Progress Report on the {Automatic Computing Engine}",
type = "Report",
number = "MA/17/1024",
institution = inst-NPL,
address = inst-NPL:adr,
pages = "????",
month = apr,
year = "1948",
bibdate = "Mon Nov 1 19:29:36 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
URL = "http://www.alanturing.net/turing_archive/archive/l/l10/L10-001.html",
}
@Article{Wilkinson:1948:ACE,
author = "J. H. Wilkinson",
title = "The {Automatic Computing Engine} at the {National
Physical Laboratory}",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "195",
number = "1042",
pages = "285--286",
day = "22",
month = dec,
year = "1948",
CODEN = "PRLAAZ",
ISSN = "0080-4630",
bibdate = "Thu Aug 25 09:25:29 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
URL = "http://www.jstor.org/stable/98328",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society. London. Series A.
Mathematical, Physical and Engineering Sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/content/current",
}
@TechReport{Wilkinson:1951:PCP,
author = "J. H. Wilkinson",
title = "Programming and Coding for the Pilot Model of the
{ACE}",
type = "Ma Report",
institution = inst-NPL,
address = inst-NPL:adr,
year = "1951",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@TechReport{Wilkinson:1951:PGR,
author = "J. H. Wilkinson",
title = "Programmes for the {GPO Radar Data Analyser}",
type = "Maths",
institution = inst-NPL,
address = inst-NPL:adr,
year = "1951",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@TechReport{Wilkinson:1951:RPM,
author = "J. H. Wilkinson",
title = "Report on the Pilot Model of the {Automatic Computing
Engine. II.} The Logical Design of the Pilot Model",
type = "Maths Division and Electronics Section",
institution = inst-NPL,
address = inst-NPL:adr,
year = "1951",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@TechReport{Wilkinson:1952:PCP,
author = "J. H. Wilkinson",
title = "Programming and Coding for the Pilot Model of the
{ACE}",
type = "Ma Report",
number = "No. 22",
institution = inst-NPL,
address = inst-NPL:adr,
year = "1952",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Reissue",
}
@Article{Wilkinson:1954:CLR,
author = "J. H. Wilkinson",
title = "The Calculation of the Latent Roots and Vectors of
Matrices on the {Pilot Model} of the {ACE}",
journal = j-PROC-CAMBRIDGE-PHIL-SOC,
volume = "50",
number = "4",
pages = "536--566",
year = "1954",
CODEN = "PCPSA4",
DOI = "https://doi.org/10.1017/S0305004100029674",
ISSN = "0008-1981",
MRclass = "65.0X",
MRnumber = "MR0063775 (16,178b)",
MRreviewer = "A. S. Householder",
bibdate = "Fri May 14 17:18:08 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
abstract = "The problem of finding the latent roots and vectors of
matrices has been treated in a number of papers ((2)
(7)) mainly from the point of view of desk computers.
In this paper the problem is treated from the
standpoint of users of high-speed automatic computers.
In the first section a number of iterative processes
are described and, in the second, the techniques
developed for using these processes on the Pilot Model
of the Automatic Computing Engine. It is shown that the
methods give very high accuracy and can be used to deal
with matrices of high orders even on a machine of very
limited storage capacity. They have been used on
numerous matrices of orders up to 60 mainly on problems
arising in the aircraft industry and on eigenvalue
problems for systems of ordinary differential
equations.",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Cambridge Philosophical Society.
Mathematical and physical sciences",
journal-URL = "http://journals.cambridge.org/action/displayJournal?jid=PSP",
received = "February 9, 1954",
}
@InProceedings{Wilkinson:1954:LAP,
author = "J. H. Wilkinson",
booktitle = "Automatic Digital Computation",
title = "Linear Algebra on the {Pilot ACE}",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "129--136",
year = "1954",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Proceedings of Symposium at the National Physical
Laboratory, 1953",
}
@InProceedings{Wilkinson:1954:PA,
author = "J. H. Wilkinson",
booktitle = "Automatic Digital Computation",
title = "The {Pilot ACE}",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "5--14",
year = "1954",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Proceedings of Symposium at the National Physical
Laboratory, 1953. Reprinted in
\cite[pp.~193--199]{Bell:1971:CSR} and in
\cite[pp.~219--228]{Williams:1989:EBC}.",
}
@Article{Wilkinson:1955:ASO,
author = "J. H. Wilkinson",
title = "An Assessment of the System of Optimum Coding Used on
the {Pilot ACE} at the {National Physical Laboratory}",
journal = j-PHILOS-TRANS-R-SOC-LOND-SER-A,
volume = "248",
pages = "253--281",
year = "1955",
CODEN = "PTRMAD, PTMSFB",
DOI = "https://doi.org/10.1098/rsta.1955.0016",
ISSN = "0080-4614",
ISSN-L = "1364-503X",
MRclass = "68.0X",
MRnumber = "MR0071885 (17,197i)",
bibdate = "Fri May 14 17:18:08 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
abstract = "The paper describes the system of optimum coding which
is used on the Pilot ACE, the electronic computer at
the National Physical Laboratory. It includes a number
of simple examples of programs prepared for the machine
and gives an assessment of the gain in speed which
results from the use of optimum coding in general. It
concludes with a description of the design of the
full-scale ACE which takes full advantage of the
general principles embodied in the design of the Pilot
ACE.",
acknowledgement = ack-nhfb,
fjournal = "Philosophical Transactions of the Royal Society of
London. Series A. Mathematical and Physical Sciences",
journal-URL = "http://rsta.royalsocietypublishing.org/",
}
@Article{Wilkinson:1955:ECM,
author = "J. H. Wilkinson",
title = "Electronic computing machines and their uses",
journal = j-sI,
volume = "32",
pages = "409--415",
year = "1955",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@TechReport{Wilkinson:1955:RVU,
author = "J. H. Wilkinson",
title = "Report on Visit to {U.S.A., 17 September--14 December
1954}",
type = "Maths",
institution = inst-NPL,
address = inst-NPL:adr,
year = "1955",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@Article{Wilkinson:1955:UIM,
author = "J. H. Wilkinson",
title = "The Use of Iterative Methods for Finding the Latent
Roots and Vectors of Matrices",
journal = j-MATH-TABLES-OTHER-AIDS-COMPUT,
volume = "9",
pages = "184--191",
year = "1955",
CODEN = "MTTCAS",
ISSN = "0891-6837",
MRclass = "65.3X",
MRnumber = "MR0079833 (18,154b)",
MRreviewer = "E. Stiefel",
bibdate = "Fri May 14 17:18:08 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
fjournal = "Mathematical Tables and Other Aids to Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Wilkinson:1957:BPD,
author = "J. H. Wilkinson",
title = "{British} Progress in Digital Computer Design",
journal = j-AP,
volume = "2",
pages = "5--9, 36",
year = "1957",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "Automn Prog.",
}
@InProceedings{Wilkinson:1957:CEC,
author = "J. H. Wilkinson",
booktitle = "Conference Proceedings",
title = "The Calculation of the Eigenvectors of Codiagonal
Matrices Produced by the {Givens} and {Lanczos}
Processes",
publisher = pub-WRE,
address = pub-WRE:adr,
pages = "112:1--112:15",
year = "1957",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@Article{Wilkinson:1957:CFG,
author = "J. H. Wilkinson",
title = "Computing Facilities in {Great Britain}",
journal = j-IP,
volume = "43",
pages = "101--107",
year = "1957",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@InCollection{Wilkinson:1957:EUD,
author = "J. H. Wilkinson",
booktitle = "Modern Computing Methods, 1st Edition",
title = "Example of the Use of {DEUCE}",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "116--122",
year = "1957",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "National Physical Laboratory, Notes on Applied
Science, Volume 16",
}
@InCollection{Wilkinson:1957:HPD,
author = "J. H. Wilkinson",
booktitle = "Modern Computing Methods, 1st Edition",
title = "Hyperbolic Partial Differential Equations",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "61--71",
year = "1957",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "National Physical Laboratory, Notes on Applied
Science, Volume 16",
}
@InCollection{Wilkinson:1957:LEM,
author = "J. H. Wilkinson",
booktitle = "Modern Computing Methods, 1st Edition",
title = "Linear Equations and Matrices",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "12--19",
year = "1957",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "National Physical Laboratory, Notes on Applied
Science, Volume 16",
}
@Article{Wilkinson:1957:LOW,
author = "J. H. Wilkinson",
title = "Loading on an Oscillating Wing of Infinite Aspect
Ratio in a Subsonic Stream",
journal = "ARC",
volume = "19",
pages = "344",
year = "1957",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Comp. 125.",
}
@InCollection{Wilkinson:1957:LRM,
author = "J. H. Wilkinson",
booktitle = "Modern Computing Methods, 1st Edition",
title = "Latent Roots of Matrices",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "27--35",
year = "1957",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "National Physical Laboratory, Notes on Applied
Science, Volume 16",
}
@Article{Wilkinson:1958:CEC,
author = "J. H. Wilkinson",
title = "The Calculation of the Eigenvectors of Codiagonal
Matrices",
journal = j-COMP-J,
volume = "1",
number = "2",
pages = "90--96",
month = jul,
year = "1958",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/1.2.90",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:55:03 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/010090.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/90.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/91.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/92.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/93.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/94.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/95.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_02/tiff/96.tif",
abstract = "In the Givens method for calculating the eigenvalues
and eigenvectors of a matrix, a collineatory
transformations is constructed which reduces the matrix
to codiagonal form. Givens (1954) has given a complete
analysis of the problem of finding the eigenvalues and
has described a very satisfactory practical procedure
for evaluating them. No such analysis has been given
for the eigenvectors, though Givens in an unpublished
paper has described a procedure which, in his
experience, has given accurate results. In this note an
analysis of the problem is given, which explains why
the straightforward use of the recursions often gives
vectors which are catastrophically in error. A method
of solution is described which has been used
extensively for calculating the vectors on DEUCE. Much
of what is written applies equally well to the
codiagonal matrices produced by the method of Lanczos
(1950), but because this method is usually programmed
using floating-point arithmetic, there are one or two
additional complications. These will be the subject of
a later note.",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Wilkinson:1958:CEM,
author = "J. H. Wilkinson",
title = "The Calculation of Eigenvectors by the Method of
{Lanczos}",
journal = j-COMP-J,
volume = "1",
number = "3",
pages = "148--152",
month = oct,
year = "1958",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/1.3.148",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.00",
MRnumber = "MR0102915 (21 \#1700)",
MRreviewer = "H. Rutishauser",
bibdate = "Fri Sep 29 08:55:05 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/010148.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/tiff/148.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/tiff/149.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/tiff/150.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/tiff/151.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_01/Issue_03/tiff/152.tif",
abstract = "This paper describes a technique for calculating the
eigenvectors of a matrix automatically by means of the
Lanczos transformation. Both the symmetric and the
unsymmetric forms are treated. It shows that with
suitable modifications, the method described by the
author for finding the eigenvectors by means of the
Givens transformation, can be made to give accurate
results for both of the Lanczos transformations.",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Wilkinson:1958:MPN,
author = "J. H. Wilkinson",
title = "Matrix Programs at the {National Physical
Laboratory}",
journal = j-ACM,
volume = "5",
pages = "113--114",
year = "1958",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@TechReport{Wilkinson:1958:SRM,
author = "J. H. Wilkinson",
title = "Stability of the Reduction of a Matrix to Almost
Triangular and Triangular Forms by Elementary
Similarity Transformations",
type = "Mathematics Division",
number = "No. 22",
institution = inst-NPL,
address = inst-NPL:adr,
year = "1958",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Reprinted 1962. Published as
\cite{Wilkinson:1959:SRM}.",
}
@Article{Davies:1959:ACE,
author = "D. W. Davies and J. H. Wilkinson",
title = "The {Automatic Computing Engine} at the {National
Physical Laboratory}",
journal = j-NatureL,
volume = "183",
pages = "22--23",
year = "1959",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@Article{Wilkinson:1959:EZIa,
author = "J. H. Wilkinson",
title = "The evaluation of the zeros of ill-conditioned
polynomials. {I}",
journal = j-NUM-MATH,
volume = "1",
pages = "150--166",
month = dec,
year = "1959",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386381",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.00",
MRnumber = "MR0109435 (22 \#321)",
MRreviewer = "H. Rutishauser",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Wilkinson:1959:EZIb,
author = "J. H. Wilkinson",
title = "The evaluation of the zeros of ill-conditioned
polynomials. {II}",
journal = j-NUM-MATH,
volume = "1",
pages = "167--180",
month = dec,
year = "1959",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386382",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.00",
MRnumber = "MR0109435 (22 \#321)",
MRreviewer = "H. Rutishauser",
bibdate = "Mon Oct 18 01:28:20 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Wilkinson:1959:SRM,
author = "J. H. Wilkinson",
title = "Stability of the Reduction of a Matrix to Almost
Triangular and Triangular Forms by Elementary
Similarity Transformations",
journal = j-ACM,
volume = "6",
number = "3",
pages = "336--359",
year = "1959",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
MRclass = "65.00",
MRnumber = "MR0106542 (21 \#5273)",
MRreviewer = "B. A. Chartres",
bibdate = "Fri May 14 17:18:08 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Computing Machinery",
}
@Article{Wilkinson:1960:EAF,
author = "J. H. Wilkinson",
title = "Error Analysis of Floating-Point Computation",
journal = j-NUM-MATH,
volume = "2",
number = "1",
pages = "319--340",
month = dec,
year = "1960",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01386233",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.00",
MRnumber = "MR0116477 (22 \#7264)",
MRreviewer = "C. B. Haselgrove",
bibdate = "Fri May 14 17:18:08 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/nummath.bib",
URL = "https://link.springer.com/article/10.1007/BF01386233",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Wilkinson:1960:HMS,
author = "J. H. Wilkinson",
title = "{Householder}'s Method for the Solution of the
Algebraic Eigenproblem",
journal = j-COMP-J,
volume = "3",
number = "1",
pages = "23--27",
month = apr,
year = "1960",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/3.1.23",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.00",
MRnumber = "MR0111131 (22 \#1995)",
MRreviewer = "A. S. Householder",
bibdate = "Fri Sep 29 08:55:18 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/030023.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/tiff/23.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/tiff/24.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/tiff/25.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/tiff/26.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_03/Issue_01/tiff/27.tif",
abstract = "In this paper a practical procedure is described for
the solution of the eigenproblem based on a method due
to Householder. It is claimed that the technique
described is the most satisfactory of known methods for
general symmetric matrices and may have considerable
advantages for unsymmetric matrices. The details of the
computation for a simple numerical example are given,
and also the results obtained for a $ 14 \times 14 $
matrix using the ACE computer.",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@InProceedings{Wilkinson:1960:MSL,
author = "J. H. Wilkinson",
booktitle = "Proceedings of UNESCO Conference on Information
Processing, 1959",
title = "On Methods for Solving Linear Equations",
publisher = pub-But,
address = pub-But:adr,
pages = "108--109",
year = "1960",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@InProceedings{Wilkinson:1960:REA,
author = "J. H. Wilkinson",
booktitle = "Proceedings of UNESCO Conference on Information
Processing, 1959",
title = "Rounding Errors in Algebraic Processes",
publisher = pub-But,
address = pub-But:adr,
pages = "44--53",
year = "1960",
MRclass = "65.00",
MRnumber = "MR0121976 (22 \#12703)",
MRreviewer = "B. A. Chartres",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@Article{Rollett:1961:ESC,
author = "J. S. Rollett and J. H. Wilkinson",
title = "An efficient scheme for the co-diagonalization of a
symmetric matrix by {Givens}' method in a computer with
a two-level store",
journal = j-COMP-J,
volume = "4",
number = "2",
pages = "177--180",
month = jul,
year = "1961",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.35",
MRnumber = "MR0129126 (23 \#B2163)",
MRreviewer = "B. A. Chartres",
bibdate = "Fri Sep 29 08:55:29 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_02/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_02/040177.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_02/tiff/177.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_02/tiff/178.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_02/tiff/179.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_02/tiff/180.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@InCollection{Wilkinson:1961:EA,
author = "J. H. Wilkinson",
booktitle = "Modern Computing Methods, 2nd Edition",
title = "Error Analysis",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "41--52",
year = "1961",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "National Physical Laboratory, Notes on Applied
Science, Volume 16",
}
@Article{Wilkinson:1961:EAD,
author = "J. H. Wilkinson",
title = "Error Analysis of Direct Methods of Matrix Inversion",
journal = j-J-ACM,
volume = "8",
number = "3",
pages = "281--330",
year = "1961",
CODEN = "JACOAH",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65.35",
MRnumber = "MR0176602 (31 \#874)",
MRreviewer = "V. K. Saud{\cprime}ev",
bibdate = "Fri May 14 17:18:08 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
}
@InCollection{Wilkinson:1961:HPD,
author = "J. H. Wilkinson",
booktitle = "Modern Computing Methods, 2nd Edition",
title = "Hyperbolic Partial Differential Equations",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "101--111",
year = "1961",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "National Physical Laboratory, Notes on Applied
Science, Volume 16",
}
@InCollection{Wilkinson:1961:LEM,
author = "J. H. Wilkinson",
booktitle = "Modern Computing Methods, 2nd Edition",
title = "Linear Equations and Matrices",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "13--33",
year = "1961",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "National Physical Laboratory, Notes on Applied
Science, Volume 16",
}
@Article{Wilkinson:1961:RA,
author = "J. H. Wilkinson",
title = "Remarks on {Algorithms 2} and 3",
journal = j-CACM,
volume = "4",
number = "3",
pages = "153--153",
month = mar,
year = "1961",
CODEN = "CACMA2",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Fri Nov 25 18:19:31 MST 2005",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Wilkinson:1961:REB,
author = "J. H. Wilkinson",
title = "Rigorous Error Bounds for Computed Eigensystems",
journal = j-COMP-J,
volume = "4",
number = "3",
pages = "230--241",
month = oct,
year = "1961",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/4.3.230",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.40",
MRnumber = "MR0129124 (23 \#B2161)",
MRreviewer = "A. S. Householder",
bibdate = "Fri Sep 29 08:55:31 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/040230.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/230.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/231.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/232.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/233.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/234.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/235.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/236.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/237.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/238.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/239.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/240.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_04/Issue_03/tiff/241.tif",
abstract = "This paper describes techniques for the automatic
determination of rigorous error bounds for a computer
eigensystem. The methods used, lead directly to an
improved eigensystem and the error bounds are for the
improved system. They have the same theoretical basis
as the method of H. Jahn, but here the main emphasis is
on the organization of the computation which is
necessary for the determination of the error bounds.",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@InCollection{Jacobson:1962:SEA,
author = "A. W. Jacobson and S. Rosen and J. H. Wilkinson",
editor = "H. D. Huskey and G. A. Korn",
booktitle = "Computer Handbook",
title = "Scientific and Engineering Applications of Digital
Computers",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "21:2--21:13",
year = "1962",
bibdate = "Tue Aug 15 18:20:34 MDT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Section 2.1.",
}
@Article{Rollett:1962:LEG,
author = "J. S. Rollett and J. H. Wilkinson",
title = "Letter to the Editor: [{Givens} and {Householder}
processes]",
journal = j-COMP-J,
volume = "4",
number = "4",
pages = "279--279",
month = jan,
year = "1962",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Thu Dec 06 12:14:55 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/4/4.toc;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/compj1960.bib",
URL = "http://comjnl.oxfordjournals.org/cgi/reprint/4/4/279;
http://comjnl.oxfordjournals.org/content/4/4/279.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Wilkinson:1962:BRB,
author = "J. H. Wilkinson",
title = "Book Review: {{\booktitle{Solutions Num{\'e}riques des
{\'E}quations Alg{\'e}braiques}}, by E. Durand (Paris:
Masson et Cie., 1960, pp. 328, 65 NF)}",
journal = j-COMP-J,
volume = "5",
number = "1",
pages = "32--32",
month = apr,
year = "1962",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/5.1.32",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:28 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/5/1.toc;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/compj1960.bib",
URL = "http://comjnl.oxfordjournals.org/content/5/1/28.full.pdf;
http://comjnl.oxfordjournals.org/content/5/1/32.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Wilkinson:1962:CESa,
author = "J. H. Wilkinson",
title = "Calculation of the eigenvalues of a symmetric
tridiagonal matrix by the method of bisection",
journal = j-NUM-MATH,
volume = "4",
pages = "362--367",
month = dec,
year = "1962",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.35",
MRnumber = "MR0148208 (26 \#5716)",
MRreviewer = "A. S. Householder",
bibdate = "Mon Oct 18 20:10:40 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "Handbook Series Linear Algebra",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Wilkinson:1962:CESb,
author = "J. H. Wilkinson",
title = "Calculation of the eigenvectors of a symmetric
tridiagonal matrix by inverse iteration",
journal = j-NUM-MATH,
volume = "4",
pages = "368--376",
month = dec,
year = "1962",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.35",
MRnumber = "MR0148209 (26 \#5717)",
MRreviewer = "A. S. Householder",
bibdate = "Mon Oct 18 20:10:40 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "Handbook Series Linear Algebra",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Wilkinson:1962:EAE,
author = "J. H. Wilkinson",
title = "Error Analysis of Eigenvalue Techniques Based on
Orthogonal Transformations",
journal = j-J-SIAM,
volume = "10",
pages = "162--195",
year = "1962",
CODEN = "JSIMAV",
ISSN = "0368-4245 (print), 1095-712X (electronic)",
MRclass = "65.40",
MRnumber = "MR0137294 (25 \#749)",
MRreviewer = "A. S. Householder",
bibdate = "Fri May 14 17:18:08 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Society for Industrial and Applied
Mathematics",
journal-URL = "http://epubs.siam.org/loi/smjmap.1",
}
@Article{Wilkinson:1962:HMS,
author = "J. H. Wilkinson",
title = "{Householder}'s method for symmetric matrices",
journal = j-NUM-MATH,
volume = "4",
pages = "354--361",
month = dec,
year = "1962",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.35",
MRnumber = "MR0148207 (26 \#5715)",
MRreviewer = "A. S. Householder",
bibdate = "Mon Oct 18 20:10:40 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "Handbook Series Linear Algebra",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Wilkinson:1962:IEM,
author = "J. H. Wilkinson",
title = "Instability of the Elimination Method of Reducing a
Matrix to Tri-Diagonal Form",
journal = j-COMP-J,
volume = "5",
number = "1",
pages = "61--70",
month = apr,
year = "1962",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.35",
MRnumber = "MR0137292 (25 \#747)",
MRreviewer = "A. S. Householder",
bibdate = "Fri Sep 29 08:55:36 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/050061.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/61.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/62.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/63.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/64.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/65.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/66.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/67.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/68.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/69.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_05/Issue_01/tiff/70.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Wilkinson:1962:NQC,
author = "J. H. Wilkinson",
title = "Note on the quadratic convergence of the cyclic
{Jacobi} process",
journal = j-NUM-MATH,
volume = "4",
pages = "296--300",
month = dec,
year = "1962",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.40",
MRnumber = "MR0146954 (26 \#4473)",
MRreviewer = "S. V. Parter",
bibdate = "Mon Oct 18 20:10:40 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Wilkinson:1963:BRB,
author = "J. H. Wilkinson",
title = "Book Review: {{\booktitle{Solutions Num{\'e}riques des
{\'E}quations Alg{\'e}braiques}}, Volume II, by E.
