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- 1
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E. ANDERSON, Z. BAI, C. BISCHOF, L. S. BLACKFORD, J. DEMMEL, J. DONGARRA,
J. DU CROZ, A. GREENBAUM, S. HAMMARLING, A. MCKENNEY, AND D. SORENSEN, LAPACK Users' Guide, Society for Industrial and Applied Mathematics,
Philadelphia, PA, third ed., 1999.
- 2
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Z. BAI AND J. W. DEMMEL, Computing the generalized singular value
decomposition, SIAM J. Sci. Comp., 14 (1993), pp. 1464-1486.
(Also LAPACK Working Note #46).
- 3
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Z. BAI AND H. ZHA, A new preprocessing algorithm for the computation
of the generalized singular value decomposition, SIAM J. Sci. Comp., 14
(1993), pp. 1007-1012.
- 4
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L. S. BLACKFORD AND J. DONGARRA, Installation guide for LAPACK,
Computer Science Dept. Technical Report CS-92-151, University of
Tennessee, Knoxville, TN, March 1992.
(Also LAPACK Working Note #41).
- 5
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height 2pt depth -1.6pt width 23pt, Quick installation
guide for LAPACK on Unix systems, Computer Science Dept.
Technical Report CS-94-249, University of Tennessee, Knoxville, TN,
September 1994.
(LAPACK Working Note #81).
- 6
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L. S. BLACKFORD, J. DONGARRA, J. DU CROZ, S. HAMMARLING, AND
J. WASNIEWSKI, A Fortran 90 Interface for LAPACK,
Computer Science Dept. Technical Report CS-96-341, University of
Tennessee, Knoxville, TN, 1996.
(Also LAPACK Working Note #117).
- 7
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COMPAQ CORPORATION, Compaq Extended Math Library.
http://www.compaq.com/hpc/software/dxml.html.
- 8
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J. DEMMEL AND W. KAHAN, Computing Small Singular Values of
Bidiagonal Matrices with Guaranteed High Relative Accuracy, SIAM
J. Sci. Statist. Comput., 11 (1990), pp. 873-912.
Also (LAPACK Working Note # 3:
http://www.netlib.org/lapack/lawns/lawn03.ps or
http://www.netlib.org/lapack/lawnspdf/lawn03.pdf).
- 9
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J. W. DEMMEL, Applied Numerical Linear Algebra, Society for
Industrial and Applied Mathematics, Philadelphia, PA, USA, first ed., 1997.
- 10
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J. W. DEMMEL AND B. KÅGSTR¨OM, Computing stable
eigendecompositions of matrix pencils, Lin. Alg. Appl., 88/89 (1987),
pp. 139-186.
- 11
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I. DHILLON, A New O() Algorithm for the Symmetric
Tridiagonal Eigenvalue / Eigenvector Problem, Tech. Rep.
UCB/CSD-97-971, UC Berkeley, Computer Science Division, May 1997.
- 12
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J. DONGARRA, J. DU CROZ, S. HAMMARLING, J. WASNIEWSKI, AND
A. ZEMA, A Proposal for a Fortran 90 Interface for
LAPACK, Computer Science Dept. Technical Report CS-95-295,
University of Tennessee, Knoxville, TN, 1995.
(Also LAPACK Working Note #101).
- 13
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J. DONGARRA, W. OWCZARZ, J. WASNIEWSKI, AND P. YALAMOV, Testing Software for LAPACK90, Computer Science Dept.
Technical Report CS-98-401, University of Tennessee, Knoxville, TN,
1998.
(Also LAPACK Working Note #138).
- 14
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J. DONGARRA AND J. WASNIEWSKI, High Performance Linear
Algebra Package - LAPACK90, Computer Science Dept. Technical
Report CS-98-384, University of Tennessee, Knoxville, TN, 1998.
(Also LAPACK Working Note #134).
- 15
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J. J. DONGARRA, J. DU CROZ, I. S. DUFF, AND S. HAMMARLING, A set of
Level 3 Basic Linear Algebra Subprograms, ACM Trans. Math.
Soft., 16 (1990), pp. 1-17.
- 16
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J. J. DONGARRA, J. DU CROZ, S. HAMMARLING, AND R. J. HANSON, An
extended set of FORTRAN basic linear algebra subroutines, ACM Trans.
Math. Soft., 14 (1988), pp. 1-17.
- 17
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J. J. DONGARRA, I. S. DUFF, D. SORENSEN, AND H. A. VAN DER VORST, Numerical Linear Algebra for High-Performance Computers, SIAM,
Second ed., 1998.
- 18
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J. J. DONGARRA AND E. GROSSE, Distribution of mathematical software
via electronic mail, Communications of the ACM, 30 (1987), pp. 403-407.
- 19
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F. GANTMACHER, The Theory of Matrices, vol. II (transl.),
Chelsea, New York, 1959.
- 20
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G. GOLUB AND C. F. VAN LOAN, Matrix Computations, Johns Hopkins
University Press, Baltimore, MD, third ed., 1996.
- 21
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N. J. HIGHAM, Accuracy and Stability of Numerical Algorithms, SIAM,
1996.
- 22
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IBM, IBM Engineering and Scientific Subroutine Library
for AIX, Version 3, Volume 1 ed., December 1997.
Pub. number SA22-7272-0.
- 23
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height 2pt depth -1.6pt width 23pt, Engineering and
Scientific Subroutine Library for AIX Guide and Reference.
http://www.rs6000.ibm.com/resource/aix_resource/sp_books/essl/index.html,
2000.
- 24
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B. KåGSTRÖM, A Perturbation Analysis of the
Generalized Sylvester Equation
, SIAM
J. Matrix Anal. Appl., 15 (1994), pp. 1045-1060.
- 25
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B. KåGSTRÖM AND P. POROMAA, Computing Eigenspaces with
Specified Eigenvalues of a Regular Matrix Pair (A,B) and
Condition Estimation: Theory, Algorithms and Software, Numerical
Algorithms, 12 (1996), pp. 369-407.
Also Report # UMINF - 94.04 at Umeå University and LAPACK
Working Note # 87.
- 26
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height 2pt depth -1.6pt width 23pt, LAPACK-Style
Algorithms and Software for Solving the Generalized Sylvester
Equation and Estimating the Separation between Regular Matrix
Pairs, ACM Trans. on Math. Software, 22 (1996), pp. 78-103.
Also Report # UMINF - 93.23 at Umeå University (Sweden) and
LAPACK Working Note # 75.
- 27
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B. KåGSTRÖM AND L. WESTIN, Generalized Schur Methods
with Condition Estimators for Solving the Generalized Sylvester
Equation, IEEE Transactions on Automatic Control, 34 (1989), pp. 745-751.
- 28
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B. KÅGSTRÖM, A Direct Method for Reordering
Eigenvalues in the Generalized Real Schur Form of a Regular
Matrix Pair (A, B), in Linear Algebra for Large Scale and Real-Time
Applications, M. S. Moonen et al., eds., Kluwer Academic Publ., 1993,
pp. 195-218.
- 29
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W. KAHAN, Accurate Eigenvalues of a Symmetric Tridiagonal
Matrix, Tech. Rep. CS41, Stanford University, Computer Science Dept., July
1966.
- 30
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C. L. LAWSON, R. J. HANSON, D. KINCAID, AND F. T. KROGH, Basic
linear algebra subprograms for Fortran usage, ACM Trans. Math. Soft., 5
(1979), pp. 308-323.
- 31
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M. METCALF AND J