Durand (Paris: Masson et Cie., 1961, pp. 445, 90 NF)}",
journal = j-COMP-J,
volume = "5",
number = "4",
pages = "263--263",
month = jan,
year = "1963",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/5.4.263",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:29 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/5/4.toc;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/compj1960.bib",
URL = "http://comjnl.oxfordjournals.org/content/5/4/258.full.pdf;
http://comjnl.oxfordjournals.org/content/5/4/263.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Wilkinson:1963:ELS,
author = "J. H. Wilkinson",
title = "Errors in Large-Scale Numerical Problems",
journal = j-CompB,
volume = "6",
pages = "124--125",
year = "1963",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@InProceedings{Wilkinson:1963:PRF,
author = "J. H. Wilkinson",
title = "Plane Rotations in Floating-Point Arithmetic",
crossref = "Metropolis:1963:PFS",
pages = "185--198",
year = "1963",
MRclass = "65.35",
MRnumber = "MR0158521 (28 \#1744)",
MRreviewer = "A. S. Householder",
bibdate = "Mon Jun 18 11:32:12 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Oettli:1964:ASL,
author = "W. Oettli and W. Prager and J. H. Wilkinson",
title = "Admissible Solutions of Linear Systems with not
Sharply Defined Coefficients",
type = "Research Paper",
number = "RZ-166",
institution = "IBM Research Division",
address = "IBM Zurich Research Laboratory, R{\"{u}}schlikon,
Zurich, Switzerland",
year = "1964",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Published as \cite{Oettli:1965:ASL}.",
}
@Article{Martin:1965:SDPa,
author = "R. S. Martin and J. H. Wilkinson",
title = "Symmetric Decomposition of Positive Definite Band
Matrices",
journal = j-NUM-MATH,
volume = "7",
number = "5",
pages = "355--361",
month = oct,
year = "1965",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01436248",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553944",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
Theory/Matrix.bib",
note = "Also in \cite[pp. 50--56]{Wilkinson:1971:LA}.",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "band matrix; lud; nla; software; symmetric matrix",
}
@Article{Martin:1965:SDPb,
author = "R. S. Martin and G. Peters and J. H. Wilkinson",
title = "Symmetric Decomposition of a Positive Definite
Matrix",
journal = j-NUM-MATH,
volume = "7",
number = "5",
pages = "362--383",
month = oct,
year = "1965",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01436249",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553945",
bibdate = "Sun Oct 17 16:12:48 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
Theory/Matrix.bib",
note = "Also in \cite[pp. 9--30]{Wilkinson:1971:LA}.",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "Cholesky decomposition; nla; software",
}
@Article{Oettli:1965:ASL,
author = "W. Oettli and W. Prager and J. H. Wilkinson",
title = "Admissible Solutions of Linear Systems with not
Sharply Defined Coefficients",
journal = j-SINum,
volume = "2",
pages = "291--299",
year = "1965",
MRclass = "65.35",
MRnumber = "MR0184416 (32 \#1888)",
MRreviewer = "L. W. Ehrlich",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@Book{Wilkinson:1965:AEP,
author = "J. H. Wilkinson",
booktitle = "The Algebraic Eigenvalue Problem",
title = "The Algebraic Eigenvalue Problem",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xviii + 662",
year = "1965",
ISBN = "0-19-853403-5",
ISBN-13 = "978-0-19-853403-7",
LCCN = "QA218 .W686 1965",
MRclass = "65.40",
MRnumber = "MR0184422 (32 \#1894)",
MRreviewer = "A. S. Householder",
bibdate = "Tue Aug 15 18:20:34 MDT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib",
shorttableofcontents = "1. Theoretical Background \\
2. Perturbation Theory \\
3. Error Analysis \\
4. Solution of Linear Algebraic Equations \\
5. Hermitian Matrices \\
6. Reduction of a General Matrix to Condensed Form \\
7. Eigenvalues of Matrices of Condensed Forms \\
8. The $ L R $ and $ Q R $ Algorithms \\
9. Iterative Methods \\
Bibliography / 649 \\
Index / 657",
tableofcontents = "1. Theoretical Background \\
Introduction / 1 \\
Definitions / 2 \\
Eigenvalues and eigenvectors of the transposed matrix /
3 \\
Distinct eigenvalues / 4 \\
Similarity transformations / 6 \\
Multiple eigenvalues and canonical forms for general
matrices / 7 \\
Defective system of eigenvectors / 9 \\
The Jordan (classical) canonical form / 10 \\
The elementary divisors / 12 \\
Companion matrix of the characteristic polynomial of
$A$ / 12 \\
Non-derogatory matrices / 13 \\
The Frobenius (rational) canonical form / 15 \\
Relationship between the Jordan and Frobenius canonical
forms / 16 \\
Equivalence transformations / 17 \\
Lambda matrices / 18 \\
Elementary operations / 19 \\
Smith's canonical form / 19 \\
The highest common factor of $k$-rowed minors of a
$A$-matrix / 22 \\
Invariant factors of $ (A - \lambda M) $ / 22 \\
The triangular canonical form / 24 \\
Hermitian and symmetric matrices / 24 \\
Elementary properties of Hermitian matrices / 25 \\
Complex symmetric matrices / 26 \\
Reduction to triangular form by unitary transformations
/ 27 \\
Quadratic forms / 27 \\
Necessary and sufficient conditions for positive
definiteness / 28 \\
Differential equations with constant coefficients / 30
\\
Solutions corresponding to non-linear elementary
divisors / 31 \\
Differential equations of higher order / 32 \\
Second-order equations of special form / 34 \\
Explicit solution of $ B \ddot{y} = -A y$ / 35 \\
Equations of the form $(AB - \lambda I) x = 0$ / 35 \\
The minimum polynomial of a vector / 36 \\
The minimum polynomial of a matrix / 37 \\
Cayley--Hamilton theorem / 38 \\
Relation between minimum polynomial and canonical forms
/ 39 \\
Principal vectors / 42 \\
Elementary similarity transformations / 43 \\
Properties of elementary matrices / 45 \\
Reduction to triangular canonical form by elementary
similarity transformations / 46 \\
Elementary unitary transformations / 47 \\
Elementary unitary Hermitian matrices / 48 \\
Reduction to triangular form by elementary unitary
transformations / 50 \\
Normal matrices / 51 \\
Commuting matrices / 52 \\
Eigenvalues of $A B$ / 54 \\
Vector and matrix norms / 55 \\
Subordinate matrix norms / 56 \\
The Euclidean and spectral norms / 57 \\
Norms and limits / 58 \\
Avoiding use of infinite matrix series / 60 \\
2. Perturbation Theory \\
Introduction / 62 \\
Ostrowski's theorem on continuity of the eigenvalues /
63 \\
Algebraic functions / 64 \\
Numerical examples / 65 \\
Perturbation theory for simple eigenvalues / 66 \\
Perturbation of corresponding eigenvectors / 67 \\
Matrix with linear elementary divisors / 68 \\
First-order perturbations of eigenvalues / 68 \\
First-order perturbations of eigenvectors / 69 \\
Higher-order perturbations / 70 \\
Multiple eigenvalues / 70 \\
Gerschgorin's theorems / 71 \\
Perturbation theory based on Gerschgorin's theorems /
72 \\
Case 1. Perturbation of a simple eigenvalue $\lambda_1$
of a matrix having linear elementary divisors / 72 \\
Case 2. Perturbation of a multiple eigenvalue
$\lambda_1$ of a matrix having linear elementary
divisors / 75 \\
Case 3. Perturbation of a simple eigenvalue of a matrix
having one or more non-linear elementary divisors / 77
\\
Case 4. Perturbations of the eigenvalues corresponding
to a non-linear elementary divisor of a non-derogatory
matrix / 79 \\
Case 5. Perturbations of eigenvalues $\lambda_i$ when
there is more than one divisor involving $(\lambda_i -
\lambda_)$ and at least one of them is non-linear / 80
\\
Perturbations corresponding to the general distribution
of non-linear divisors / 81 \\
Perturbation theory for the eigenvectors from Jordan
canonical form / 81 \\
Perturbations of eigenvectors corresponding to a
multiple eigenvalue (linear elementary divisors) / 83
\\
Limitations of perturbation theory / 84 \\
Relationships between the $s_i$ / 85 \\
The condition of a computing problem / 86 \\
Condition numbers / 86 \\
Spectral condition number of A with respect to its
eigenproblem / 87 \\
Properties of spectral condition number / 88 \\
Invariant properties of condition numbers / 89 \\
Very ill-conditioned matrices / 90 \\
Perturbation theory for real symmetric matrices / 93
\\
Unsymmetric perturbations / 93 \\
Symmetric perturbations / 94 \\
Classical techniques / 94 \\
Symmetric matrix of rank unity / 97 \\
Extremal properties of eigenvalues / 98 \\
Minimax characterization of eigenvalues / 99 \\
Eigenvalues of the sum of two symmetric matrices / 101
\\
Practical applications / 102 \\
Further applications of minimax principle / 103 \\
Separation theorem / 103 \\
The Wielandt--Hoffman theorem / 104 \\
3. Error Analysis \\
Introduction / 110 \\
Fixed-point operations / 110 \\
Accumulation of inner-products / 111 \\
Floating-point operations / 112 \\
Simplified expressions for error bounds / 113 \\
Error bounds for some basic floating-point computations
/ 114 \\
Bounds for norms of the error matrices / 115 \\
Accumulation of inner-products in floating-point
arithmetic / 116 \\
Error bounds for some basic $\fl_2( )$ computations /
117 \\
Computation of square roots / 118 \\
Block-floating vectors and matrices / 119 \\
Fundamental limitations oft-digit computation / 120 \\
Eigenvalue techniques based on reduction by similarity
transformations / 123 \\
Error analysis of methods based on elementary
non-unitary transformations / 124 \\
Error analysis of methods based on elementary unitary
transformations / 126 \\
Superiority of the unitary transformation / 128 \\
Real symmetric matrices / 129 \\
Limitations of unitary transformations / 129 \\
Error analysis of floating-point computation of plane
rotations / 131 \\
Multiplication by a plane rotation / 133 \\
Multiplication by a sequence of plane rotations / 134
\\
Error in product of approximate plane rotations / 139
\\
Errors in similarity transforms / 140 \\
Symmetric matrices / 141 \\
Plane rotations in fixed-point arithmetic / 143 \\
Alternative computation of $\sin \theta$ and $\cos
\theta$ / 145 \\
Pre-multiplication by an approximate fixed-point
rotation / 145 \\
Multiplication by a sequence of plane rotations
(fixed-point) / 147 \\
The computed product of an approximate set of plane
rotations / 148 \\
Errors in similarity transformations / 148 \\
General comments on the error bounds / 151 \\
Elementary Hermitian matrices in floating-point / 152
\\
Error analysis of the computation of an elementary
Hermitian matrix / 153 \\
Numerical example / 156 \\
Pre-multiplication by an approximate elementary
Hermitian matrix / 157 \\
Multiplication by a sequence of approximate elementary
Hermitians / 160 \\
Non-unitary elementary matrices analogous to plane
rotations / 162 \\
Non-unitary elementary matrices analogous to elementary
Hermitian matrices / 163 \\
Pre-multiplication by a sequence of non-unitary
matrices / 165 \\
A priori error bounds / 166 \\
Departure from normality / 167 \\
Simple examples / 169 \\
A posteriori bounds / 170 \\
A posteriori bounds for normal matrices / 170 \\
Rayleigh quotient / 172 \\
Error in Rayleigh quotient / 173 \\
Hermitian matrices / 174 \\
Pathologically close eigenvalues / 176 \\
Non-normal matrices / 178 \\
Error analysis for a complete eigensystem / 180 \\
Numerical example / 181 \\
Conditions limiting attainable accuracy / 181 \\
Non-linear elementary, divisors / 182 \\
Approximate invariant subspaces / 184 \\
Almost normal matrices / 187 \\
4. Solution of Linear Algebraic Equations \\
Introduction / 189 \\
Perturbation theory / 189 \\
Condition numbers / 191 \\
Equilibrated matrices / 192 \\
Simple practical examples / 193 \\
Condition of matrix of eigenvectors / 193 \\
Explicit solution / 194 \\
General comments on condition of matrices / 195 \\
Relation of ill-conditioning to near-singularity / 196
\\
Limitations imposed by t-digit arithmetic / 197 \\
Algorithms for solving linear equations / 198 \\
Gaussian elimination / 200 \\
Triangular decomposition / 201 \\
Structure of triangular decomposition matrices / 201
\\
Explicit expressions for elements of the triangles /
202 \\
Breakdown of Gaussian elimination / 204 \\
Numerical stability / 205 \\
Significance of the interchanges / 206 \\
Numerical example / 207 \\
Error analysis of Gaussian elimination / 209 \\
Upper bounds for the perturbation matrices using
fixed-point arithmetic / 211 \\
Upper bound for elements of reduced matrices / 212 \\
Complete pivoting / 212 \\
Practical procedure with partial pivoting / 214 \\
Floating-point error analysis / 214 \\
Floating-point decomposition without pivoting / 215 \\
Loss of significant figures / 217 \\
A popular fallacy / 217 \\
Matrices of special form / 218 \\
Gaussian elimination on a high-speed computer / 220 \\
Solutions corresponding to different right-hand sides /
221 \\
Direct triangular decomposition / 221 \\
Relations between Gaussian elimination and direct
triangular decomposition / 223 \\
Examples of failure and non-uniqueness of decomposition
/ 224 \\
Triangular decomposition with row interchanges / 225
\\
Error analysis of triangular decomposition / 227 \\
Evaluation of determinants / 228 \\
Cholesky decomposition / 229 \\
Symmetric matrices which are not positive definite /
230 \\
Error analysis of Cholesky decomposition in fixed-point
arithmetic / 231 \\
An ill-conditioned matrix / 233 \\
Triangularization using elementary Hermitian matrices /
233 \\
Error analysis of Householder triangularization / 236
\\
Triangularization by elementary stabilized matrices of
the type M1, / 236 \\
Evaluation of determinants of leading principal minors
/ 237 \\
Triangularization by plane rotations / 239 \\
Error analysis of Givens reduction / 240 \\
Uniqueness of orthogonal triangularization / 241 \\
Schmidt orthogonalization / 242 \\
Comparison of the methods of triangularization / 244
\\
Back-substitution / 247 \\
High accuracy of computed solutions of triangular sets
of equations / 249 \\
Solution of a general set of equations / 251 \\
Computation of the inverse of a general matrix / 252
\\
Accuracy of computed solutions / 253 \\
Ill-conditioned matrices which give no small pivots /
254 \\
Iterative improvements of approximate solution / 255
\\
Effect of rounding errors on the iterative process /
256 \\
The iterative procedure in fixed-point computation /
257 \\
Simple example of iterative procedure / 258 \\
General comments on the iterative procedure / 260 \\
Related iterative procedures / 261 \\
Limitations of the iterative procedure / 261 \\
Rigorous justification of the iterative method / 262
\\
5. Hermitian Matrices \\
Introduction / 265 \\
The classical Jacobi method for real symmetric matrices
/ 266 \\
Rate of convergence / 267 \\
Convergence to fixed diagonal matrix / 268 \\
Serial Jacobi method / 269 \\
The Gerschgorin discs / 269 \\
Ultimate quadratic convergence of Jacobi methods / 270
\\
Close and multiple eigenvalues / 271 \\
Numerical examples / 273 \\
Calculation of cos 8 and sin B / 274 \\
Simpler determination of the angles of rotation / 276
\\
The threshold Jacobi method / 277 \\
Calculation of the eigenvectors / 278 \\
Numerical example / 279 \\
Error analysis of the Jacobi method / 279 \\
Accuracy of the computed eigenvectors / 280 \\
Error bounds for fixed-point computation / 281 \\
Organizational problems / 282 \\
Givens' method / 282 \\
Givens' process on a computer with a two-level store /
284 \\
Floating-point error analysis of Givens' process / 286
\\
Fixed-point error analysis / 287 \\
Numerical example / 288 \\
Householder's method / 290 \\
Taking advantage of symmetry / 292 \\
Storage considerations / 293 \\
Householder's process on a computer with a two-level
store / 294 \\
Householder's method in fixed-point arithmetic / 294
\\
Numerical example / 296 \\
Error analyses of Householder's method / 297 \\
Eigenvalues of a symmetric tri-diagonal matrix / 299
\\
Sturm sequence property / 300 \\
Method of bisection / 302 \\
Numerical stability of the bisection method / 302 \\
Numerical example / 305 \\
General comments on the bisection method / 306 \\
Small eigenvalues / 307 \\
Close eigenvalues and small $\beta_i$ / 308 \\
Fixed-point computation of the eigenvalues / 312 \\
Computation of the eigenvectors of a tri-diagonal form
/ 315 \\
Instability of the explicit expression for the
eigenvector / 316 \\
Numerical examples / 319 \\
Inverse iteration / 321 \\
Choice of initial vector $b$ / 322 \\
Error analysis / 323 \\
Numerical example / 325 \\
Close eigenvalues and small $\beta_i$ / 327 \\
Independent vectors corresponding to coincident
eigenvalues / 328 \\
Alternative method for computing the eigenvectors / 330
\\
Numerical example / 331 \\
Comments on the eigenproblem for tri-diagonal matrices
/ 332 \\
Completion of the Givens and Householder methods / 333
\\
Comparison of methods / 334 \\
Quasi-symmetric tri-diagonal matrices / 335 \\
Calculation of the eigenvectors / 336 \\
Equations of the form $A x = \lambda B x$ and $A B x =
\lambda X $ / 337 \\
Numerical example / 339 \\
Simultaneous reduction of $A$ and $B$ to diagonal form
/ 340 \\
Tri-diagonal $A$ and $B$ / 340 \\
Complex Hermitian matrices / 342 \\
6. Reduction of a General Matrix to Condensed Form \\
Introduction / 345 \\
Givens' method / 345 \\
Householder's method / 347 \\
Storage considerations / 350 \\
Error analysis / 350 \\
Relationship between the Givens and Householder methods
/ 351 \\
Elementary stabilized transformations / 353 \\
Significance of the permutations / 355 \\
Direct reduction to Hessenberg form / 357 \\
Incorporation of interchanges / 359 \\
Numerical example / 360 \\
Error analysis / 363 \\
Related error analyses / 365 \\
Poor determination of the Hessenberg matrix / 368 \\
Reduction to Hessenberg form using stabilized matrices
of the type $ M^'_{ji} $ / 368 \\
The method of Krylov / 369 \\
Gaussian elimination by columns / 370 \\
Practical difficulties / 371 \\
Condition of O for some standard distributions of
eigenvalues / 372 \\
Initial vectors of grade less than n / 374 \\
Practical experience / 376 \\
Generalized Hessenberg processes / 377 \\
Failure of the generalized Hessenberg process / 378 \\
The Hessenberg method / 379 \\
Practical procedure / 380 \\
Relation between the Hessenberg method and earlier
methods / 381 \\
The method of Arnoldi / 382 \\
Practical considerations / 383 \\
Significance of re-orthogonalization / 385 \\
The method of Lanczos / 388 \\
Failure of procedure / 389 \\
Numerical example / 390 \\
The practical Lanczos process / 391 \\
Numerical example / 392 \\
General comments on the unsymmetric Lanczos process /
394 \\
The symmetric Lanczos process / 394 \\
Reduction of a Hessenberg matrix to a more compact form
/ 395 \\
Reduction of a lower Hessenberg matrix to tri-diagonal
form / 396 \\
The use of interchanges / 397 \\
Effect of a small pivotal element / 398 \\
Error analysis / 399 \\
The Hessenberg process applied to a lower Hessenberg
matrix / 402 \\
Relationship between the Hessenberg process and the
Lanczos process / 402 \\
Reduction of a general matrix to tri-diagonal form /
403 \\
Comparison with Lanczos method / 404 \\
Re-examination of reduction to tri-diagonal form / 404
\\
Reduction from upper Hessenberg form to Frobenius form
/ 405 \\
Effect of small pivot / 407 \\
Numerical example / 408 \\
General comments on the stability / 408 \\
Specialized upper Hessenberg form / 409 \\
Direct determination of the characteristic polynomial /
410 \\
7. Eigenvalues of Matrices of Condensed Forms \\
Introduction / 413 \\
Explicit polynomial form / 413 \\
Condition numbers of explicit polynomials / 416 \\
Some typical distributions of zeros / 417 \\
Final assessment of Krylov's method / 421 \\
General comments on explicit polynomials / 421 \\
Tri-diagonal matrices / 423 \\
Determinants of Hessenberg matrices / 426 \\
Effect of rounding errors / 427 \\
Floating-point accumulation / 428 \\
Evaluation by orthogonal transformations / 429 \\
Evaluation of determinants of general matrices / 431
\\
The generalized eigenvalue problem / 432 \\
Indirect determinations of the characteristic
polynomial / 432 \\
Le Verrier's method / 434 \\
Iterative methods based on interpolation / 435 \\
Asymptotic rate of convergence / 436 \\
Multiple zeros / 437 \\
Inversion of the functional relationship / 439 \\
The method of bisection / 440 \\
Newton's method / 441 \\
Comparison of Newton's method with interpolation / 442
\\
Methods giving cubic convergence / 443 \\
Laguerre's method / 443 \\
Complex zeros / 446 \\
Complex conjugate zeros / 447 \\
Bairstow's method / 449 \\
The generalized Bairstow method / 450 \\
Practical considerations / 452 \\
Effect of rounding errors on asymptotic convergence /
453 \\
The method of bisection / 453 \\
Successive linear interpolation / 455 \\
Multiple and pathologically close eigenvalues / 457 \\
Other interpolation methods / 458 \\
Methods involving the use of a derivative / 459 \\
Criterion for acceptance of a zero / 461 \\
Effect of rounding errors / 462 \\
Suppression of computed zeros / 464 \\
Deflation for Hessenberg matrices / 465 \\
Deflation of tri-diagonal matrices / 468 \\
Deflation by rotations or stabilized elementary
transformations / 469 \\
Stability of the deflation / 472 \\
General comments on deflation / 474 \\
Suppression of computed zeros / 474 \\
Suppression of computed quadratic factors / 475 \\
General comments on the methods of suppression / 476
\\
Asymptotic rates of convergence / 478 \\
Convergence in the large / 478 \\
Complex zeros / 481 \\
Recommendations / 482 \\
Complex matrices / 483 \\
Matrices containing an independent parameter / 483 \\
8. The $ L R $ and $ Q R $ Algorithms \\
Introduction / 485 \\
Real matrices with complex eigenvalues / 486 \\
The $ L R $ algorithm / 487 \\
Proof of the convergence of the $A_s$ / 489 \\
Positive definite Hermitian matrices / 493 \\
Complex conjugate eigenvalues / 494 \\
Introduction of interchanges / 498 \\
Numerical example / 499 \\
Convergence of the modified process / 501 \\
Preliminary reduction of original matrix / 501 \\
Invariance of upper Hessenberg form / 502 \\
Simultaneous row and column operations / 504 \\
Acceleration of convergence / 505 \\
Incorporation of shifts of origin / 506 \\
Choice of shift of origin / 507 \\
Deflation of the matrix / 509 \\
Practical experience of convergence / 510 \\
Improved shift strategy / 511 \\
Complex conjugate eigenvalues / 512 \\
Criticisms of the modified $ L R $ algorithm. / 515 \\
The $ Q R $ algorithm / 515 \\
Convergence of the $ Q R $ algorithm / 516 \\
Formal proof of convergence / 517 \\
Disorder of the eigenvalues / 519 \\
Eigenvalues of equal modulus / 520 \\
Alternative proof for the $ L R $ technique / 521 \\
Practical application of the $ Q R $ algorithm / 523
\\
Shifts of origin / 524 \\
Decomposition of A8 / 525 \\
Numerical example / 527 \\
Practical procedure / 527 \\
Avoiding complex conjugate shifts / 528 \\
Double $ Q R $ step using elementary Hermitians / 532
\\
Computational details / 534 \\
Decomposition of A8 / 535 \\
Double-shift technique for $ L R $ / 537 \\
Assessment of $ L R $ and $ Q R $ algorithms / 538 \\
Multiple eigenvalues / 540 \\
Special use of the deflation process / 543 \\
Symmetric matrices / 544 \\
Relationship between $ L R $ and $ Q R $ algorithms /
545 \\
Convergence of the Cholesky $ L R $ algorithm / 546 \\
Cubic convergence of the $ Q R $ algorithm / 548 \\
Shift of origin in Cholesky $ L R $ / 549 \\
Failure of the Cholesky decomposition / 550 \\
Cubically convergent $ L R $ process / 551 \\
Band matrices / 553 \\
$ Q R $ decomposition of a band matrix / 557 \\
Error analysis / 561 \\
Unsymmetric band matrices / 562 \\
Simultaneous decomposition and recombination in $ Q R $
algorithm / 565 \\
Reduction of band width / 567 \\
9. ITERATIVE METHODS \\
Introduction / 570 \\
The power method / 570 \\
Direct iteration with a single vector / 571 \\
Shift of origin / 572 \\
Effect of rounding errors / 573 \\
Variation of $p$ / 576 \\
{\em Ad hoc\/} choice of $p$ / 577 \\
Aitken's acceleration technique / 578 \\
Complex conjugate eigenvalues / 579 \\
Calculation of the complex eigenvector / 581 \\
Shift of origin / 582 \\
Non-linear divisors / 582 \\
Simultaneous determination of several eigenvalues / 583
\\
Complex matrices / 584 \\
Deflation / 584 \\
Deflation based on similarity transformations / 585 \\
Deflation using invariant subspaces / 587 \\
Deflation using stabilized elementary transformations /
587 \\
Deflation using unitary transformations / 589 \\
Numerical stability / 590 \\
Numerical example / 592 \\
Stability of unitary transformations / 594 \\
Deflation by non-similarity transformations / 596 \\
General reduction using invariant subspaces / 599 \\
Practical application / 601 \\
Treppen-iteration / 602 \\
Accurate determination of complex conjugate eigenvalues
/ 604 \\
Very close eigenvalues / 606 \\
Orthogonalization techniques / 606 \\
Analogue of treppen-iteration using orthogonalization /
607 \\
Bi-iteration / 609 \\
Numerical example / 610 \\
Richardson's purification process / 614 \\
Matrix squaring / 615 \\
Numerical stability / 616 \\
Use of Chebyshev polynomials / 617 \\
General assessment of methods based on direct iteration
/ 618 \\
Inverse iteration / 619 \\
Error analysis of inverse iteration / 620 \\
General comments on the analysis / 621 \\
Further refinement of eigenvectors / 622 \\
Non-linear elementary divisors / 626 \\
Inverse iteration with Hessenberg matrices / 626 \\
Degenerate cases / 627 \\
Inverse iteration with band matrices / 628 \\
Complex conjugate eigenvectors / 629 \\
Error analysis / 631 \\
Numerical example / 633 \\
The generalized eigenvalue problem / 633 \\
Variation of approximate eigenvalues / 635 \\
Refinement of eigensystems / 637 \\
Numerical example / 639 \\
Refinement of the eigenvectors / 641 \\
Complex conjugate eigenvalues / 643 \\
Coincident and pathologically close eigenvalues / 644
\\
Comments on the ACE programmes / 646 \\
Bibliography / 649 \\
Index / 657",
}
@Article{Wilkinson:1965:ARS,
author = "J. H. Wilkinson",
title = "The {$ Q R $} Algorithm for Real Symmetric Matrices
with Multiple Eigenvalues",
journal = j-COMP-J,
volume = "8",
number = "1",
pages = "85--87",
month = apr,
year = "1965",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.40",
MRnumber = "MR0181100 (31 \#5329)",
MRreviewer = "E. R. Hansen",
bibdate = "Fri Sep 29 08:56:03 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/080085.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/85.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/86.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/87.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/88.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Wilkinson:1965:CLP,
author = "J. H. Wilkinson",
title = "The Calculation of {Lam{\'e}} Polynomials",
journal = j-COMP-J,
volume = "8",
number = "3",
pages = "273--277",
month = oct,
year = "1965",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.25",
MRnumber = "MR0184412 (32 \#1884)",
bibdate = "Fri Sep 29 08:56:08 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_03/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_03/080273.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_03/tiff/273.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_03/tiff/274.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_03/tiff/275.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_03/tiff/276.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_03/tiff/277.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Wilkinson:1965:CRA,
author = "J. H. Wilkinson",
title = "Convergence of the {$ L R $}, {$ Q R $} and related
algorithms",
journal = j-COMP-J,
volume = "8",
number = "1",
pages = "77--84",
month = apr,
year = "1965",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.40",
MRnumber = "MR0183108 (32 \#590)",
MRreviewer = "E. R. Hansen",
bibdate = "Fri Sep 29 08:56:03 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/;
Theory/Matrix.bib",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/080077.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/77.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/78.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/79.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/80.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/81.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/82.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/83.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_08/Issue_01/tiff/84.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "nla, eig, QR algorithm, LR algorithm",
}
@InProceedings{Wilkinson:1965:EAT,
author = "J. H. Wilkinson",
title = "Error Analysis for Transformations Based on the Use of
Matrices of the form {$ I - 2 w w^H $}",
crossref = "Rall:1965:EDCb",
pages = "77--101",
year = "1965",
MRclass = "65.80",
MRnumber = "MR0189284 (32 \#6711)",
MRreviewer = "J. M. Ortega",
bibdate = "Mon Jun 18 11:38:02 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
xxtitle = "Error Analysis of Transformations Based on the Use of
Matrices of the form {$ I - 2 w w^H $}",
}
@Article{Bowdler:1966:SRC,
author = "H. J. Bowdler and R. S. Martin and G. Peters and J. H.
Wilkinson",
title = "Solution of Real and Complex Systems of Linear
Equations",
journal = j-NUM-MATH,
volume = "8",
number = "3",
pages = "217--234",
year = "1966",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02162559",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553947",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "See also \cite[pp.~93--110]{Wilkinson:1971:LA}.",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@InProceedings{Golub:1966:IRL,
author = "G. H. Golub and J. H. Wilkinson",
booktitle = "Proceedings of the IFIP Congress 65, Volume 2",
title = "Iterative Refinement of Least Square Solution",
publisher = "International Federation for Information Processing
(IFIP)",
pages = "606--607",
year = "1966",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@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 = "Sun Oct 17 19:01:15 MDT 1999",
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;
http://www.math.utah.edu/pub/tex/bib/gvl.bib;
Theory/Matrix.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "condition; iterative refinement; la; lsq; nla; pert",
}
@Article{Martin:1966:IRS,
author = "R. S. Martin and G. Peters and J. H. Wilkinson",
title = "Iterative Refinement of the Solution of a Positive
Definite System of Equations",
journal = j-NUM-MATH,
volume = "8",
number = "3",
pages = "203--216",
month = may,
year = "1966",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02162558",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553946",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
Theory/Matrix.bib",
note = "Also in \cite[pp. 31--44]{Wilkinson:1971:LA}.",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "iterative refinement; linear system; nla; positive
definite matrix; software",
}
@InProceedings{Wilkinson:1966:CEM,
author = "J. H. Wilkinson",
editor = "J. Walsh",
booktitle = "Numerical Analysis: An Introduction",
title = "Calculation of Eigensystems of Matrices",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "27--61",
year = "1966",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@Article{Wilkinson:1967:BRB,
author = "J. H. Wilkinson",
title = "Book Review: {{\booktitle{The Matrix Analysis of
Vibration}}, by R. E. D. Bishop, G. M. L. Gladwell, and
S. Michaelson, 1965; 404 pages (London: Cambridge
University Press, 100s)}",
journal = j-COMP-J,
volume = "10",
number = "1",
pages = "77--77",
month = may,
year = "1967",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/10.1.77",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:37 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/10/1.toc;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/compj1960.bib",
URL = "http://comjnl.oxfordjournals.org/content/10/1/74.full.pdf;
http://comjnl.oxfordjournals.org/content/10/1/77.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Book{Wilkinson:1967:BZW,
author = "J. H. Wilkinson",
title = "Bledy Zaokragle{\'n} w Procesach Algebraicznych.
({Polish}) [{Rounding} errors in algebraic Processes]",
publisher = "PWW",
address = "Warszawa, Poland",
pages = "????",
year = "1967",
bibdate = "Thu Aug 25 09:28:02 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Polish translation of \cite{Wilkinson:1963:REA}",
acknowledgement = ack-nhfb,
language = "Polish",
}
@Article{Barth:1967:CES,
author = "R. S. Martin W. Barth and J. H. Wilkinson",
title = "Calculation of the Eigenvalues of a Symmetric
Tridiagonal matrix by the Method of Bisection",
journal = j-NUM-MATH,
volume = "9",
number = "5",
pages = "386--393",
month = apr,
year = "1967",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02162154",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553954",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
Theory/Matrix.bib",
note = "Also in \cite[pp. 249--256]{Wilkinson:1971:LA}.",
series = "Handbook Series Linear Algebra",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "eig; nla; software; Sturm sequence; symmetric matrix;
tridiagonal matrix",
}
@Article{Martin:1967:SSU,
author = "R. S. Martin and J. H. Wilkinson",
title = "Solution of Symmetric and Unsymmetric Band Equations
and the Calculation of Eigenvectors of Band Matrices",
journal = j-NUM-MATH,
volume = "9",
number = "4",
pages = "279--301",
month = feb,
year = "1967",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02162421",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553951",
bibdate = "Sun Oct 17 12:54:13 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
Theory/Matrix.bib",
note = "Also in \cite[pp. 70--92]{Wilkinson:1971:LA}.",
series = "Handbook Series Linear Algebra",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "band matrix; eig; linear system; nla; software",
}
@TechReport{Wilkinson:1967:ADM,
author = "J. H. Wilkinson",
title = "Almost Diagonal Matrices with Multiple or Close
Eigenvalues",
type = "Technical Report",
number = "CS 59",
institution = inst-SU-cs,
address = inst-SU:adr,
year = "1967",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Published as \cite{Wilkinson:1968:ADM}.",
}
@InCollection{Wilkinson:1967:SIC,
author = "J. H. Wilkinson",
editor = "A. Ralston and H. Wilf",
booktitle = "Mathematical Methods for Digital Computers, Volume 2",
title = "The Solution of Ill-Conditioned Linear Equations",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "65--93",
year = "1967",
bibdate = "Tue Aug 15 18:20:34 MDT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@InCollection{Wilkinson:1967:SLA,
author = "J. H. Wilkinson",
editor = "M. Klarer and G. A. Korn",
booktitle = "Digital Computer Users' Handbook",
title = "Solution of Linear Algebraic Equations and Matrix
Problems by Direct Methods",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
pages = "2:18--2:55",
year = "1967",
bibdate = "Tue Aug 15 18:20:34 MDT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@TechReport{Wilkinson:1967:TAB,
author = "J. H. Wilkinson",
title = "Two Algorithms Based on Successive Linear
Interpolation",
type = "Technical Report",
number = "CS 60",
institution = inst-SU-cs,
address = inst-SU:adr,
year = "1967",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@Article{Bowdler:1968:ASM,
author = "H. J. Bowdler and R. S. Martin and C. Reinsch and J.
H. Wilkinson",
title = "The {$ Q R $} and {$ Q L $} Algorithms for Symmetric
Matrices",
journal = j-NUM-MATH,
volume = "11",
number = "4",
pages = "293--306",
year = "1968",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02166681",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553961",
bibdate = "Fri May 14 17:18:08 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "See also \cite[pp.~227--240]{Wilkinson:1971:LA}.",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Martin:1968:HTS,
author = "R. S. Martin and C. Reinsch and J. H. Wilkinson",
title = "{Householder}'s tridiagonalization of a symmetric
matrix",
journal = j-NUM-MATH,
volume = "11",
number = "3",
pages = "181--195",
month = mar,
year = "1968",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02161841",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553959",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
Theory/Matrix.bib",
note = "Also in \cite[pp. 212--226]{Wilkinson:1971:LA}.",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "eig; Householder transformation; nla; software;
symmetric matrix; tridiagonal matrix",
}
@Article{Martin:1968:IA,
author = "Roger S. Martin and J. H. Wilkinson",
title = "The Implicit {$ Q L $} Algorithm",
journal = j-NUM-MATH,
volume = "12",
number = "5",
pages = "377--383",
month = dec,
year = "1968",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02161360",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553967",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
Theory/Matrix.bib",
note = "Also in \cite[pp.~241--248]{Wilkinson:1971:LA}, where
A. A. Dubrulle and is listed as the lead author.",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "eig; nla; QL algorithm; QR algorithm; software;
tridiagonal matrix",
}
@Article{Martin:1968:MAC,
author = "Roger S. Martin and J. H. Wilkinson",
title = "The Modified {$ L R $} Algorithm for Complex
{Hessenberg} Matrices",
journal = j-NUM-MATH,
volume = "12",
number = "5",
pages = "369--376",
month = dec,
year = "1968",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02161359",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553966",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
Theory/Matrix.bib",
note = "Also in \cite[pp. 396--403]{Wilkinson:1971:LA}.",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "complex matrix; eig; Hessenberg matrix; LR algorithm;
nla; software",
}
@Article{Martin:1968:RSE,
author = "R. S. Martin and J. H. Wilkinson",
title = "Reduction of the Symmetric Eigenproblem {$ A x =
\lambda B x $} and Related Problems to Standard Form",
journal = j-NUM-MATH,
volume = "11",
number = "2",
pages = "99--110",
month = feb,
year = "1968",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02165306",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553957",
bibdate = "Sun Oct 17 16:12:48 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
Theory/Matrix.bib",
note = "Also in \cite[pp. 303--314]{Wilkinson:1971:LA}.",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "geig; nla; software; symmetric matrix",
}
@Article{Martin:1968:SRG,
author = "R. S. Martin and J. H. Wilkinson",
title = "Similarity Reduction of a General Matrix to
{Hessenberg} Form",
journal = j-NUM-MATH,
volume = "12",
number = "5",
pages = "349--368",
month = dec,
year = "1968",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02161358",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553965",
bibdate = "Sun Oct 17 16:12:48 MDT 1999",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
Theory/Matrix.bib",
note = "Also in \cite[pp. 339--358]{Wilkinson:1971:LA}.",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "eig; Hessenberg matrix; nla; nonsymmetric matrix;
software",
}
@Article{Wilkinson:1968:ADM,
author = "J. H. Wilkinson",
title = "Almost Diagonal Matrices with Multiple or Close
Eigenvalues",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "1",
pages = "1--12",
year = "1968",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15.25 (65.00)",
MRnumber = "MR0225794 (37 \#1386)",
MRreviewer = "John Todd",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@InProceedings{Wilkinson:1968:BFE,
author = "J. H. Wilkinson",
booktitle = "Programmation en Math{\'e}matiques Num{\'e}riques",
title = "The Basic Forms of Error Analysis of Matrix
Processes",
publisher = "{\'E}ditions Centre Nat. Recherche Sci.",
address = "Paris, France",
pages = "127--133",
year = "1968",
MRclass = "65.35",
MRnumber = "MR0231522 (37 \#7075)",
MRreviewer = "L. W. Ehrlich",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Colloq. Int. Cent. Nat. Rech. Sci. 165,
Besan{\c{c}}on, Paris",
}
@Article{Wilkinson:1968:GCT,
author = "J. H. Wilkinson",
title = "Global Convergence of Tridiagonal {$ Q R $} Algorithm
with Origin Shifts",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "1",
number = "3",
pages = "409--420",
month = jul,
year = "1968",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(68)90017-7",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65.40",
MRnumber = "MR0234622 (38 \#2938)",
MRreviewer = "E. R. Hansen",
bibdate = "Tue Feb 16 18:47:41 MST 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/linala1960.bib;
http://www.math.utah.edu/pub/tex/bib/linala1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0024379568900177",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@InProceedings{Wilkinson:1968:PEA,
author = "J. H. Wilkinson",
editor = "I. G. Petrovsky",
booktitle = "Proc. Int. Congr. Mthns",
title = "A Priori Error Analysis of Algebraic Processes",
publisher = "Izdatel'stvo Mir",
address = "Moscow, USSR",
pages = "629--640",
year = "1968",
MRclass = "65.80",
MRnumber = "MR0233532 (38 \#1853)",
MRreviewer = "A. S. Householder",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@Article{Wilkinson:1968:SEA,
author = "James Hardy Wilkinson",
title = "A Survey of Error Analysis of Matrix Algorithms",
journal = j-APL-MAT,
volume = "13",
pages = "93--102",
year = "1968",
CODEN = "APMTAK",
ISSN = "0373-6725",
MRclass = "65.80",
MRnumber = "MR0228213 (37 \#3797)",
MRreviewer = "B. N. Parlett",
bibdate = "Fri May 14 17:09:52 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "\v Ceskoslovensk\'a Akademie V\v ed. Aplikace
Matematiky",
}
@Article{Peters:1969:EBS,
author = "G. Peters and J. H. Wilkinson",
title = "Eigenvalues of {$ A x = \lambda B x $} with Band
Symmetric {$A$} and {$B$}",
journal = j-COMP-J,
volume = "12",
number = "4",
pages = "398--404",
month = nov,
year = "1969",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "65.35",
MRnumber = "MR0253543 (40 \#6757)",
bibdate = "Fri Sep 29 08:51:40 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/120397.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/398.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/399.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/400.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/401.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/402.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/403.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_12/Issue_04/tiff/404.tif",
acknowledgement = ack-nhfb,
classcodes = "C4140 (Linear algebra)",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "algebra; eigenvalues and eigenfunctions;
interpolation; matrix; nla, geig, band matrix,
symmetric matrix; poles and zeros; subroutines",
}
@InProceedings{Wilkinson:1969:GCA,
author = "James H. Wilkinson",
booktitle = "Proceedings of the IFIP Congress 1968, Edinburgh,
Volume 1",
title = "Global Convergence of {$ Q R $} Algorithm (with
discussion)",
publisher = pub-NORTH-HOLLAND,
address = pub-NORTH-HOLLAND:adr,
pages = "130--133",
year = "1969",
MRclass = "65.40",
MRnumber = "MR0255039 (40 \#8246)",
bibdate = "Fri May 14 17:13:35 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@Book{Wilkinson:1969:R,
author = "J. H. Wilkinson",
title = "{Rundungsfehler}",
volume = "44",
publisher = pub-SV,
address = pub-SV:adr,
pages = "x + 208",
year = "1969",
MRclass = "68.00 (12.00)",
MRnumber = "MR0242399 (39 \#3730)",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "German translation by G. Goos.",
series = "Heidelberger Taschenb{\"u}cher",
}
@Article{Householder:1970:NGI,
author = "Alston S. Householder and Richard S. Varga and James
H. Wilkinson",
title = "A Note on {Gerschgorin}'s Inclusion Theorem for
Eigenvalues of Matrices",
journal = j-NUM-MATH,
volume = "16",
pages = "141--144",
year = "1970",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65.40 (15.00)",
MRnumber = "MR0275648 (43 \#1401)",
MRreviewer = "J. Stoer",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@Article{Martin:1970:ABS,
author = "R. S. Martin and C. Reinsch and J. H. Wilkinson",
title = "The {$ Q R $} algorithm for band symmetric matrices",
journal = j-NUM-MATH,
volume = "16",
number = "2",
pages = "85--92",
month = nov,
year = "1970",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02308862",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553977",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "See also \cite[pp.~266--272]{Wilkinson:1971:LA}.",
acknowledgement = ack-nhfb,
classification = "C4140 (Linear algebra)",
corpsource = "Nat. Phys. Lab., Teddington, UK",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "eigenvalues and eigenfunctions and matrix algebra",
}
@Article{Martin:1970:ARH,
author = "R. S. Martin and G. Peters and J. H. Wilkinson",
title = "The {$ Q R $} Algorithm for real {Hessenberg}
matrices",
journal = j-NUM-MATH,
volume = "14",
number = "3",
pages = "219--231",
month = feb,
year = "1970",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02163331",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553971",
bibdate = "Tue Jan 28 17:21:29 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
Theory/Matrix.bib",
note = "Also in \cite[pp. 359--371]{Wilkinson:1971:LA}.",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "eig; Hessenberg matrix; nla; QR algorithm; software",
}
@Article{Peters:1970:ERC,
author = "G. Peters and J. H. Wilkinson",
title = "Eigenvectors of Real and Complex Matrices by {$ L R $}
and {$ Q R $} Triangularization",
journal = j-NUM-MATH,
volume = "16",
number = "3",
pages = "181--204",
month = dec,
year = "1970",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF02219772",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553978",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
Theory/Matrix.bib",
note = "Also in \cite[pp. 372--395]{Wilkinson:1971:LA}.",
acknowledgement = ack-nhfb,
classification = "C4140 (Linear algebra)",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "complex matrix; eig; eigenvalues and eigenfunctions;
matrix algebra; nla; nonsymmetric matrix; software",
}
@Article{Peters:1970:GE,
author = "G. Peters and J. H. Wilkinson",
title = "{$ A x = \lambda B x $} and the Generalized
Eigenproblem",
journal = j-SIAM-J-NUMER-ANAL,
volume = "7",
pages = "479--492",
year = "1970",
CODEN = "SJNAAM",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65.40",
MRnumber = "MR0277106 (43 \#2843)",
MRreviewer = "E. Deutsch",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
}
@Article{Peters:1970:LSP,
author = "G. Peters and J. H. Wilkinson",
title = "The Least Squares Problem and Pseudo-Inverses",
journal = j-COMP-J,
volume = "13",
number = "3",
pages = "309--316",
month = aug,
year = "1970",
CODEN = "CMPJA6",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Fri Sep 29 08:51:46 MDT 2000",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/130309.sgm.abs.html;
http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/tiff/309.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/tiff/310.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/tiff/311.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/tiff/312.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/tiff/313.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/tiff/314.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/tiff/315.tif;
http://www3.oup.co.uk/computer_journal/hdb/Volume_13/Issue_03/tiff/316.tif",
acknowledgement = ack-nhfb,
classcodes = "C4140 (Linear algebra)",
corpsource = "Nat. Phys. Lab., Teddington, UK",
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
keywords = "least squares approximations; matrix algebra",
}
@Book{Wilkinson:1970:APS,
author = "J. H. Wilkinson",
title = "Algebraicheskaya problema sobstvennyh znachenii'.
({Russian}) [The Algebraic Eigenvalue Problem]",
publisher = pub-NAUKA,
address = pub-NAUKA:adr,
pages = "564",
year = "1970",
bibdate = "Thu Aug 25 09:30:04 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Russian translation of \cite{Wilkinson:1965:AEP}",
acknowledgement = ack-nhfb,
language = "Russian",
}
@Article{Wilkinson:1970:BRB,
author = "J. H. Wilkinson",
title = "Book Review: {{\booktitle{A Collection of Matrices for
Testing Computational Algorithms}}, by Robert T.
Gregory, D. L. Karney, 1969; 154 pages. (John Wiley and
Sons Ltd., \pounds 4.75)}",
journal = j-COMP-J,
volume = "13",
number = "4",
pages = "391--391",
month = nov,
year = "1970",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/13.4.391",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:46 MST 2012",
bibsource = "ftp://ftp.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://comjnl.oxfordjournals.org/content/13/4.toc;
http://www.math.utah.edu/pub/tex/bib/compj1970.bib",
URL = "http://comjnl.oxfordjournals.org/content/13/4/387.full.pdf;
http://comjnl.oxfordjournals.org/content/13/4/391.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{Wilkinson:1970:BRH,
author = "J. H. Wilkinson",
title = "Book Review: {{\em A Handbook of Numerical Matrix
Inversion and Solution of Linear Equations}, by Joan
Westlake: pp. 171; 90s. (John Wiley and Sons, New York,
1968)}",
journal = j-BULL-LOND-MATH-SOC,
volume = "2",
number = "3",
pages = "378--379",
month = nov,
year = "1970",
CODEN = "LMSBBT",
DOI = "https://doi.org/10.1112/blms/2.3.378",
ISSN = "0024-6093 (print), 1469-2120 (electronic)",
ISSN-L = "0024-6093",
bibdate = "Thu Aug 25 10:29:07 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
URL = "http://blms.oxfordjournals.org/content/2/3/378.full.pdf",
acknowledgement = ack-nhfb,
fjournal = "Bulletin of the London Mathematical Society",
journal-URL = "http://blms.oxfordjournals.org/content/by/year",
}
@TechReport{Wilkinson:1970:EPW,
author = "J. H. Wilkinson",
title = "Elementary Proof of the {Wielandt--Hoffman} Theorem
and of its Generalization",
type = "Technical Report",
number = "CS 150",
institution = inst-SU-cs,
address = inst-SU:adr,
year = "1970",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@InCollection{Barth:1971:CES,
author = "W. Barth and R. S. Martin and J. H. Wilkinson",
title = "Calculation of the eigenvalues of a symmetric
tridiagonal matrix by the method of bisection",
crossref = "Wilkinson:1971:LA",
pages = "249--256",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@Book{Bell:1971:CSR,
editor = "C. G. Bell and A. Newell",
title = "Computer Structures: Readings and Examples",
publisher = pub-MCGRAW-HILL,
address = pub-MCGRAW-HILL:adr,
year = "1971",
ISBN = "0-07-004357-4",
ISBN-13 = "978-0-07-004357-2",
LCCN = "TK7888.3 .B4",
bibdate = "Tue Aug 15 18:20:34 MDT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@InCollection{Bowdler:1971:ASM,
author = "H. Bowdler and R. S. Martin and C. H. Reinsch and J.
H. Wilkinson",
title = "The {$ Q R $} and {$ Q L $} algorithms for symmetric
matrices",
crossref = "Wilkinson:1971:LA",
pages = "227--240",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Bowdler:1971:SRC,
author = "H. J. Bowdler and R. S. Martin and G. Peters and J. H.
Wilkinson",
title = "Solution of real and complex systems of linear
equations",
crossref = "Wilkinson:1971:LA",
pages = "93--110",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Dubrulle:1971:IA,
author = "A. Dubrulle and R. S. Martin and J. H. Wilkinson",
title = "The implicit {$ Q L $} algorithm",
crossref = "Wilkinson:1971:LA",
pages = "241--248",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Martin:1971:ABS,
author = "R. S. Martin and C. H. Reinsch and J. H. Wilkinson",
title = "The {$ Q R $} algorithm for band symmetric matrices",
crossref = "Wilkinson:1971:LA",
pages = "266--272",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Martin:1971:ARH,
author = "R. S. Martin and G. Peters and J. H. Wilkinson",
title = "The {$ Q R $} algorithm for real {Hessenberg}
matrices",
crossref = "Wilkinson:1971:LA",
pages = "359--371",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Martin:1971:HTS,
author = "R. S. Martin and C. H. Reinsch and J. H. Wilkinson",
title = "Householder's tridiagonalization of a symmetric
matrix",
crossref = "Wilkinson:1971:LA",
pages = "212--226",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Martin:1971:IRS,
author = "R. S. Martin and G. Peters and J. H. Wilkinson",
title = "Iterative refinement of the solution of a positive
definite system of equations",
crossref = "Wilkinson:1971:LA",
pages = "31--44",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Martin:1971:MAC,
author = "R. S. Martin and J. H. Wilkinson",
title = "The modified {$ L R $} algorithm for complex
{Hessenberg} matrices",
crossref = "Wilkinson:1971:LA",
pages = "396--403",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Martin:1971:RSE,
author = "R. S. Martin and J. H. Wilkinson",
title = "Reduction of the symmetric eigenproblem {$ A x =
\lambda B x $} and related problems to standard form",
crossref = "Wilkinson:1971:LA",
pages = "303--314",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Martin:1971:SDPa,
author = "R. S. Martin and G. Peters and J. H. Wilkinson",
title = "Symmetric decomposition of a positive definite
matrix",
crossref = "Wilkinson:1971:LA",
pages = "9--30",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Martin:1971:SDPb,
author = "R. S. Martin and J. H. Wilkinson",
title = "Symmetric decomposition of positive definite band
matrices",
crossref = "Wilkinson:1971:LA",
pages = "50--56",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Martin:1971:SRG,
author = "R. S. Martin and J. H. Wilkinson",
title = "Similarity reduction of a general matrix to
{Hessenberg} form",
crossref = "Wilkinson:1971:LA",
pages = "339--358",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Martin:1971:SSU,
author = "R. S. Martin and J. H. Wilkinson",
title = "Solution of symmetric and unsymmetric band equations
and the calculation of eigenvectors of band matrices",
crossref = "Wilkinson:1971:LA",
pages = "70--92",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Peters:1971:CSE,
author = "G. Peters and J. H. Wilkinson",
title = "The calculation of specified eigenvectors by inverse
iteration",
crossref = "Wilkinson:1971:LA",
pages = "418--439",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Peters:1971:ERC,
author = "G. Peters and J. H. Wilkinson",
title = "Eigenvectors of real and complex matrices by {$ L R $}
and {$ Q R $} triangularizations",
crossref = "Wilkinson:1971:LA",
pages = "372--395",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@Article{Peters:1971:PPA,
author = "G. Peters and J. H. Wilkinson",
title = "Practical Problems Arising in the Solution of
Polynomial Equations",
journal = j-J-INST-MATH-APPL,
volume = "8",
pages = "16--35",
year = "1971",
CODEN = "JMTAA8",
ISSN = "0020-2932",
MRclass = "65H05",
MRnumber = "MR0298931 (45 \#7980)",
MRreviewer = "R. F. Albrecht",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "Journal of the Institute of Mathematics and its
Applications",
journal-URL = "http://imamat.oxfordjournals.org/content/by/year",
}
@Article{Wilkinson:1971:DNA,
author = "J. H. Wilkinson",
title = "A Discussion on Numerical Analysis of Partial
Differential Equations. {Introductory} Remarks",
journal = j-PRSL,
volume = "A 323",
pages = "153",
year = "1971",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@InCollection{Wilkinson:1971:IPI,
author = "J. H. Wilkinson",
title = "Introduction to {Part II}: The Algebraic Eigenvalue
Problem",
crossref = "Wilkinson:1971:LA",
pages = "191--201",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@InCollection{Wilkinson:1971:IPL,
author = "J. H. Wilkinson",
title = "Introduction to {Part I}: Linear Systems, Least
Squares and Linear Programming",
crossref = "Wilkinson:1971:LA",
pages = "1--8",
year = "1971",
bibdate = "Tue May 08 14:20:56 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@Article{Wilkinson:1971:IR,
author = "J. H. Wilkinson",
title = "Introductory Remarks",
journal = j-PROC-R-SOC-LOND-SER-A-MATH-PHYS-SCI,
volume = "323",
number = "??",
pages = "153--153",
day = "8",
month = jun,
year = "1971",
CODEN = "PRLAAZ",
DOI = "https://doi.org/10.1098/rspa.1971.0092",
ISSN = "0080-4630",
bibdate = "Tue Sep 27 18:55:27 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
fjournal = "Proceedings of the Royal Society of London. Series A,
Mathematical and physical sciences",
journal-URL = "http://rspa.royalsocietypublishing.org/content/current",
}
@Article{Wilkinson:1971:MEA,
author = "J. H. Wilkinson",
title = "Modern Error Analysis",
journal = j-SIAM-REVIEW,
volume = "13",
number = "4",
pages = "548--568",
month = "????",
year = "1971",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1013095",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65G05",
MRnumber = "MR0305578 (46 \#4708)",
MRreviewer = "R. P. Brent",
bibdate = "Thu Mar 27 09:06:33 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/13/4;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
note = "The 1970 von Neumann lecture.",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "October 1971",
}
@Article{Wilkinson:1971:SCN,
author = "J. H. Wilkinson",
title = "Some Comments from a Numerical Analyst",
journal = j-J-ACM,
volume = "18",
number = "2",
pages = "137--147",
month = apr,
year = "1971",
CODEN = "JACOAH",
DOI = "https://doi.org/10.1145/321637.321638",
ISSN = "0004-5411 (print), 1557-735X (electronic)",
ISSN-L = "0004-5411",
MRclass = "65.00",
MRnumber = "MR0282494 (43 \#8205)",
bibdate = "Sat Dec 10 15:00:46 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
fjournal = "Journal of the Association for Computing Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J401",
remark = "This is the 1970 ACM Turing Award Lecture. Subsequent
lectures are published in {\em Communications of the
ACM}. Wilkinson comments ``It is perhaps salutary to be
reminded that as early as 1946 Turing had considered
the possibility of working with both interval and
significant digit arithmetic and the report recalled
forgotten conversations, not to mention heated
arguments, which we had on this topic.'' He also says
``I think it is of vital importance that all the work
that has been expended on the development of
satisfactory algorithms should be made fully available
to the people who need to use it. I would go further
than this and claim that it is a social duty to see
that this is achieved.''",
}
@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 = "CS-72-270",
institution = inst-SU-cs,
address = inst-SU:adr,
year = "1972",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@InProceedings{Wilkinson:1972:IIT,
author = "J. H. Wilkinson",
booktitle = "Symposia Matematico {X}",
title = "Inverse Iteration in Theory and in Practice",
publisher = "Istituto Nazionale di Alta Matematica",
address = "Bologna, Italy",
pages = "361--379",
year = "1972",
MRclass = "65F15",
MRnumber = "MR0366017 (51 \#2268)",
MRreviewer = "G. Maess",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Monograph, Volume 10.",
}
@Article{Wilkinson:1972:NAN,
author = "J. H. Wilkinson",
title = "Numerical Analysis at the {National Physical
Laboratory}",
journal = j-BULL-INST-MATH-APPL,
volume = "8",
number = "9--10",
pages = "297--298",
year = "1972",
CODEN = "IMTABW",
ISSN = "0950-5628",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "Bulletin of the Institute of Mathematics and its
Applications",
}
@Article{Wilkinson:1972:NMV,
author = "J. H. Wilkinson",
title = "Note on matrices with a very ill-conditioned
eigenproblem",
journal = j-NUM-MATH,
volume = "19",
number = "2",
pages = "176--178",
month = apr,
year = "1972",
CODEN = "NUMMA7",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F15",
MRnumber = "MR0311092 (46 \#10188)",
MRreviewer = "G. W. Stewart",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
classification = "C4140 (Linear algebra)",
corpsource = "Nat. Phys. Lab., Teddington, UK",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "eigenvalues and eigenfunctions; eigenvectors; ill
conditioned eigenproblem; matrices; matrix algebra;
multiple eigenvalue; numerical methods",
treatment = "T Theoretical or Mathematical",
}
@InCollection{Peters:1974:ACE,
author = "G. Peters and J. H. Wilkinson",
crossref = "Scaife:1974:SNA",
title = "Accuracy of Computed Eigensystems and Invariant
Subspaces",
pages = "115--135",
year = "1974",
MRclass = "65F15",
MRnumber = "MR0356471 (50 \#8941)",
MRreviewer = "L. W. Ehrlich",
bibdate = "Tue Aug 15 18:20:34 MDT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Festschrift in honour of C. Lanczos commissioned by
the Royal Irish Academy.",
}
@TechReport{Peters:1974:APD,
author = "G. Peters and J. H. Wilkinson",
title = "On an Algorithm for Polynomial Deflation by {Broyden
and Ford}",
type = "Technical Report",
number = "NAC 55",
institution = inst-NPL,
address = inst-NPL:adr,
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@Unpublished{Peters:1974:SAS,
author = "G. Peters and J. H. Wilkinson",
title = "Some Algorithms for the Solution of the Generalized
Symmetric Eigenvalue Problem {$ A u = \lambda B u $}",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Unpublished, Circa 1974. National Physical Laboratory,
Teddington, Middlesex TW11 0LW, UK.",
}
@Article{Wilkinson:1974:CEA,
author = "J. H. Wilkinson",
title = "The Classical Error Analysis for the Solution of
Linear Systems",
journal = j-BULL-INST-MATH-APPL,
volume = "10",
number = "5--6",
pages = "175--180",
year = "1974",
CODEN = "IMTABW",
ISSN = "0950-5628",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "Bulletin of the Institute of Mathematics and its
Applications",
}
@Unpublished{Wilkinson:1974:HPE,
author = "J. H. Wilkinson",
title = "Handbook p139 Expanded or Expounded",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Unpublished, Circa 1974. National Physical Laboratory,
Teddington, Middlesex TW11 0LW, UK.",
}
@InProceedings{Wilkinson:1974:LAA,
author = "J. H. Wilkinson",
title = "Linear Algebra Algorithms",
crossref = "Evans:1974:SNM",
pages = "17--25 (discussion 27--28)",
year = "1974",
MRclass = "65F99",
MRnumber = "MR0362880 (50 \#15318)",
MRreviewer = "L. W. Ehrlich",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "With discussion by J. D. Beasley, E. L. Albasiny, O.
Tingleff, Linda Hayes, M. G. Cox, M. J. D. Powell and
J. H. Wilkinson",
}
@Article{Wilkinson:1974:NII,
author = "J. H. Wilkinson",
title = "Note on Inverse Iteration and Ill-Conditioned
Eigensystems",
journal = "Acta Univ. Carol. Math. Phys.",
volume = "15",
number = "1--2",
pages = "173--177",
year = "1974",
MRclass = "65F15",
MRnumber = "MR0386244 (52 \#7102)",
MRreviewer = "W. C. Rheinboldt",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@Article{Wilkinson:1974:NLA,
author = "J. H. Wilkinson",
title = "Numerical Linear Algebra on Digital Computers",
journal = j-BULL-INST-MATH-APPL,
volume = "10",
number = "9--10",
pages = "354--356",
year = "1974",
CODEN = "IMTABW",
ISSN = "0950-5628",
MRclass = "65-03 (01A65)",
MRnumber = "MR0655456 (58 \#31698)",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "Bulletin of the Institute of Mathematics and its
Applications",
}
@Unpublished{Wilkinson:1974:SVD,
author = "J. H. Wilkinson",
title = "The Singular Value Decomposition and minfit",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Unpublished, Circa 1974. National Physical Laboratory,
Teddington, Middlesex TW11 0LW, UK.",
}
@Unpublished{Wilkinson:1974:TMA,
author = "J. H. Wilkinson",
title = "Test Matrices for Algorithms for Solving Linear
Systems and Inverting Matrices",
year = "1974",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Unpublished, Circa 1974. National Physical Laboratory,
Teddington, Middlesex TW11 0LW, UK.",
}
@InCollection{Fox:1975:F,
author = "L. Fox and J. H. Wilkinson",
booktitle = "The NAG Library Manual",
title = "Foreward",
publisher = pub-NAG,
address = pub-NAG:adr,
pages = "1--3",
year = "1975",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@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-SU-cs,
address = inst-SU:adr,
year = "1975",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Published as \cite{Golub:1976:ICE}.",
}
@Article{Peters:1975:SGJ,
author = "G. Peters and J. H. Wilkinson",
title = "On the Stability of {Gauss--Jordan} Elimination with
Pivoting",
journal = j-CACM,
volume = "18",
number = "1",
pages = "20--24",
month = jan,
year = "1975",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/360569.360653",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
MRclass = "65F05 (65G05)",
MRnumber = "MR0371038 (51 \#7261)",
MRreviewer = "L. B. Rall",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Collection of articles honoring Alston S.
Householder",
fjournal = "Communications of the Association for Computing
Machinery",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
}
@Article{Wilkinson:1975:AHA,
author = "J. H. Wilkinson",
title = "{Alston S. Householder} award",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "11",
number = "1",
pages = "1",
month = "????",
year = "1975",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Tue Feb 16 18:49:00 MST 2016",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/linala1970.bib",
URL = "http://www.sciencedirect.com/science/article/pii/0024379575901111",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795/",
}
@InProceedings{Wilkinson:1975:IS,
author = "J. H. Wilkinson",
title = "Invariant Subspaces",
crossref = "ICM:1974:PIC",
pages = "443--448",
year = "1975",
MRclass = "65F15",
MRnumber = "MR0426394 (54 \#14337)",
MRreviewer = "F. Pecka",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@Article{Wilkinson:1975:PAN,
author = "J. H. Wilkinson",
title = "The {Pilot ACE at the NPL}",
journal = j-RADIO-ELECTRON-ENG,
volume = "45",
number = "7",
pages = "336--340",
month = jul,
year = "1975",
CODEN = "RDEEA4",
ISSN = "0033-7722",
bibdate = "Mon Nov 1 18:34:26 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "The Radio and Electronic Engineer",
}
@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",
year = "1976",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1018113",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65F15 (15A21)",
MRnumber = "MR0413456 (54 \#1570)",
MRreviewer = "Robert Todd Gregory",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
}
@TechReport{Hammarling:1976:PBL,
author = "S. Hammarling and J. H. Wilkinson",
title = "The Practical Behaviour of Linear Iterative Methods
with Particular Reference to {S.O.R.}",
type = "Technical Report",
number = "NAC 69",
institution = inst-NPL,
address = inst-NPL:adr,
year = "1976",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@InProceedings{Wilkinson:1976:LDE,
author = "J. H. Wilkinson",
title = "Linear Differential Equations and {$ A x = \lambda B x
$}",
crossref = "Hartnell:1976:PFM",
pages = "137--158",
year = "1976",
MRclass = "65F30",
MRnumber = "MR0408226 (53 \#11991)",
MRreviewer = "J. D. P. Donnelly",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@TechReport{Wilkinson:1977:DSG,
author = "J. H. Wilkinson",
title = "The Differential System {$ B \dot {x} = A x $} and the
Generalized Eigenvalue Problem {$ A u = \lambda B u
$}",
type = "Technical Report",
number = "NAC 73",
institution = inst-NPL,
address = inst-NPL:adr,
year = "1977",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@InProceedings{Wilkinson:1977:SRA,
author = "J. H. Wilkinson",
title = "Some Recent Advances in Numerical Linear Algebra",
crossref = "Jacobs:1976:SAN",
pages = "3--23",
year = "1977",
MRclass = "65F15 (65-02)",
MRnumber = "MR0455326 (56 \#13565)",
MRreviewer = "Alan L. Andrew",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
xxpages = "3--53",
}
@Unpublished{Wilkinson:1977:USP,
author = "J. H. Wilkinson",
title = "The Use of the Single-Precision Residual in the
Solution of Linear Systems",
year = "1977",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Unpublished, Circa 1977. National Physical Laboratory,
Teddington, Middlesex TW11 0LW, UK.",
}
@Article{Wilkinson:1978:AHA,
author = "J. H. Wilkinson",
title = "The {Alston S. Householder Award}",
journal = j-NUM-MATH,
volume = "29",
number = "4",
pages = "463--463",
month = apr,
year = "1978",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01432882",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "Contributed Item",
MRnumber = "MR1553992",
bibdate = "Sun Mar 18 11:40:16 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
}
@TechReport{Wilkinson:1978:KCF,
author = "J. H. Wilkinson",
title = "{Kronecker}'s Canonical Form and the {$ Q Z $}
Algorithm",
type = "Technical Report",
number = "DNACS 10/78",
institution = inst-NPL,
address = inst-NPL:adr,
year = "1978",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Published as \cite{Wilkinson:1979:KCF}.",
}
@InProceedings{Wilkinson:1978:LDE,
author = "J. H. Wilkinson",
title = "Linear Differential Equations and {Kronecker}'s
Canonical Form",
crossref = "deBoor:1978:RAN",
pages = "231--265",
year = "1978",
MRclass = "65L05",
MRnumber = "MR519065 (80e:65077)",
MRreviewer = "Ekkehard Wagenf{\"u}hrer",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@TechReport{Wilkinson:1978:NPS,
author = "J. H. Wilkinson",
title = "Note on the Practical Significance of the {Drazin}
Inverse",
type = "Technical Report",
number = "DNACS 13/79",
institution = inst-NPL,
address = inst-NPL:adr,
year = "1978",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Also produced as Stanford University, Computer Science
Department Report STAN-CS-79-736. Published as
\cite{Wilkinson:1982:NPS}.",
}
@InProceedings{Wilkinson:1978:PNL,
author = "J. H. Wilkinson",
title = "A Problem in Numerical Linear Algebra",
crossref = "Powell:1977:CDJ",
pages = "76--91",
year = "1978",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@InProceedings{Wilkinson:1978:SVD,
author = "J. H. Wilkinson",
title = "Singular-Value Decomposition -- Basic Aspects",
crossref = "Jacobs:1978:NSN",
pages = "109--135",
year = "1978",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@Article{Cline:1979:ECN,
author = "A. K. Cline and C. B. Moler and G. W. Stewart and J.
H. Wilkinson",
title = "An Estimate for the Condition Number of a Matrix",
journal = j-SIAM-J-NUMER-ANAL,
volume = "16",
number = "2",
pages = "368--375",
month = apr,
year = "1979",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0716029",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F35 (65F05)",
MRnumber = "80g:65048",
MRreviewer = "R. P. Tewarson",
bibdate = "Fri Oct 16 06:57:22 MDT 1998",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
JSTOR database",
ZMnumber = "Zbl 0403.65012",
acknowledgement = ack-nhfb,
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "cond, err, math, nla, condition estimation",
}
@Article{Peters:1979:III,
author = "G. Peters and J. H. Wilkinson",
title = "Inverse Iteration, Ill-Conditioned Equations and
{Newton}'s Method",
journal = j-SIAM-REVIEW,
volume = "21",
number = "3",
pages = "339--360",
year = "1979",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1021052",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
MRclass = "65F10 (65F15)",
MRnumber = "MR535118 (80f:65040)",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "SIAM Review. A Publication of the Society for
Industrial and Applied Mathematics",
journal-URL = "http://epubs.siam.org/sirev",
}
@Article{Wilkinson:1979:KCF,
author = "J. H. Wilkinson",
title = "{Kronecker}'s Canonical Form and the {$ Q Z $}
Algorithm",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "28",
pages = "285--303",
year = "1979",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(79)90140-X",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A21 (65F15)",
MRnumber = "MR549441 (81a:15015)",
MRreviewer = "I. Enescu",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Dedicated to the 75th birthday of A. S. Householder.",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@TechReport{Hammarling:1980:LSA,
author = "S. Hammarling and J. H. Wilkinson",
title = "On Linear Systems Arising from Finite Difference
Approximations to Elliptic Differential Equations",
type = "Technical Report",
number = "DNACS 34/80",
institution = inst-NPL,
address = inst-NPL:adr,
year = "1980",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@TechReport{Symm:1980:REBa,
author = "H. J. Symm and J. H. Wilkinson",
title = "Realistic Error Bounds for a Simple Eigenvalue and its
Associated Eigenvector",
type = "Technical Report",
number = "STAN-CS-80-787",
institution = inst-SU-cs,
address = inst-SU:adr,
year = "1980",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Published as \cite{Symm:1980:REBb}.",
}
@Article{Symm:1980:REBb,
author = "H. J. Symm and J. H. Wilkinson",
title = "Realistic error bounds for a simple eigenvalue and its
associated eigenvector",
journal = j-NUM-MATH,
volume = "35",
number = "2",
pages = "113--126",
month = jun,
year = "1980",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01396310",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F15",
MRnumber = "83b:65037",
MRreviewer = "Alan L. Andrew",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
Theory/Matrix.bib",
acknowledgement = ack-nhfb,
annote = "Cited in \cite{govl:89}.",
classification = "C1100 (Mathematical techniques); C4110 (Error
analysis in numerical methods)",
corpsource = "Div. of Numerical Analysis and Computer Sci., Nat.
Phys. Lab., Teddington, UK",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "eig; eigenvalue; eigenvalues and eigenfunctions;
eigenvector; error analysis; error bounds; error
estimates; la; pert",
treatment = "T Theoretical or Mathematical",
}
@Article{Wilkinson:1980:SRA,
author = "J. H. Wilkinson",
title = "Some recent advances in numerical linear algebra",
journal = "Yingyong Shuxue yu Jisuan Shuxue",
volume = "6",
pages = "1--19",
year = "1980",
MRclass = "65-02 (65F15)",
MRnumber = "MR653134 (83d:65006)",
bibdate = "Fri May 14 18:02:56 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Translated from the English by Ji Guang Sun.",
acknowledgement = ack-nhfb,
fjournal = "Yingyong Shuxue yu Jisuan Shuxue. Applied Mathematics
and Computational Mathematics",
}
@InProceedings{Wilkinson:1980:TWN,
author = "J. H. Wilkinson",
title = "{Turing}'s Work at the {National Physical Laboratory}
and the Construction of {Pilot ACE}, {DEUCE}, and
{ACE}",
crossref = "Metropolis:1980:HCT",
pages = "101--114",
year = "1980",
bibdate = "Sat Mar 31 18:08:36 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@TechReport{Dongarra:1981:IAC,
author = "J. J. Dongarra and C. B. Moler and J. H. Wilkinson",
title = "Improving the Accuracy of Computed Eigenvalues and
Eigenvectors",
type = "Technical Report",
number = "ANL-81-43",
institution = inst-ANL-am,
address = inst-ANL:adr,
year = "1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Published as \cite{Dongarra:1983:IAC}.",
}
@InProceedings{Symm:1981:ADM,
author = "Hilary J. Symm and J. H. Wilkinson",
title = "Almost Defective Matrices",
crossref = "Meek:1981:PTM",
pages = "89--131",
year = "1981",
MRclass = "15A12 (65F15)",
MRnumber = "MR635937 (82m:15009)",
MRreviewer = "Alan L. Andrew",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@TechReport{Symm:1981:EBC,
author = "H. J. Symm and J. H. Wilkinson",
title = "Error Bounds for Computed Invariant Subspaces",
type = "Research Report",
number = "81-02",
institution = inst-ETH-AM,
address = inst-ETH:adr,
year = "1981",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Lecture presented at a Symposium in honour of H.
Rutishauser, October 15--17, 1980.",
}
@TechReport{Dongarra:1982:EPH,
author = "J. J. Dongarra and J. R. Gabriel and J. H. Wilkinson",
title = "The Eigenvalue Problem for {Hermitian} Matrices with
Time Reversal Symmetry",
type = "Technical Memorandum",
number = "3",
institution = inst-ANL-mcs,
address = inst-ANL:adr,
year = "1982",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Published as \cite{Dongarra:1984:EPH} where D. D.
Koelling is also an author.",
}
@Article{Olver:1982:PEB,
author = "F. W. J. Olver and J. H. Wilkinson",
title = "A Posteriori Error Bounds for {Gaussian} Elimination",
journal = j-IMA-J-NUMER-ANAL,
volume = "2",
number = "4",
pages = "377--406",
year = "1982",
CODEN = "IJNADH",
DOI = "https://doi.org/10.1093/imanum/2.4.377",
ISSN = "0272-4979 (print), 1464-3642 (electronic)",
ISSN-L = "0272-4979",
MRclass = "65F05 (65G05)",
MRnumber = "MR692286 (84m:65044)",
MRreviewer = "E. R. Hansen",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "IMA (Institute of Mathematics and its Applications).
Journal of Numerical Analysis",
journal-URL = "http://imajna.oxfordjournals.org/content/by/year",
}
@InCollection{Wilkinson:1982:NPS,
author = "J. H. Wilkinson",
editor = "S. L. Campbell",
booktitle = "Recent Applications of Generalized Inverses",
title = "Note on the Practical Significance of the {Drazin}
Inverse",
chapter = "3",
volume = "66",
publisher = pub-PITMAN,
address = pub-PITMAN:adr,
pages = "82--99",
year = "1982",
MRclass = "65F30 (15-04 15A09 47A50 65L05)",
MRnumber = "MR666724 (84c:65071)",
MRreviewer = "M. Z. Nashed",
bibdate = "Tue Aug 15 18:20:34 MDT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "Res. Notes in Math.",
}
@Article{Dongarra:1983:IAC,
author = "J. J. Dongarra and C. B. Moler and J. H. Wilkinson",
title = "Improving the Accuracy of Computed Eigenvalues and
Eigenvectors",
journal = j-SIAM-J-NUMER-ANAL,
volume = "20",
number = "1",
pages = "23--45",
month = feb,
year = "1983",
CODEN = "SJNAAM",
DOI = "https://doi.org/10.1137/0720002",
ISSN = "0036-1429 (print), 1095-7170 (electronic)",
ISSN-L = "0036-1429",
MRclass = "65F15",
MRnumber = "MR687365 (84c:65063)",
MRreviewer = "M. Lotkin",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
classcodes = "B0290B (Error analysis in numerical methods); B0290H
(Linear algebra); C4110 (Error analysis in numerical
methods); C4140 (Linear algebra)",
corpsource = "Argonne Nat. Lab., Argonne, IL, USA",
fjournal = "SIAM Journal on Numerical Analysis",
journal-URL = "http://epubs.siam.org/sinum",
keywords = "accuracy; computed eigenvalues; computed eigenvectors;
convergence of numerical methods; eigenfunctions;
eigenvalues and; EISPACK; error analysis; extended;
matrix algebra; matrix eigenvalues; matrix
eigenvectors; Newton's method; nla, eig, iterative
refinement; numerical; numerical accuracy; numerically
stable implementation; precision arithmetic; residuals;
standard; subroutines",
reviewer = "M. Lotkin",
treatment = "T Theoretical or Mathematical",
}
@Article{Dongarra:1984:EPH,
author = "J. J. Dongarra and J. R. Gabriel and D. D. Koelling
and J. H. Wilkinson",
title = "The Eigenvalue Problem for {Hermitian} Matrices with
Time-Reversal Symmetry",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "60",
pages = "27--42",
year = "1984",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(84)90068-5",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "65F15 (81G55)",
MRnumber = "MR749173 (85j:65013)",
MRreviewer = "Cs. J. Heged{\H{u}}s",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Article{Dongarra:1984:SSE,
author = "J. J. Dongarra and J. R. Gabriel and D. D. Koelling
and J. H. Wilkinson",
title = "Solving the Secular Equation Including Spin Orbit
Coupling for Systems with Inversion and Time-Reversal
Symmetry",
journal = j-J-COMPUT-PHYS,
volume = "54",
number = "2",
pages = "278--288",
month = may,
year = "1984",
CODEN = "JCTPAH",
DOI = "https://doi.org/10.1016/0021-9991(84)90119-0",
ISSN = "0021-9991 (print), 1090-2716 (electronic)",
ISSN-L = "0021-9991",
bibdate = "Sun Jan 1 15:59:19 MST 2012",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputphys1980.bib",
URL = "http://www.netlib.org/utk/people/JackDongarra/PAPERS/Inversion-and-Time-Reversal-Symmetry.pdf;
http://www.sciencedirect.com/science/article/pii/0021999184901190",
acknowledgement = ack-nhfb,
classcodes = "A0230 (Function theory, analysis); A0250 (Probability
theory, stochastic processes, and statistics); A0365C
(Formalism in quantum theory)",
corpsource = "Math. and Computer Sci. Div., Argonne Nat. Lab.,
Argonne, IL, USA",
fjournal = "Journal of Computational Physics",
journal-URL = "http://www.sciencedirect.com/science/journal/00219991",
keywords = "computational method; eigenvalues; eigenvalues and
eigenfunctions; eigenvectors; inversion symmetry;
numerical methods; quantum; quantum mechanics; secular
equation; spin orbit coupling; spin-orbit interactions;
symmetry; T invariance; theory; time reversal",
treatment = "T Theoretical or Mathematical",
}
@Article{Wilkinson:1984:NMQ,
author = "J. H. Wilkinson",
title = "On neighbouring matrices with quadratic elementary
divisors",
journal = j-NUM-MATH,
volume = "44",
number = "1",
pages = "1--21",
month = jun,
year = "1984",
CODEN = "NUMMA7",
DOI = "https://doi.org/10.1007/BF01389751",
ISSN = "0029-599X (print), 0945-3245 (electronic)",
ISSN-L = "0029-599X",
MRclass = "65F99",
MRnumber = "85h:65096",
MRreviewer = "Colette Lebaud",
bibdate = "Mon May 26 11:49:34 MDT 1997",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "In honour of the 60th birthday of F. L. Bauer.",
acknowledgement = ack-nhfb,
classification = "B0210 (Algebra); C1110 (Algebra)",
corpsource = "Computer Sci. Dept., Stanford Univ., Stanford, CA,
USA",
fjournal = "Numerische Mathematik",
journal-URL = "http://link.springer.com/journal/211",
keywords = "matrix algebra; neighbouring matrices; quadratic
elementary divisors",
treatment = "T Theoretical or Mathematical",
}
@InCollection{Wilkinson:1984:PP,
author = "James H. Wilkinson",
editor = "G. H. Golub",
booktitle = "Studies in Numerical Analysis",
title = "The Perfidious Polynomial",
chapter = "1",
volume = "24",
publisher = pub-MATH-ASSOC-AMER,
address = pub-MATH-ASSOC-AMER:adr,
pages = "1--28",
year = "1984",
MRclass = "65H05 (65D15)",
MRnumber = "MR925210",
bibdate = "Fri May 14 17:12:31 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Awarded the Chauvenet Prize of the Mathematical
Association of America.",
series = "MAA Stud. Math.",
}
@TechReport{Wilkinson:1984:SAE,
author = "J. H. Wilkinson",
title = "The State of the Art in Error Analysis",
type = "Technical Memorandum",
number = "42",
institution = inst-ANL-mcs,
address = inst-ANL:adr,
year = "1984",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Informal Proceedings of the Symposium on Computational
Mathematics -- State of the Art held at Argonne
National Laboratory, September 20--21, 1984 in honour
of the 65th birthday of James H. Wilkinson.",
}
@Article{Wilkinson:1984:SE,
author = "J. H. Wilkinson",
title = "Sensitivity of Eigenvalues",
journal = j-UM,
volume = "25",
pages = "5--76",
year = "1984",
CODEN = "UTMADA",
ISSN = "0315-3681",
MRclass = "65F15 (15A18)",
MRnumber = "MR752846 (85i:65051)",
MRreviewer = "Ludwig Elsner",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "Utilitas Mathematica. An International Journal of
Discrete and Combinatorial Mathematics, and Statistical
Design",
}
@Article{Nash:1985:BC,
author = "J. C. Nash and J. H. Wilkinson",
title = "The Birth of a Computer",
journal = j-BYTE,
volume = "10",
number = "2",
pages = "177--??",
month = "????",
year = "1985",
CODEN = "BYTEDJ",
ISSN = "0360-5280 (print), 1082-7838 (electronic)",
ISSN-L = "0360-5280",
bibdate = "Tue Jun 4 11:27:38 MDT 2013",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
fjournal = "BYTE Magazine",
}
@Article{Wilkinson:1985:SAE,
author = "J. H. Wilkinson",
title = "The State of the Art in Error Analysis",
journal = j-NAG,
volume = "2/85",
pages = "5--28",
year = "1985",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Invited lecture for the NAG 1984 Annual General
Meeting.",
}
@Article{Wilkinson:1986:EAR,
author = "J. H. Wilkinson",
title = "Error Analysis Revisited",
journal = j-BULL-INST-MATH-APPL,
volume = "22",
number = "11--12",
pages = "192--200",
year = "1986",
CODEN = "IMTABW",
ISSN = "0950-5628",
MRclass = "65G05",
MRnumber = "MR900724",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Invited lecture at Lancaster University in honour of
C. W. Clenshaw, 1985.",
fjournal = "Bulletin of the Institute of Mathematics and its
Applications",
}
@Article{Wilkinson:1986:ICN,
author = "J. H. Wilkinson",
title = "Ill-Condition in Numerical Linear Algebra",
journal = j-CONG-NUM,
volume = "51",
pages = "59--81",
year = "1986",
ISSN = "0384-9864",
MRclass = "65F35 (65F15)",
MRnumber = "MR883981 (88e:65048)",
MRreviewer = "David R. Kincaid",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Proceedings of the fifteenth Manitoba conference on
numerical mathematics and computing (Winnipeg,
Manitoba, 1985).",
fjournal = "Congressus Numerantium. A Conference Journal on
Numerical Themes",
}
@Article{Wilkinson:1986:SEI,
author = "J. H. Wilkinson",
title = "Sensitivity of Eigenvalues {II}",
journal = j-UM,
volume = "30",
pages = "243--286",
year = "1986",
CODEN = "UTMADA",
ISSN = "0315-3681",
MRclass = "65F15 (15A18 47A55)",
MRnumber = "MR864826 (88f:65066)",
MRreviewer = "William W. Hager",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "Utilitas Mathematica. An International Journal of
Discrete and Combinatorial Mathematics, and Statistical
Design",
}
@InProceedings{Wilkinson:1987:EP,
author = "J. H. Wilkinson",
title = "Eigenvalue Problems",
crossref = "Iserles:1987:SAN",
pages = "1--39",
year = "1987",
MRclass = "65F15 (15A21 15A22 65-02)",
MRnumber = "MR921660 (89d:65042)",
MRreviewer = "Alan L. Andrew",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Proceedings of the IMA/SIAM Conference, University of
Birmingham, 1986.",
}
@InCollection{Wilkinson:1987:SCN,
author = "J. H. Wilkinson",
title = "Some comments from a numerical analyst",
crossref = "Ashenhurst:1987:ATA",
pages = "??--??",
year = "1987",
DOI = "https://doi.org/10.1145/1283920.1283925",
bibdate = "Tue Jun 21 11:01:04 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/acm-turing-awards.bib",
acknowledgement = ack-nhfb,
}
@Article{Wilkinson:1987:TF,
author = "J. H. Wilkinson",
title = "On a Theorem of {Feingold}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "88/89",
pages = "13--30",
year = "1987",
CODEN = "LAAPAW",
DOI = "https://doi.org/10.1016/0024-3795(87)90100-5",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
MRclass = "15A42 (15A60)",
MRnumber = "MR882438 (88d:15022)",
MRreviewer = "Lajos L{\'a}szl{\'o}",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Issue in honour of the 65th birthday of J. H.
Wilkinson.",
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Book{Wilkinson:1988:AEP,
author = "J. H. Wilkinson",
title = "The Algebraic Eigenvalue Problem",
publisher = "The Clarendon Press, Oxford University Press",
address = "New York",
pages = "xviii + 662",
year = "1988",
ISBN = "0-19-853418-3",
ISBN-13 = "978-0-19-853418-1",
MRclass = "65Fxx (15-02 65-02)",
MRnumber = "MR950175 (89j:65031)",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Oxford Science Publications",
series = "Monographs on Numerical Analysis",
tableofcontents = "Theoretical background \\
Perturbation theory \\
Error analysis \\
Solution of linear algebraic equations \\
Hermitian matrices \\
Reduction of a general matrix to condensed form \\
Eigenvalues of matrices of condensed forms \\
The LR and QR algorithms \\
Iterative methods \\
Bibliography \\
Index",
}
@Book{Williams:1989:EBC,
editor = "M. R. Williams and Martin Campbell-Kelly",
title = "The Early {British} Computer Conferences",
volume = "14",
publisher = pub-MIT,
address = pub-MIT:adr,
pages = "xvi + 508",
year = "1989",
ISBN = "0-262-23136-0",
ISBN-13 = "978-0-262-23136-7",
LCCN = "QA76.17 .E171 1989",
bibdate = "Wed Sep 06 11:19:04 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "{Charles Babbage Institute} Reprint Series for the
History of Computing",
}
@TechReport{Dongarra:1990:NCC,
author = "J. J. Dongarra and S. Hammarling and J. H. Wilkinson",
title = "Numerical Considerations in Computing Invariant
Subspaces. {LAPACK Working Note No.~25}",
type = "Technical Report",
number = "CS-90-117",
institution = inst-UTK-cs,
address = inst-UTK:adr,
year = "1990",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Also produced as Oak Ridge National Laboratory Report,
ORNL/TM-11704. Published as \cite{Dongarra:1992:NCC}.",
}
@Article{Dongarra:1992:NCC,
author = "Jack J. Dongarra and Sven Hammarling and James H.
Wilkinson",
title = "Numerical considerations in computing invariant
subspaces",
journal = j-SIAM-J-MAT-ANA-APPL,
volume = "13",
number = "1",
pages = "145--161",
year = "1992",
CODEN = "SJMAEL",
DOI = "https://doi.org/10.1137/0613013",
ISSN = "0895-4798 (print), 1095-7162 (electronic)",
ISSN-L = "0895-4798",
MRclass = "65F15",
MRnumber = "MR1146658 (93a:65049)",
MRreviewer = "Colette Lebaud",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
fjournal = "SIAM Journal on Matrix Analysis and Applications",
journal-URL = "http://epubs.siam.org/simax",
}
@InCollection{Turing:2005:TWL,
author = "Alan M. Turing and James H. Wilkinson",
title = "The {Turing--Wilkinson} lecture series (1946--1947)",
crossref = "Copeland:2005:ATA",
pages = "??--??",
year = "2005",
DOI = "https://doi.org/10.1093/acprof:oso/9780198565932.003.0023",
bibdate = "Mon Nov 01 18:18:06 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Edited with an introduction by B. Jack Copeland.",
abstract = "This chapter presents the nine lectures given by
Turing and his assistant Jim Wilkinson from December
1946 to February 1947. The lectures add substantially
to the understanding of the evolution of the design of
the ACE. Turing and Wilkinson describe Versions V, VI,
and VII of the design.",
acknowledgement = ack-nhfb,
}
@InCollection{Wilkinson:2005:PAN,
author = "James H. Wilkinson",
title = "The {Pilot ACE} at the {National Physical
Laboratory}",
crossref = "Copeland:2005:ATA",
pages = "93--105",
year = "2005",
DOI = "https://doi.org/10.1093/acprof:oso/9780198565932.003.0005",
bibdate = "Mon Nov 01 18:18:06 2010",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
URL = "http://www.ingentaconnect.com/content/oso/2353639/2005/00000001/00000001/art00006",
abstract = "This chapter discusses the pilot Automatic Computing
Engine (ACE) project at the National Physical
Laboratory. The Pilot ACE had been designed purely as
an experimental machine to demonstrate the competence
of the team as computer engineers. It was originally
intended that when it was successfully completed a
full-scale computer would be built. However, when it
was successful, it was the only electronic computer in
a government department and the engineers came under
very heavy pressure to use the Pilot ACE for serious
computing. They implemented a small set of
modifications which included the addition of an
automatic multiplier and improvements to the control
unit which made programming a little less arduous. The
computer was then put into general use and did yeoman
service for a number of years.",
acknowledgement = ack-nhfb,
remark = "Reprint of article in {\em The Radio and Electronic
Engineer, Vol. 45, No. 7, pp. 336--340, July 1975}.
From the article:\par
``A great deal of quite detailed coding was done by the
ACE team in the period from 1946--1948. It included
basic subroutines for such things as multi-length
arithmetic (including multiplication, division and
square roots), floating-point arithmetic (both
single-precision and double-precision) and interval
arithmetic. The subroutines for floating-point
arithmetic were particularly detailed; they were coded
by G. G. Alway and myself in 1947 and were for both
Version V and Version VII. They were almost certainly
the earliest floating-point subroutines and it is
interesting that those for the Version V were
essentially the same as the subroutines which were
subsequently used on the Pilot ACE itself. At a time
when the arithmetic provided on modern computers is
often so disappointing it is interesting to recall that
the subroutines included provision for accumulating
inner-products in double-precision floating-point
arithmetic and all rounding was
immaculate.''\par
``Even double precision and triple precision
floating-point routines were reasonably fast and we
gained extensive experience with such computation long
before it was much used elsewhere. I think it is not
unreasonable to claim that the development of
floating-point error analysis at NPL, which was well in
advance of that elsewhere, was an indirect consequence
of our use of optimum coding.''",
}
%%% ====================================================================
%%% Part 2 (of 2) --- publications about James H. Wilkinson and his
%%% works
%%%
%%% Bibliography entries, sorted by year, and then by citation label,
%%% with `bibsort -byyear':
@Article{Grau:1966:BRB,
author = "A. A. Grau",
title = "Book Review: {{\booktitle{Rounding Errors in Algebraic
Processes}} (J. H. Wilkinson)}",
journal = j-SIAM-REVIEW,
volume = "8",
number = "3",
pages = "397--398",
month = "????",
year = "1966",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1008087",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:37 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/8/3;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "July 1966",
}
@Article{Parlett:1966:BRB,
author = "B. N. Parlett",
title = "Book Review: {{\booktitle{The Algebraic Eigenvalue
Problem}} (J. H. Wilkinson)}",
journal = j-SIAM-REVIEW,
volume = "8",
number = "4",
pages = "543--545",
month = "????",
year = "1966",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1008125",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:05:39 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/8/4;
http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "October 1966",
}
@Article{Wilkes:1966:BRB,
author = "M. V. Wilkes",
title = "Book Review: {{\booktitle{The Algebraic Eigenvalue
Problem}}}",
journal = j-COMP-J,
volume = "8",
number = "4",
pages = "382--382",
month = jan,
year = "1966",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/8.4.382",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
bibdate = "Tue Dec 4 14:47:34 MST 2012",
bibsource = "http://comjnl.oxfordjournals.org/content/8/4.toc;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/compj1960.bib",
URL = "http://comjnl.oxfordjournals.org/content/8/4/382.full.pdf+html",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@Article{I:1970:BRJ,
author = "E. I.",
title = "Book Review: {J. A. Wilkinson,
\booktitle{Rundungsfehler}, translated from English
into German by G. Goos, Springer-Verlag, New York,
1969, x + 208 pp., 21 cm. Price \$3.70 (paperbound)}",
journal = j-MATH-COMPUT,
volume = "24",
number = "109",
pages = "229--230",
month = jan,
year = "1970",
CODEN = "MCMPAF",
DOI = "",
ISSN = "0025-5718 (print), 1088-6842 (electronic)",
ISSN-L = "0025-5718",
bibdate = "Wed Aug 26 06:40:47 2020",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
URL = "http://www.jstor.com/stable/2004899",
acknowledgement = ack-nhfb,
fjournal = "Mathematics of Computation",
journal-URL = "http://www.ams.org/mcom/",
}
@Article{Partlett:1972:BRB,
author = "B. Partlett",
title = "Book Review: {{\booktitle{Handbook for Automatic
Computation, Vol. II, Linear Algebra}} (J. H. Wilkinson
and C. Reinsch)}",
journal = j-SIAM-REVIEW,
volume = "14",
number = "4",
pages = "658--661",
month = "????",
year = "1972",
CODEN = "SIREAD",
DOI = "https://doi.org/10.1137/1014116",
ISSN = "0036-1445 (print), 1095-7200 (electronic)",
ISSN-L = "0036-1445",
bibdate = "Thu Mar 27 09:06:44 MDT 2014",
bibsource = "http://epubs.siam.org/toc/siread/14/4;
http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/siamreview.bib",
acknowledgement = ack-nhfb,
fjournal = "SIAM Review",
journal-URL = "http://epubs.siam.org/sirev",
onlinedate = "October 1972",
}
@Article{Fox:1987:JHW,
author = "L. Fox",
title = "{James Hardy Wilkinson: 27 September 1919--5 October
1986}",
journal = j-BIOGRAPH-MEMOIRS-FELLOWS-ROY-SOC,
volume = "33",
pages = "671--708",
month = dec,
year = "1987",
CODEN = "BMFRA3",
ISSN = "0080-4606 (print), 1748-8494 (electronic)",
ISSN-L = "0080-4606",
bibdate = "Thu Jun 9 12:00:24 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
URL = "http://www.jstor.org/stable/769967",
acknowledgement = ack-nhfb,
fjournal = "Biographical Memoirs of Fellows of the Royal Society",
journal-URL = "http://www.jstor.org/journals/00804606.html",
}
@Article{Fox:1987:ODJ,
author = "Leslie Fox",
title = "Obituary: {Dr. J. H. Wilkinson, F.R.S.}",
journal = j-COMP-J,
volume = "30",
number = "1",
pages = "1--1",
year = "1987",
CODEN = "CMPJA6",
DOI = "https://doi.org/10.1093/comjnl/30.1.1",
ISSN = "0010-4620 (print), 1460-2067 (electronic)",
ISSN-L = "0010-4620",
MRclass = "01A70",
MRnumber = "88e:01054",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www3.oup.co.uk/computer_journal/hdb/Volume_30/Issue_01/",
URL = "http://www3.oup.co.uk/computer_journal/hdb/Volume_30/Issue_01/tiff/1.tif",
acknowledgement = ack-nhfb,
fjournal = "The Computer Journal",
journal-URL = "http://comjnl.oxfordjournals.org/",
}
@TechReport{Parlett:1987:CJH,
author = "Beresford N. Parlett",
title = "A contribution of {J. H. Wilkinson} to numerical
analysis",
type = "Technical Report",
number = "PAM-372",
institution = inst-CPAM-UCB,
address = inst-CPAM-UCB:adr,
month = apr,
year = "1987",
bibdate = "Fri Nov 11 09:09:56 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
xxnote = "Check author list??",
}
@Article{Barrio:2002:REB,
author = "Roberto Barrio",
title = "Rounding error bounds for the {Clenshaw} and
{Forsythe} algorithms for the evaluation of orthogonal
polynomial series",
journal = j-J-COMPUT-APPL-MATH,
volume = "138",
number = "2",
pages = "185--204",
day = "15",
month = jan,
year = "2002",
CODEN = "JCAMDI",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
bibdate = "Sat Feb 25 12:45:23 MST 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
URL = "http://www.sciencedirect.com/science/article/pii/S037704270100382X",
acknowledgement = ack-nhfb,
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
}
@Article{Barrio:2003:URE,
author = "R. Barrio",
title = "A unified rounding error bound for polynomial
evaluation",
journal = j-ADV-COMPUT-MATH,
volume = "19",
number = "4",
pages = "385--399",
month = nov,
year = "2003",
CODEN = "ACMHEX",
DOI = "https://doi.org/10.1023/A:1024203520270",
ISSN = "1019-7168 (print), 1572-9044 (electronic)",
ISSN-L = "1019-7168",
MRclass = "65G50",
MRnumber = "1989623",
bibdate = "Sat Feb 3 18:22:17 MST 2018",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/f/forsythe-george-elmer.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/advcomputmath.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
URL = "http://link.springer.com/article/10.1023/A:1024203520270",
acknowledgement = ack-nhfb,
fjournal = "Advances in Computational Mathematics",
journal-URL = "http://link.springer.com/journal/10444",
keywords = "Bernstein polynomial; Clenshaw--Forsythe algorithm;
de-Casteljau algorithm; Horner's algorithm; polynomial
evaluation; recurrence relations; rounding errors;
Szeg{\H{o}} polynomial",
}
@Article{Watkins:2011:FA,
author = "David S. Watkins",
title = "{Francis}'s Algorithm",
journal = j-AMER-MATH-MONTHLY,
volume = "118",
number = "5",
pages = "387--403",
month = may,
year = "2011",
CODEN = "AMMYAE",
DOI = "https://doi.org/10.4169/amer.math.monthly.118.05.387",
ISSN = "0002-9890 (print), 1930-0972 (electronic)",
ISSN-L = "0002-9890",
bibdate = "Thu May 26 16:28:05 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
URL = "http://www.jstor.org/stable/info/10.4169/amer.math.monthly.118.05.387",
abstract = "John Francis's implicitly shifted QR algorithm turned
the problem of matrix eigenvalue computation from
difficult to routine almost overnight about fifty years
ago. It was named one of the top ten algorithms of the
twentieth century by Dongarra and Sullivan, and it
deserves to be more widely known and understood by the
general mathematical community. This article provides
an efficient introduction to Francis's algorithm that
follows a novel path. Efficiency is gained by omitting
the traditional but wholly unnecessary detour through
the basic QR algorithm. A brief history of the
algorithm is also included. It was not a one-man show;
some other important names are Rutishauser, Wilkinson,
and Kublanovskaya. Francis was never a specialist in
matrix computations. He was employed in the early
computer industry, spent some time on the problem of
eigenvalue computation and did amazing work, and then
moved on to other things. He never looked back, and he
remained unaware of the huge impact of his work until
many years later.",
acknowledgement = ack-nhfb,
fjournal = "American Mathematical Monthly",
journal-URL = "http://www.jstor.org/page/journal/amermathmont/about.html",
}
@Misc{Anonymous:2012:ATA,
author = "Anonymous",
title = "{Alan Turing's ACE}",
howpublished = "Web site",
day = "28",
month = may,
year = "2012",
bibdate = "Wed Jan 02 07:27:57 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
URL = "https://i-programmer.info/history/machines/11-an-ace-of-a-machine.html",
acknowledgement = ack-nhfb,
keywords = "Alan Turing; Jim Wilkinson",
remark = "From the conclusions: ``The 800-valve Pilot ACE was
several times faster than the 3000-valve EDSAC. This
allowed its users to develop programs and theories of
real significance in numerical analysis and
engineering. Eventually 32 of the commercial versions,
the DEUCE, were sold, more because companies demanded
them than because of aggressive marketing.\par
In the States another derivative of the ACE, the Bendix
G-15, sold more than 400 units and this gives you some
idea of the potential of the machine if marketed
correctly.\par
Even so the ACE/DEUCE combination did more for
computing in UK industry than any other machine. In a
sense the ACE was the UK's `national' computer.''",
}
@Article{Campbell-Kelly:2012:ATO,
author = "Martin Campbell-Kelly",
title = "{Alan Turing}'s other universal machine",
journal = j-CACM,
volume = "55",
number = "7",
pages = "31--33",
month = jul,
year = "2012",
CODEN = "CACMA2",
DOI = "https://doi.org/10.1145/2209249.2209277",
ISSN = "0001-0782 (print), 1557-7317 (electronic)",
ISSN-L = "0001-0782",
bibdate = "Tue Jul 3 13:54:33 MDT 2012",
bibsource = "http://www.acm.org/pubs/contents/journals/cacm/;
http://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/cacm2010.bib",
abstract = "Reflections on the Turing ACE computer and its
influence.",
acknowledgement = ack-nhfb,
fjournal = "Communications of the ACM",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J79",
keywords = "ACE; Alan Turing; Bendix G-15; DEUCE; Donald Davis;
EDSAC; EDVAC; English Electric Company; Harry Huskey;
James Hardy Wilkinson; Manchester Mark I; Maurice
Wilkes; Pilot ACE",
}
@Misc{Hammarling:2019:CCJ,
author = "Sven Hammarling and Nick Higham",
title = "Celebrating the Centenary of {James H. Wilkinson}'s
Birth",
howpublished = "Web site and conference",
day = "29--30",
month = may,
year = "2019",
bibdate = "Thu Jun 27 14:41:00 2019",
URL = "https://nla-group.org/2019/01/21/celebrating-the-centenary-of-james-h-wilkinsons-birth/",
acknowledgement = ack-nhfb,
}
@Misc{Hammarling:2019:HAN,
author = "Sven Hammarling and Nick Higham and Fran{\c{c}}oise
Tisseur",
title = "Highlights of {Advances in Numerical Linear Algebra
Conference}",
howpublished = "Web site.",
day = "19",
month = jun,
year = "2019",
bibdate = "Thu Jun 27 14:41:00 2019",
URL = "https://nla-group.org/2019/06/19/highlights-of-advances-in-numerical-linear-algebra-conference/",
acknowledgement = ack-nhfb,
}
@Misc{Hammarling:2019:WQ,
author = "Sven Hammarling and Nick Higham",
title = "{Wilkinson} Quotes",
howpublished = "Web site",
day = "13",
month = may,
year = "2019",
bibdate = "Thu Jun 27 14:44:45 2019",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
URL = "https://nla-group.org/2019/05/13/wilkinson-quotes/",
abstract = "We collect here some quotes from the work of Jim
Wilkinson. These reflect his unique perspective as a
mathematician who was involved in designing and
building one of the first digital computers and who
subsequently developed and analyzed a variety of
numerical algorithms",
acknowledgement = ack-nhfb,
}
%%% ====================================================================
%%% Cross-referenced entries must come last:
@Proceedings{Metropolis:1963:PFS,
editor = "N. Metropolis and A. H. Taub and John Todd and C. B.
Tompkins",
booktitle = "{Experimental arithmetic, high speed computing and
mathematics: Proceedings of the fifteenth Symposium in
Applied Mathematics of the American Mathematical
Society held in Chicago, Illinois, April 12--14, 1962
and Atlantic City, New Jersey, April 16-19, 1962}",
title = "{Experimental arithmetic, high speed computing and
mathematics: Proceedings of the fifteenth Symposium in
Applied Mathematics of the American Mathematical
Society held in Chicago, Illinois, April 12--14, 1962
and Atlantic City, New Jersey, April 16-19, 1962}",
volume = "15",
publisher = pub-AMS,
address = pub-AMS:adr,
pages = "ix + 396",
year = "1963",
LCCN = "QA297 .S987 1962",
bibdate = "Tue Mar 20 10:37:16 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
tableofcontents = "1. Purposeful and unpurposeful computing / Cohn \\
2. Eliminating the irrelevant from mechanical proofs /
Davis \\
3. The mechanization of mathematical arguments / Wang
\\
4. Towards more versatile mechanical translators /
Irons \\
5. Information theory and decoding computations / Elias
\\
6. Adaptive neural networks as brain models / Block \\
7. Computer investigation of orthogonal Latin squares
of order ten / Parker \\
8. Determination of division algebra with 32 elements /
Walker \\
9. How programming difficulties lead to theoretical
advances / Dade and Zassenhaus \\
10. Methods of successive restrictions in computational
problems involving discrete variables / Tompkins \\
11. An experimental study of the simplex method / Kuhn
and Quandt \\
12. Large and nonconvex problems in linear programming
/ GoMory \\
13. Some high speed logic / Lehmer \\
14. Stability questions for some numerical methods for
ordinary differential equations / Dahlquist \\
15. Some applications of the quotient--difference
algorithm / Henrici \\
16. Plane-rotations in floating-point arithmetic /
Wilkinson \\
17. New aspects in numerical quadrature / Bauer,
kutishauser, and Stiefel \\
18. On Jacobi rotation patterns / Rutishauser \\
19. Automatic numerical integration of ordinary
differential equations / Nordsieck \\
20. Survey of stability of different schemes for
solving initial value problems for hyperbolic equations
/ Lax \\
21. Unexpected dividends in the theory of prime numbers
/ Rosser \\
22. The particle-in-cell method for numerical solution
of problems in fluid dynamics / Harlow \\
23. Numerical experiments in atmospheric hydrodynamics
/ Charney \\
24. The oscillations of the earth and of the atmosphere
/ MacDonald \\
25. Few particle experiments in statistical mechanics /
Alder \\
26. An approach to the Ising problem using a large
scale fast digital computer / Yang \\
27. Applied mathematics as used in theoretical
chemistry / Hirschfelder \\
28. The mechanization of science / Hamming",
}
@Book{Wilkinson:1963:REA,
author = "J. H. Wilkinson",
booktitle = "Rounding Errors in Algebraic Processes",
title = "Rounding Errors in Algebraic Processes",
volume = "32",
publisher = pub-HMSO,
address = pub-HMSO:adr,
pages = "vi + 161",
year = "1963",
ISBN = "0-486-67999-3 (Dover)",
ISBN-13 = "978-0-486-67999-0 (Dover)",
LCCN = "QA76.5 .W53 1964",
MRclass = "65.80",
MRnumber = "MR0161456 (28 \#4661)",
MRreviewer = "A. S. Householder",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Also published by Prentice-Hall, Englewood Cliffs, NJ,
USA, 1964, translated into Polish as {\em Bledy
Zaokragle{\'n} w Procesach Algebraicznych\/} by PWW,
Warsaw, Poland, 1967 and translated into German as {\em
Rundungsfehler\/} by Springer-Verlag, Berlin, Germany,
1969. Reprinted by Dover Publications, New York,
1994.",
series = "Notes on Applied Science",
tableofcontents = "1. The Fundamental Arithmetic Operations \\
Digital computation / 1 \\
Fixed-point and floating-point computation / 1 \\
Notational conventions / 2 \\
Rounding errors in fixed-point computation / 4 \\
Fixed-point accumulation of inner-products / 6 \\
Rounding errors in floating-point computation / 7 \\
Round-off with single-precision accumulator / 11 \\
Comparison of fixed-point and floating-point
computation / 14 \\
Common floating-point operations / 16 \\
More precise bounds / 19 \\
Floating-point accumulation of sums and inner-products
/ 23 \\
Statistical error bounds / 25 \\
Block-floating vectors and matrices / 26 \\
Fundamental limitations oft-digit computation / 27 \\
Ill-conditioned problems / 28 \\
Condition numbers / 29 \\
Rounding errors in the computation / 30 \\
Additional comments / 33 \\
2. Computations Involving Polynomials \\
Evaluation of power series / 34 \\
Fixed-point representation / 34 \\
Floating-point representation / 36 \\
Calculation of zeros of functions defined by power
series / 37 \\
Polynomials with arbitrary coefficients / 38 \\
Condition of a polynomial with respect to the
computation of its zeros / 38 \\
Some typical distributions of zeros / 41 \\
Linear distributions of zeros / 41 \\
Geometric distribution / 44 \\
Chebyshev polynomial / 46 \\
Significance of the condition of the zeros of
polynomials 4 / 7 \\
Determination of the zeros / 49 \\
Iterative methods / 52 \\
Effect of rounding errors on Newton's process / 53 \\
Simple examples / 54 \\
Polynomial deflation / 55 \\
Analysis of errors inherent in deflation / 56 \\
Examples of deflation / 59 \\
Deflation of ill-conditioned polynomials / 62 \\
General comments on iteration and deflation / 64 \\
Purification in the original polynomial / 65 \\
Other iterative methods / 66 \\
The root-squaring process / 67 \\
Forward error analysis of root-squaring / 69 \\
Relative error in computed coefficients / 71 \\
Numerical example / 72 \\
Deterioration of condition / 74 \\
General comments on the computation of zeros of
polynomials / 76 \\
Additional comments / 78 \\
3. Matrix Computations \\
Introduction / 79 \\
Vector and matrix norms / 80 \\
Error analysis of simple matrix operations / 82 \\
Matrix multiplication / 83 \\
Matrix operations in block-floating arithmetic / 85 \\
Matrices which are not infinity row standardized / 85
\\
Orthogonalization of vectors / 86 \\
Numerical example / 87 \\
General case / 89 \\
Solution of equations and matrix inversion / 91 \\
Rounding of matrix of coefficients / 93 \\
Error analysis of Gaussian elimination / 94 \\
Computational equations / 95 \\
Floating-point bounds / 96 \\
Gaussian elimination in fixed-point / 99 \\
Determinant evaluation / 99 \\
Solution of a triangular set of equations using
standard floating-point arithmetic / 99 \\
Accuracy of computed solution / 102 \\
Solution of triangular set of equations with
floating-point accumulation of inner-products / 103 \\
Inversion of a triangular matrix / 104 \\
High accuracy of solutions of triangular equations /
105 \\
Solution of a general set of equations / 107 \\
Inversion of a general matrix / 109 \\
Left-handed and right-handed inverses / 110 \\
Numerical example / 111 \\
Comments on example / 113 \\
Compact methods of triangular decomposition / 114 \\
Triangular decomposition with partial pivoting / 115
\\
Positive definite matrix / 117 \\
Numerical example / 118 \\
Comments on the solution / 119 \\
Residual corresponding to block-floating solution / 120
\\
Iterative refinement of the solution / 121 \\
Practical procedure / 122 \\
Analysis of the practical procedure / 124 \\
Assessment of accuracy of the computed solution / 126
\\
The use of an estimate for $||A^{-1}||$ / 126 \\
Assessment of a computed inverse / 127 \\
Use of the approximate inverse to solve equations / 128
\\
Iterative procedure based on use of the approximate
inverse / 130 \\
Numerical example / 131 \\
Sensitivity of the eigenvalues of a matrix / 134 \\
Sensitivity of individual eigenvalues / 137 \\
Example of ill-conditioned eigenvalues / 138 \\
A posteriori estimates for a computed eigenvalue and
eigenvector of a real symmetric matrix / 139 \\
Calculation of the eigenvectors of a symmetric
tri-diagonal matrix / 142 \\
Effect of rounding errors / 143 \\
Calculation of the eigenvalues of a lower Hessenberg
matrix / 147 \\
Calculation of $f(\lambda)$ using floating-point
accumulation / 149 \\
Perturbation of the eigenvalues / 150 \\
Numerical example / 151 \\
Additional comments / 155 \\
Bibliography / 157 \\
Index / 159",
}
@Proceedings{Rall:1965:EDCa,
editor = "L. B. Rall",
booktitle = "Error in Digital Computation",
title = "Error in Digital Computation",
volume = "1",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "338",
year = "1965",
MRclass = "65.80",
MRnumber = "MR0189284 (32 \#6711)",
MRreviewer = "J. M. Ortega",
bibdate = "Tue Aug 15 18:20:34 MDT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/moore-ramon-e.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Proceedings of an advanced seminar conducted by the
Mathematics Research Center, United States Army, at the
University of Wisconsin, Madison, October 5--7, 1964.",
tableofcontents = "1. The problem of error in digital computation /
Todd \\
2. Techniques for automatic error monitoring and
control / Ashenhurst \\
3. The automatic analysis and control of error in
digital computing based on the use of interval numbers
/ Moore \\
4. Error in digital solution of linear problems /
Albasiny \\
5. The propagation of error in the digital integration
of ordinary differential equations / Henrici \\
6. Bibliography on error in digital computation (114
pp.)",
}
@Proceedings{Rall:1965:EDCb,
editor = "L. B. Rall",
booktitle = "Error in Digital Computation",
title = "Error in Digital Computation",
volume = "2",
publisher = pub-WILEY,
address = pub-WILEY:adr,
pages = "288",
year = "1965",
MRclass = "65.80",
MRnumber = "MR0189284 (32 \#6711)",
MRreviewer = "J. M. Ortega",
bibdate = "Tue Aug 15 18:20:34 MDT 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/moore-ramon-e.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
http://www.math.utah.edu/pub/tex/bib/fparith.bib",
note = "Proceedings of an advanced seminar conducted by the
Mathematics Research Center, United States Army, at the
University of Wisconsin, Madison, October 5--7, 1964.",
tableofcontents = "1. Experimental investigation of unnormalize1
arithmetic / Ashenhurst \\
2. Error bounds for computations with continued
fractions / Henrici \\
3. Error bounds for asymptotic expansions of special
functions in the complex plane / Olver \\
4. Error analysis for transformations based on the use
of matrices of the form $I -2 w w^H$. / Wilkinson \\
5. Automatic local coordinate transformations to reduce
the growth of error bounds in interval computation of
solutions of ordinary differential equations / Moore
\\
6. Differential inequalities and error bounds /
Schroder \\
7. Discrete representations of partial differential
operators / Young and Dauwalder \\
8. Upper and lower bounds for solutions of integral
equations / Brown \\
9. Convergence ana error bounds for approximate
solutions of integral and operator equations / Anselone
\\
10. Applications of functional analysis to error
estimation / Collatz \\
11. Error in the solution of linear programming
problems / Wolfe",
}
@Book{Wilkinson:1971:LA,
editor = "James H. Wilkinson and Christian Reinsch",
booktitle = "Linear Algebra",
title = "Linear Algebra",
volume = "II",
publisher = pub-SV,
address = pub-SV:adr,
pages = "viii + 439",
year = "1971",
ISBN = "0-387-05414-6, 3-540-05414-6",
ISBN-13 = "978-0-387-05414-8, 978-3-540-05414-6",
LCCN = "QA251 .W67",
bibdate = "Wed Dec 15 18:44:50 1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
http://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/householder-alston-s.bib;
http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
http://www.math.utah.edu/pub/tex/bib/gnu.bib;
http://www.math.utah.edu/pub/tex/bib/master.bib;
http://www.math.utah.edu/pub/tex/bib/nummath.bib",
series = "Handbook for Automatic Computation, Editors: {F. L.
Bauer, A. S. Householder, F. W. J. Olver, H.
Rutishauser, K. Samelson and E. Stiefel}",
acknowledgement = ack-nhfb,
tableofcontents = "Part I: Linear systems, least squares and linear
programming \\
J. H. Wilkinson / Introduction to Part I / 1--8 \\
1. Introduction \\
2. List of procedures \\
3. Positive definite symmetric matrices \\
4. Non-positive definite symmetric matrices \\
5. Non-Hermitian matrices \\
6. Least squares and related problems \\
7. The linear programming problem \\
R. S. Martin, G. Peters and J. H. Wilkinson / Symmetric
decomposition of a positive definite matrix / 9--30 \\
Martin, Peters and Wilkinson / Iterative refinement of
the solution of a positive definite system of equations
/ 31--44 \\
F. L. Bauer and C. Reinsch / Inversion of positive
definite matrices by the Gauss-Jordan method / 45--49
\\
Martin and Wilkinson / Symmetric decomposition of
positive definite band matrices / 50--56 \\
T. Ginsburg / The conjugate gradient method / 57--69
\\
Martin and Wilkinson / Solution of symmetric and
unsymmetric band equations and the calculation of
eigenvectors of band matrices / 70--92 \\
H. J. Bowdler, Martin, Peters and Wilkinson / Solution
of real and complex systems of linear equations /
93--110 \\
P. Businger and G. H. Golub / Linear least squares
solutions by Householder transformations / 111--118 \\
Bauer / Elimination with weighted row combinations for
solving linear equations and least squares problems /
119--133 \\
Golub and Reinsch / Singular value decomposition and
least squares solutions / 134--151 \\
R. H. Bartels, J. Stoer and Ch. Zenger / A realization
of the simplex method based on triangular
decompositions / 152--190 \\
Part II: The algebraic eigenvalue problem \\
Wilkinson / Introduction to Part II / 191--201 \\
1. Introduction \\
2. List of procedures \\
3. Real, dense, symmetric matrices \\
4. Symmetric band matrices \\
5. Simultaneous determination of dominant eigenvalues
and eigenvectors of a symmetric sparse matrix \\
6. The generalized symmetric eigenvalue problems $A x =
\lambda B x$ and $A B x = \lambda x$ \\
7. Hermitian matrices \\
8. Real dense unsymmetric matrices \\
9. Unsymmetric band matrices \\
10. Dense unsymmetric matrices with complex elements,
H. Rutishauser / The Jacobi method for real symmetric
matrices / 202--211 \\
Martin, Reinsch and Wilkinson / Householder's
tridiagonalization of a symmetric matrix / 212--226 \\
H. Bowdler, Martin, Reinsch and Wilkinson / The $QR$
and $QL$ algorithms for symmetric matrices / 227--240
\\
A. Dubrulle, Martin and Wilkinson / The implicit $QL$
algorithm / 241--248 \\
W. Barth, Martin, and Wilkinson / Calculation of the
eigenvalues of a symmetric tridiagonal matrix by the
method of bisection / 249--256 \\
Reinsch and Bauer / Rational $QR$ transformation with
Newton shift for symmetric tridiagonal matrices /
257--265 \\
Martin, Reinsch and Wilkinson / The $QR$ algorithm for
band symmetric matrices / 266--272 \\
H. R. Schwarz / Tridiagonalization of a symmetric band
matrix / 273--283 \\
Rutishauser / Simultaneous iteration method for
symmetric matrices / 284--302 \\
Martin and Wilkinson / Reduction of the symmetric
eigenproblem $A x = \lambda B x$ and related problems
to standard form / 303--314 \\
B. N. Parlett and Reinsch / Balancing a matrix for
calculation of eigenvalues and eigenvectors / 315--326
\\
P. J. Eberlein and J. Boothroyd / Solution to the
eigenproblem by a norm reducing Jacobi type method /
327--338 \\
Martin and Wilkinson / Similarity reduction of a
general matrix to Hessenberg form / 339--358 \\
Martin, Peters and Wilkinson / The $QR$ algorithm for
real Hessenberg matrices / 359--371 \\
Peters and Wilkinson / Eigenvectors of real and complex
matrices by $LR$ and $QR$ triangularizations / 372--395
\\
Martin and Wilkinson / The modified $LR$ algorithm for
complex Hessenberg matrices / 396--403 \\
Eberlein / Solution to the complex eigenproblem by a
norm reducing Jacobi type method / 404--417 \\
Peters and Wilkinson / The calculation of specified
eigenvectors by inverse iteration / 418--439",
}
@Proceedings{Evans:1974:SNM,
editor = "D. J. Evans",
title = "Software for Numerical Mathematics",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xi + 451",
year = "1974",
ISBN = "0-12-243750-0",
ISBN-13 = "978-0-12-243750-2",
LCCN = "QA297 .S591",
bibdate = "Tue Aug 15 18:38:31 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Proceedings of the IMA Conference, Loughborough
University of Technology, 1973.",
}
@Proceedings{ICM:1974:PIC,
key = "ICM'74",
title = "Proceedings of the International Congress of
Mathematicians, Vancouver, Canada, August 21--29,
1974",
publisher = "Canadian Mathematical Congress",
address = "Montr{\'{e}}al, Qu{\'e}bec, Canada",
year = "1975",
ISBN = "0-8218-3059-7",
ISBN-13 = "978-0-8218-3059-8",
LCCN = "QA3 .A572",
bibdate = "Wed Aug 16 08:54:12 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@Book{Scaife:1974:SNA,
editor = "B. K. P. (Brendan Kevin Patrick) Scaife",
booktitle = "Studies in numerical analysis: papers in honour of
{Cornelius Lanczos}",
title = "Studies in numerical analysis: papers in honour of
{Cornelius Lanczos}",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xxii + 333",
year = "1974",
ISBN = "0-12-621150-7",
ISBN-13 = "978-0-12-621150-4",
LCCN = "QA297 .S86",
bibdate = "Wed Jun 8 14:07:51 MDT 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/h/hamming-richard-w.bib;
http://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
z3950.loc.gov:7090/Voyager",
note = "Published for the Royal Irish Academy.",
URL = "http://catalog.hathitrust.org/Record/000575557",
acknowledgement = ack-nhfb,
subject = "Numerical analysis; Lanczos, Cornelius; Bibliography",
subject-dates = "1893--1974",
tableofcontents = "Contributors / v \\
Editor's Foreword / vii \\
Cornelius Lanczos --- A Biographical Note / ix \\
List of Publications by Cornelius Lanczos / xii \\
\\
Table-making at the National Bureau of Standards /
Gertrude Blanch and Ida Rhodes / 1 \\
\\
Vignette of a Cultural Episode / Wilhelm Magnus / 7 \\
\\
The Physicist as Poet / Janice Bireline / 15 \\
\\
Conservation Laws in Einstein's General Theory of
Relativity / William R. Davis / 29 \\
\\
I Introduction / 29 \\
II Historical Comments --- Field Conservation Laws
proposed for General Relativity 1916--1959 / 31 \\
III Properties of General Covariant Field Theories / 34
\\
IV Remarks on Symmetry Properties and Invariance
Principles in Physical Theories / 37 \\
V Conservation Laws of Particle Mechanics in Riemannian
Spacetime / 40 \\
VI Particle Conservation Laws for Symmetry Properties
not representable by Point Deformations / 41 \\
VII Field Conservation Law Generators in General
Relativity / 43 \\
VIII Comments on Application of Conservation Laws for
Physically Closed Systems / 45 \\
IX Tensorial Tetrad Conservation Law Generators / 47
\\
X Conservation Laws for Curve Congruences with Special
Kinematical and Symmetry Properties / 50 \\
XI Other Integral Conservation Expressions / 52 \\
XII Conclusions / 54 \\
\\
An elementary procedure for the evaluation of electric
networks / L. Janossy / 65 \\
\\
Canonical Polynomials in the Lanczos Tau Method ---
Eduardo L. Ortiz / 73 \\
\\
I Introduction / 73 \\
II Mathematical Tables and Machine Tables / 74 \\
III The Tau Method / 76 \\
IV The Canonical Polynomials / 77 \\
V The Recursive Form of the Tau Method / 78 \\
VI Algebraic Formulation / 81 \\
VII Integrated Forms of the Tau Method / 82 \\
VIII Expansion of the Approximate Solution in More
General Bases / 86 \\
IX Eigenvalue Problems / 90 \\
\\
Rational Approximations from Chebyshev Series --- C. W.
Clenshaw and K. Lord / 95 \\
\\
I Introduction / 95 \\
II The Generalized Pad{\'e} Approximation / 98 \\
III The Chebyshev--Pad{\'e} Table / 98 \\
IV The Calculation of $S_{m,n}(x)$ / 101 \\
V An Example / 102 \\
VI Case of Slow Convergence / 104 \\
VII Computational Aspects / 105 \\
VIII Numerical Results / 107 \\
\\
Accuracy of Computed Eigensystems and Invariant
Subspaces / G. Peters and J. H. Wilkinson / 115 \\
\\
I Introduction / 115 \\
II Summary of Perturbation Theory for Normal Matrices /
115 \\
III Perturbation Theory for Non-Normal Matrices / 119
\\
IV Eigenvector Perturbations / 123 \\
V Computation of Orthogonal Bases for an Invariant
Subspace / 124 \\
VI Numerical Example / 127 \\
VII Attainable Accuracy / 129 \\
VIII Low Relative Errors in Small Eigenvalues / 132 \\
\\
Buckling of a Beam under Axial Compression with Elastic
Support / A. P. Gallagher / 137 \\
\\
I Introduction / 137 \\
II Formulation of the Integro--Differential Equation /
139 \\
III Analysis of the Even Modes of Buckling / 140 \\
IV Analysis of the Odd Modes of Buckling / 142 \\
V Numerical Results / 143 \\
\\
The Frequency Approach to Numerical Analysis / R. W.
Hamming / 151 \\
\\
I Introduction / 151 \\
II The effects of Sampling-Aliasing / 152 \\
III The Finite Fourier Series / 154 \\
IV The Nyquist Interval and the Sampling Theorem / 158
\\
V The Difference Table and Noise / 160 \\
VI A Quick Look at Integration / 162 \\
VII Smoothing / 163 \\
VIII The Gibbs Phenomenon / 166 \\
IX Elementary Filter Theory / 169 \\
X More Advanced Filter Theory / 172 \\
\\
Detouring around Computational Roadblocks --- A Tale of
Two Integrals / Forman S. Acton / 177 \\
\\
The Hypercircle Method / J. L. Synge / 201 \\
\\
I Simplification / 201 \\
II An Example: The Dirichlet Problem / 203 \\
III The Pay-Off in the Dirichlet Problem / 207 \\
IV More General View. The Hypercircle / 209 \\
V Historical Note / 212 \\
VI The Significance of a Small Hypersphere / 213 \\
VII Vertices / 215 \\
\\
Lower Bounds for the Dirichlet Integral / J. J. McMahon
/ 219 \\
\\
I The Problem / 219 \\
II Essential Inequality / 220 \\
III Method of Constructing Normally-Continuous
Divergent-Free Vector-Fields / 221 \\
IV A Class of Functions and Vector-Fields / 223 \\
V Properties of $P''_{\rho \sigma}$ / ??? \\
VI Formulae for the Three Fundamental Vector-Fields /
225 \\
VII Integrals of Vector-Fields / 228 \\
VIII Use of Symmetry / 230 \\
IX A Calculation with Lattice Edge $a = 1$ / 231 \\
\\
The Koenig--Hadamard Theorem again / Alston S.
Householder / 235 \\
\\
Significance Arithmetic --- On the Algebra of Binary
Strings / N. Metropolis and Gian-Carlo Rota / 241 \\
\\
I Introduction / 241 \\
II The Arithmetic of Binary Strings / 243 \\
III Multiplication / 247 \\
IV Binary Functions / 250 \\
\\
Practical Algorithms for Finding the Type of a
Polynomial / John J. H. Miller / / 253 \\
\\
I Introduction / 253 \\
II The Type of a Polynomial Relative to the Unit Circle
/ 254 \\
III The Type of a Polynomial Relative to the Imaginary
Axis / 256 \\
IV Examples / 260 \\
\\
The Edge-Function Method in Elastostatics / P. M.
Quinlan / 265 \\
\\
Introduction / 265 \\
I The Elastostatic Problem / 266 \\
II Edge-Functions for a Polygonal Region / 267 \\
III Derived Edge-Functions / 269 \\
IV Some Particular Integrals / 271 \\
V Polygonal Beam: The Boundary Identity Problem / 272
\\
VI Trapezoidal Beam --- Illustration Examples / 276 \\
VII Polar Elasto-Functions / 278 \\
VIII Singular Loadings / 282 \\
IX Singular Loadings on Boundary / 284 \\
X Symmetrical Functions / 286 \\
XI Symmetrical Singular Loadings / 287 \\
XII Applications / 288 \\
\\
Generalised Lobatto Quadrature Formulas for Contour
Integrals / S. J. Maskell and R. A. Sack / 295 \\
\\
I Introduction / 295 \\
II General Formulas for the Coefficients / 298 \\
I II Generalized Lobatto- Mehler Quadrature / 300 \\
IV Numerical Tests / 303 \\
V Conclusions / 308 \\
\\
Spline Functions and Differential Equations --- First
Order Equations / I. J. Schoenberg / 311 \\
\\
I A Remark Due to C. Lanczos / 311 \\
II The Spline Approximations of Higher Degree / 313 \\
III The Construction of the Spline Approximation $S(x)$
/ 314 \\
IV The Unique Existence of $S_n(x)$ and on Error
Estimate / 316 \\
V All Derivatives of $S(x)$ Approximate those of $y(x)$
/ 320 \\
VI Examples / 321",
}
@InBook{Evans:1976:IJH,
author = "Christopher Evans",
title = "Interview with {J. H. Wilkinson}",
number = "10",
publisher = "Science Museum",
address = "London, UK",
pages = "??--??",
year = "1976",
bibdate = "Thu Nov 10 10:17:31 GMT 1994",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib",
series = "Pioneers of Computing, 60-Minute Recordings of
Interviews",
acknowledgement = ack-nhfb,
mynote = "Recorded Teddington 1976. He moved to NPL May 1946.
Half time with Turing, half in Desk Computing section
w/Goodwin and Fox. Moved from 32 to 40 bit words in
version 7 of ACE design. Side 1, [112]: ``Turing is a
very impressive mathematician ... He was a lousy
computer ... One of the worst performers on a desk
computer it's ever been my misfortune to work with.''
JHW thinks they produced the first fl. pt. programs
([32] of side 2) and regrets not writing them up in his
1948 progress report. ([245] of Side 2): Pilot ACE did
fl. pt. multiply in 3 millisecs - very fast for the
time (many millisecs on EDASC)!, This meant NPL got
practical fl. pt. experience before anyone else,
leading to error analysis developments.",
}
@Proceedings{Hartnell:1976:PFM,
editor = "B. L. Hartnell and H. C. Williams",
title = "Proceedings of the Fifth Manitoba Conference on
Numerical Mathematics, October 1--4, 1975",
number = "16",
publisher = pub-UMP,
address = pub-UMP:adr,
pages = "vi + 658",
year = "1976",
ISBN = "0-919628-16-8",
ISBN-13 = "978-0-919628-16-8",
LCCN = "QA297 .M33 1975",
bibdate = "Tue Aug 15 18:42:33 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "Congressus numerantium",
}
@Proceedings{Jacobs:1976:SAN,
editor = "David A. H. Jacobs",
title = "The state of the art in numerical analysis:
Proceedings of the Conference on the State of the Art
in Numerical Analysis held at the University of York,
April 12th--15th, 1976",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xix + 978",
year = "1976",
ISBN = "0-12-378650-9",
ISBN-13 = "978-0-12-378650-0",
LCCN = "QA297 .C6461 1976",
bibdate = "Tue Aug 15 18:46:30 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
}
@Proceedings{Powell:1977:CDJ,
editor = "M. J. D. Powell",
title = "The Contribution of Dr. {J}. {H}. Wilkinson to
numerical analysis: Proceedings of a symposium \ldots{}
held in London on July 6th, 1977",
number = "19",
publisher = pub-IMA,
address = pub-IMA:adr,
pages = "viii + 91",
year = "1977",
LCCN = "QA297.C66 1978",
bibdate = "Tue Aug 15 18:51:43 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "IMA Symposium Proceedings",
xxISBN = "none",
}
@Proceedings{deBoor:1978:RAN,
editor = "Carl de Boor and Gene H. Golub",
title = "Recent advances in numerical analysis: proceedings of
a symposium conducted by the Mathematics Research
Center, the University of Wisconsin--Madison, May
22--24, 1978",
volume = "41",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "ix + 270",
year = "1978",
ISBN = "0-12-208360-1",
ISBN-13 = "978-0-12-208360-0",
LCCN = "QA297 S994 1978",
bibdate = "Tue Aug 15 18:49:19 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "Publ. Math. Res. Center Univ. Wisconsin",
}
@Proceedings{Jacobs:1978:NSN,
editor = "D. A. H. Jacobs",
title = "Numerical software, needs and availability:
proceedings of the Conference on Applications of
Numerical Software, Needs and Availability, held at the
University of Sussex, September 19th--22nd, 1977",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xvii + 408",
year = "1978",
ISBN = "0-12-378660-6",
ISBN-13 = "978-0-12-378660-9",
LCCN = "QA297 C74 1977",
bibdate = "Tue Aug 15 18:54:26 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
price = "UK\pounds 11.60",
}
@Proceedings{Metropolis:1980:HCT,
editor = "Nicholas Metropolis and Jack Howlett and Gian-Carlo
Rota",
booktitle = "A History of Computing in the {Twentieth Century}: {A}
Collection of Essays",
title = "A History of Computing in the {Twentieth Century}: {A}
Collection of Essays",
publisher = pub-ACADEMIC,
address = pub-ACADEMIC:adr,
pages = "xix + 659",
year = "1980",
ISBN = "0-12-491650-3",
ISBN-13 = "978-0-12-491650-0",
LCCN = "QA75.5 .I63 1976",
bibdate = "Tue Aug 15 18:57:33 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/m/metropolis-nicholas.bib;
http://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Original versions of these papers were presented at
the International Research Conference on the History of
Computing, held at the Los Alamos Scientific
Laboratory, 10--15 June 1976.",
acknowledgement = ack-nhfb,
remark = "This book contains the edited versions of the papers
presented at the international research Conference on
the History of Computing, held at the Los Alamos
Scientific Laboratory, 10--15 June 1976. The book
provides an account of the development of the first
large-scale computers in the first half of the
twentieth century. Each chapter describes one phase of
the development and is written by either a participant
or a witness to these events. The treatment is
narrative and factual and is meant to give a first
exposition of the res gestae. The Exposition is
accessible to anyone interested in the subject and
requires no technical background.",
}
@Proceedings{Meek:1981:PTM,
editor = "D. S. Meek and Hugh C. Williams",
title = "Proceedings of the tenth Manitoba Conference on
Numerical Mathematics and Computing, October 1--4,
1980",
volume = "30--31",
publisher = pub-UMP,
address = pub-UMP:adr,
year = "1981",
ISBN = "0-919628-30-3 (vol.~1) 0-919628-31-1 (vol.~2)",
ISBN-13 = "978-0-919628-30-4 (vol.~1) 978-0-919628-31-1
(vol.~2)",
ISSN = "0384-9864",
bibdate = "Wed Aug 16 09:03:40 1995",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "Congressus Numerantium",
}
@Proceedings{Iserles:1987:SAN,
editor = "A. Iserles and M. J. D. Powell",
booktitle = "{State of the Art in Numerical Analysis. Proceedings
of the Joint IMA\slash SIAM Conference held at the
University of Birmingham, 14--18 April 1986}",
title = "{State of the Art in Numerical Analysis. Proceedings
of the Joint IMA\slash SIAM Conference held at the
University of Birmingham, 14--18 April 1986}",
volume = "9",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "x + 719",
year = "1987",
ISBN = "0-19-853614-3",
ISBN-13 = "978-0-19-853614-7",
LCCN = "QA297.J65 1986",
bibdate = "Mon Sep 9 14:56:14 MDT 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
http://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
http://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
series = "The Institute of Mathematics and Its Applications
conference series; new series",
URL = "http://www.gbv.de/dms/hbz/toc/ht002967923.pdf;
http://zbmath.org/?q=an:0611.00024",
ZMnumber = "0611.00024",
acknowledgement = ack-nhfb,
confdate = "14--18 April 1986",
conflocation = "Birmingham, UK",
confsponsor = "Inst. Math. Appl.; SIAM",
pubcountry = "UK",
tableofcontents = "Contributors / / xiii \\
1. Eigenvalue problems / J. H. Wilkinson / 1 \\
2. Numerical linear algebra in statistical computing /
N. J. Higham and G. W. Stewart / 41 \\
3. Sparse matrices / J. K. Reid / 59 \\
4. Multivariate approximation / Carl de Boor / 87 \\
5. Data approximation by splines in one and two
independent variables / M. G. Cox / 111 \\
6. Methods for best approximation and regression
problems / G. A. Watson / 139 \\
7. Branch cuts for complex elementary functions / W.
Kahan / 165 \\
8. Recent developments in linear and quadratic
programming / R. Fletcher / 213 \\
9. Solving systems of nonlinear equations by tensor
methods / R. B. Schnabel and P. D. Frank / 245 \\
10. Numerical methods for bifurcation problems / A. D.
Jepson and A. Spence / 273 \\
11. On the iterative solution of differential and
integral equations using secant updating techniques /
A. Griewank / 299 \\
12. Methods for nonlinear constraints in optimization
calculations / M. J. D. Powell / 325 \\
13. The influence of vector and parallel processors on
numerical analysis / I. S. Duff / 359 \\
14. Developments in stability theory for ordinary
differential equations / J. D. Lambert / 409 \\
15. Stiff ODE initial value problems and their solution
/ A. R. Curtis / 433 \\
16. Order stars and stability / G. Wanner / 451 \\
17. The state of the art in the numerical treatment of
integral equations / C. T. H. Baker / 473 \\
18. Strongly elliptic boundary integral equations / W.
L. Wendland / 511 \\
19. Collocation methods for one-dimensional Fredholm
and Volterra integral equations / H. Brunner / 563 \\
20. Numerical methods for free and moving boundary
problems / C. W. Cryer / 601 \\
21. Multigrid methods for elliptic equations / J. Walsh
/ 623 \\
22. Galerkin finite element methods and their
generalizations / K. W. Morton / 645 \\
23. Recent developments in the numerical solution of
nonlinear conservation laws / S. Osher and P. K. Sweby
/ 681 \\
Index / 701",
}
@Book{Ashenhurst:1987:ATA,
editor = "Robert L. Ashenhurst",
booktitle = "{ACM Turing Award Lectures}: the first twenty years,
1966--1985",
title = "{ACM Turing Award Lectures}: the first twenty years,
1966--1985",
publisher = pub-ACM # " and " # pub-AW,
address = pub-ACM:adr # " and " # pub-AW:adr,
pages = "xviii + 483",
year = "1987",
ISBN = "0-201-07794-9",
ISBN-13 = "978-0-201-07794-0",
LCCN = "QA76.24 .A33 1987",
bibdate = "Tue Jun 21 11:01:04 2011",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
http://www.math.utah.edu/pub/tex/bib/acm-turing-awards.bib;
z3950.loc.gov:7090/Voyager",
series = "ACM Press anthology series",
acknowledgement = ack-nhfb,
subject = "Electronic data processing; Computers",
tableofcontents = "The synthesis of algorithmic systems / Alan J.
Perlis \\
Computers then and now / Maurice V. Wilkes \\
One man's view of computer science / R. W. Hamming \\
Form and content in computer science / Marvin Minsky
\\
Some comments from a numerical analyst / J. H.
Wilkinson \\
Generality in artificial intelligence / John McCarthy
\\
The humble programmer / Edsger W. Dijkstra \\
The programmer as navigator / Charles W. Bachman \\
Computer programming as an art / Donald E. Knuth \\
Computer science as empirical inquiry: symbols and
search / Allen Newell and Herbert A. Simon \\
Complexity of computations / Michael O. Rabin \\
Logic and programming languages / Dana S. Scott \\
Can programming be liberated from the von Neumann
style?: a functional style and its algebra of programs
/ John Backus \\
The paradigms of programming / Robert W. Floyd \\
Notation as a tool of thought / Kenneth E. Iverson \\
The emperor's old clothes / Charles Antony Richard
Hoare \\
Relational database: a practical foundation for
productivity / E. F. Codd \\
An overview of computational complexity / Stephen A.
Cook \\
Reflections on software research / Dennis M. Ritchie
\\
Reflections on trusting trust / Ken Thompson \\
From programming language design to computer
construction / Niklaus Wirth \\
Combinatorics, complexity, and randomness / Richard M.
Karp \\
Algorithm design / Robert E. Tarjan \\
Computer science: the emergence of a discipline / John
E. Hopcroft \\
The search for performance in scientific processors /
John Cocke \\
Micropipelines / Ivan E. Sutherland \\
On building systems that will fail / Fernando J.
Corbat{\'o} \\
Elements of interaction / Robin Milner \\
Turing Award Lecture: it's time to reconsider time /
Richard Edwin Stearns \\
Turing Award Lecture: on computational complexity and
the nature of computer science / Juris Hartmanis \\
How the `what' becomes the `how' / Edward A. Feigenbaum
\\
To dream the possible dream / Raj Reddy \\
The Eary Days of RSA: History and Lessons / Ronald L.
Rivest \\
Pre-RSA Days: History and Lessons / Leonard Adleman \\
Cryptography: State of the science / Adi Shamir \\
Turing Award Lecture / Alan Kay \\
Assessing the Internet: Lessons Learned, Strategies for
Evolution, and Future Possibilities / Vinton Cerf,
Robert E. Kahn \\
Computing vs. Human Thinking / Peter Naur \\
Compiling for Performance: A Personal Tour / Frances
Allen \\
Model checking: my 27-year quest to overcome the state
explosion problem / Edmund M. Clarke \\
Model checking: A Personal Perspective / E. Allen
Emerson \\
The Quest for Correctness Beyond Verification / Joseph
Sifakis \\
The Power of Abstraction / Barbara Liskov \\
Improving the Future by Examining the Past / Charles P.
Thacker",
}
@Article{Chatelin:1987:SVM,
author = "F. Chatelin and J. Dongarra and I. Duff",
title = "Special Volume in Memory of {James H. Wilkinson}",
journal = j-LINEAR-ALGEBRA-APPL,
volume = "88--89",
number = "??",
pages = "??--??",
month = "????",
year = "1987",
CODEN = "LAAPAW",
ISSN = "0024-3795 (print), 1873-1856 (electronic)",
ISSN-L = "0024-3795",
bibdate = "Mon Jan 02 09:49:28 2006",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
http://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
URL = "http://www.sciencedirect.com/science/journal/00243795/88-89",
acknowledgement = ack-nhfb,
fjournal = "Linear Algebra and its Applications",
journal-URL = "http://www.sciencedirect.com/science/journal/00243795",
}
@Proceedings{Cox:1990:RNC,
editor = "M. G. Cox and S. Hammarling",
booktitle = "Reliable numerical computation",
title = "Reliable numerical computation",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xvi + 339",
year = "1990",
ISBN = "0-19-853564-3",
ISBN-13 = "978-0-19-853564-5",
LCCN = "QA297 .R435 1990",
MRclass = "65-06",
MRnumber = "91k:65011",
bibdate = "Fri Dec 20 18:34:52 1996",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/d/dongarra-jack-j.bib;
http://www.math.utah.edu/pub/bibnet/authors/d/duff-iain-s.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;
http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
http://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Based on papers from a conference in honour of the
late James Hardy Wilkinson (died Sunday 5th October
1986) held at National Physical Laboratory, Teddington,
Middlesex, UK, 8th--10th July 1987.",
price = "US\$75.00",
abstract = "Published to honor the late Jim Wilkinson, the
respected pioneer in numerical analysis, this book
includes contributions from his colleagues and
collaborators, leading experts in their own right. The
breadth of Wilkinson's research is reflected in the
topics covered, which include linear algebra, error
analysis and computer arithmetic algorithms, and
mathematical software. An invaluable reference, the
book is completely up-to-date with the latest
developments on the Lanczos algorithm,
QR-factorizations, error propagation models, parameter
estimation problems, sparse systems, and
shape-preserving splines. Reflecting the current growth
and vitality of this field, the volume is an essential
reference for all numerical analysts.",
acknowledgement = ack-nhfb,
tableofcontents = "List of contributors / / xv \\
Prologue. Reflections on Jim Wilkinson / Gene Golub / 1
\\
1. Misconvergence in the Lanczos algorithm / Beresford
Parlett / 7 \\
2. The Lanczos algorithm for a pure imaginary Hermitian
matrix / Charles L. Lawson and Kajal K. Gupta / 25 \\
3. Nearest defective matrices and the geometry of
ill-conditioning / James Demmel / 35 \\
4. Computational aspects of the Jordan canonical form /
Theo Beelen and Paul Van Dooren / 57 \\
5. Some aspects of generalized QR factorizations / C.
C. Paige / 73 \\
6. The multifrontal method in a parallel environment /
I. S. Duff, N. I. M. Gould, M. Lescrenier, and J. K.
Reid / 93 \\
7. A Schur-complement method for sparse quadratic
programming / Philip E. Gill, Walter Murray, Michael A.
Saunders, and Margaret H. Wright / 113 \\
8. A probabilistic round-off error propagation model.
Application to the eigenvalue problem / Francoise
Chatelin and Marie Christine Brunet / 139 \\
9. Analysis of the Cholesky decomposition of a
semi-definite matrix / Nicholas J. Higham / 161 \\
10. On the conditioning of parameter estimation
problems / James M. Varah / 187 \\
11. Rounding errors in algebraic process-in level-index
arithmetic / F. W J. Olver / 197 \\
12. Experiments in tearing large sparse systems / Mario
Arioli and lain S. Duff / 207 \\
13. The least-squares solution of linear equations with
block-angular observation matrix / M. G. Cox / 227 \\
14. An iterative method for solving linear inequalities
/ G. W Stewart / 241 \\
15. Iterative refinement and reliable computing / Ake
Bjorck / 249 \\
16. Software for shape-preserving spline interpolation
/ Christian H. Reinsch / 267 \\
17. Experiences with some software engineering
practices in numerical software / D. A. H. Jacobs and
G. Markham / 277 \\
18. Evolution of numerical software for dense linear
algebra / Jack Dongarra and Sven Hammarling / 297 \\
Epilogue. Jim Wilkinson: some after-dinner sentiments /
L. Fox / 329",
}
@InProceedings{Parlett:1990:CJH,
author = "B. N. Parlett",
title = "The Contribution of {J. H. Wilkinson} to Numerical
Analysis",
crossref = "Nash:1990:HSC",
pages = "17--30",
year = "1990",
bibdate = "Tue Mar 13 14:04:57 2007",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
acknowledgement = ack-nhfb,
}
@Proceedings{Nash:1990:HSC,
editor = "Stephen G. Nash",
booktitle = "A History of Scientific Computing",
title = "A History of Scientific Computing",
publisher = pub-AW # " and " # pub-ACM,
address = pub-AW # " and " # pub-ACM:adr,
pages = "xix + 359",
year = "1990",
ISBN = "0-201-50814-1",
ISBN-13 = "978-0-201-50814-7",
LCCN = "QA76.17 .H59 1990",
bibdate = "Wed Dec 15 10:39:57 1993",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
z3950.loc.gov:7090/Voyager",
series = "ACM Press history series",
remark = "Based on papers presented at the Conference on the
History of Scientific and Numeric Computation, held in
Princeton, N.J., 1987.",
subject = "Electronic data processing; History; Science; Data
processing",
}
@Book{Wilkinson:1994:REA,
author = "J. H. Wilkinson",
title = "Rounding errors in algebraic processes",
publisher = pub-DOVER,
address = pub-DOVER:adr,
pages = "viii + 161",
year = "1994",
ISBN = "0-486-67999-3",
ISBN-13 = "978-0-486-67999-0",
MRclass = "65G05",
MRnumber = "MR1280465",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib",
note = "Reprint of the 1963 original [Prentice-Hall, Englewood
Cliffs, NJ; MR0161456 (28 \#4661)]",
acknowledgement = ack-nhfb,
tableofcontents = "1. The Fundamental Arithmetic Operations \\
Digital computation / 1 \\
Fixed-point and floating-point computation / 1 \\
Notational conventions / 2 \\
Rounding errors in fixed-point computation / 4 \\
Fixed-point accumulation of inner-products / 6 \\
Rounding errors in floating-point computation / 7 \\
Round-off with single-precision accumulator / 11 \\
Comparison of fixed-point and floating-point
computation / 14 \\
Common floating-point operations / 16 \\
More precise bounds / 19 \\
Floating-point accumulation of sums and inner-products
/ 23 \\
Statistical error bounds / 25 \\
Block-floating vectors and matrices / 26 \\
Fundamental limitations oft-digit computation / 27 \\
Ill-conditioned problems / 28 \\
Condition numbers / 29 \\
Rounding errors in the computation / 30 \\
Additional comments / 33 \\
2. Computations Involving Polynomials \\
Evaluation of power series / 34 \\
Fixed-point representation / 34 \\
Floating-point representation / 36 \\
Calculation of zeros of functions defined by power
series / 37 \\
Polynomials with arbitrary coefficients / 38 \\
Condition of a polynomial with respect to the
computation of its zeros / 38 \\
Some typical distributions of zeros / 41 \\
Linear distributions of zeros / 41 \\
Geometric distribution / 44 \\
Chebyshev polynomial / 46 \\
Significance of the condition of the zeros of
polynomials 4 / 7 \\
Determination of the zeros / 49 \\
Iterative methods / 52 \\
Effect of rounding errors on Newton's process / 53 \\
Simple examples / 54 \\
Polynomial deflation / 55 \\
Analysis of errors inherent in deflation / 56 \\
Examples of deflation / 59 \\
Deflation of ill-conditioned polynomials / 62 \\
General comments on iteration and deflation / 64 \\
Purification in the original polynomial / 65 \\
Other iterative methods / 66 \\
The root-squaring process / 67 \\
Forward error analysis of root-squaring / 69 \\
Relative error in computed coefficients / 71 \\
Numerical example / 72 \\
Deterioration of condition / 74 \\
General comments on the computation of zeros of
polynomials / 76 \\
Additional comments / 78 \\
3. Matrix Computations \\
Introduction / 79 \\
Vector and matrix norms / 80 \\
Error analysis of simple matrix operations / 82 \\
Matrix multiplication / 83 \\
Matrix operations in block-floating arithmetic / 85 \\
Matrices which are not infinity row standardized / 85
\\
Orthogonalization of vectors / 86 \\
Numerical example / 87 \\
General case / 89 \\
Solution of equations and matrix inversion / 91 \\
Rounding of matrix of coefficients / 93 \\
Error analysis of Gaussian elimination / 94 \\
Computational equations / 95 \\
Floating-point bounds / 96 \\
Gaussian elimination in fixed-point / 99 \\
Determinant evaluation / 99 \\
Solution of a triangular set of equations using
standard floating-point arithmetic / 99 \\
Accuracy of computed solution / 102 \\
Solution of triangular set of equations with
floating-point accumulation of inner-products / 103 \\
Inversion of a triangular matrix / 104 \\
High accuracy of solutions of triangular equations /
105 \\
Solution of a general set of equations / 107 \\
Inversion of a general matrix / 109 \\
Left-handed and right-handed inverses / 110 \\
Numerical example / 111 \\
Comments on example / 113 \\
Compact methods of triangular decomposition / 114 \\
Triangular decomposition with partial pivoting / 115
\\
Positive definite matrix / 117 \\
Numerical example / 118 \\
Comments on the solution / 119 \\
Residual corresponding to block-floating solution / 120
\\
Iterative refinement of the solution / 121 \\
Practical procedure / 122 \\
Analysis of the practical procedure / 124 \\
Assessment of accuracy of the computed solution / 126
\\
The use of an estimate for $||A^{-1}||$ / 126 \\
Assessment of a computed inverse / 127 \\
Use of the approximate inverse to solve equations / 128
\\
Iterative procedure based on use of the approximate
inverse / 130 \\
Numerical example / 131 \\
Sensitivity of the eigenvalues of a matrix / 134 \\
Sensitivity of individual eigenvalues / 137 \\
Example of ill-conditioned eigenvalues / 138 \\
A posteriori estimates for a computed eigenvalue and
eigenvector of a real symmetric matrix / 139 \\
Calculation of the eigenvectors of a symmetric
tri-diagonal matrix / 142 \\
Effect of rounding errors / 143 \\
Calculation of the eigenvalues of a lower Hessenberg
matrix / 147 \\
Calculation of $f(\lambda)$ using floating-point
accumulation / 149 \\
Perturbation of the eigenvalues / 150 \\
Numerical example / 151 \\
Additional comments / 155 \\
Bibliography / 157 \\
Index / 159",
}
@Book{Copeland:2005:ATA,
editor = "B. Jack Copeland",
booktitle = "{Alan Turing}'s {Automatic Computing Engine}: the
master codebreaker's struggle to build the modern
computer",
title = "{Alan Turing}'s {Automatic Computing Engine}: the
master codebreaker's struggle to build the modern
computer",
publisher = pub-OXFORD,
address = pub-OXFORD:adr,
pages = "xx + 553",
year = "2005",
ISBN = "0-19-856593-3 (hardcover)",
ISBN-13 = "978-0-19-856593-2 (hardcover)",
LCCN = "QA75 .A43 2005",
bibdate = "Sat Nov 19 18:33:05 MST 2005",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/t/turing-alan-mathison.bib;
http://www.math.utah.edu/pub/bibnet/authors/w/wilkinson-james-hardy.bib;
melvyl.cdlib.org:210/CDL90",
URL = "http://ukcatalogue.oup.com/product/9780198565932.do;
http://www.oxfordscholarship.com/oso/public/content/maths/9780198565932/toc.html",
abstract = "The mathematical genius Alan Turing (1912--1954) was
one of the greatest scientists and thinkers of the 20th
century. Now well known for his crucial wartime role in
breaking the ENIGMA code, he was the first to conceive
of the fundamental principle of the modern computer ---
the idea of controlling a computing machine's
operations by means of coded instructions, stored in
the machine's `memory'. In 1945, Turing drew up his
revolutionary design for an electronic computing
machine --- his Automatic Computing Engine (`ACE'). A
pilot model of the ACE ran its first programme in 1950
and the production version, the `DEUCE', went on to
become a cornerstone of the fledgling British computer
industry. The first `personal' computer was based on
Turing's ACE. This book describes Turing's struggle to
build the modern computer. It contains first-hand
accounts by Turing and by the pioneers of computing who
worked with him. The book describes the hardware and
software of the ACE and contains chapters describing
Turing's path-breaking research in the fields of
Artificial Intelligence (AI) and Artificial Life
(A-Life).",
acknowledgement = ack-nhfb,
remark = "Originally published: New York; London: Springer,
2003",
subject = "Turing, Alan Mathison; Computers; Great Britain;
History; Computer engineering; Great Britain; History",
subject-dates = "1912--1954",
tableofcontents = "Foreword / Donald W. Davies \\
Introduction / B. Jack Copeland \par
Part I: The National Physical Laboratory and the ACE
Project \\
A Century of Measurement and Computation at the
National Physical Laboratory, 1900--2000 / Eileen
Magnello \\
The Creation of the NPL Mathematics Division / Mary
Croarken \\
The Origins and Development of the ACE Project / B.
Jack Copeland \\
The Pilot ACE at the National Physical Laboratory,
James H. Wilkinson \par
Part II: Turing and the History of Computing \\
The ACE and the Shaping of British Computing / Martin
Campbell-Kelly \\
Computer Architecture and the ACE Computers / Robert
Doran \\
Turing and the Computer / B. Jack Copeland and Diane
Proudfoot \\
From Turing Machine to ``Electronic Brain'' / Teresa
Numerico \par
Part III: The ACE Computers \\
The Pilot ACE Instruction Format / Henry John Norton
\\
Programming the Pilot ACE / J.G. Hayes \\
The Pilot ACE: from Concept to Reality / Robin A.
Vowels \\
The DEUCE --- a User's View / Robin A. Vowels \\
Applications of the Pilot ACE and the DEUCE / Tom
Vickers \\
The ACE Test Assembly, the Pilot ACE, the Big ACE, and
the Bendix G15 / Harry D. Huskey \\
The ACE Simulator and the Cybernetic Model / Michael
Woodger \\
The Pilot Model and the Big ACE on the Web / Benjamin
Wells \par
Part IV: Electronics \\
How Valves Work / David O. Clayden \\
Recollections of Early Vacuum Tube Circuits / Maurice
Wilkes \\
Circuit Design of the Pilot ACE and the Big ACE / David
O. Clayden \par
Part V: Technical Reports and Lectures on the ACE and
the Pilot ACE, 1945--1951 \\
Proposed Electronic Calculator (1945) / Alan M. Turing
\\
Notes on Memory (1945) / Alan M. Turing \\
The Turing--Wilkinson Lecture Series (1946--1947) /
Alan M. Turing and James H. Wilkinson \\
The State of the Art in Electronic Digital Computing in
Britain and the United States (1947) / Harry D.
Huskey",
}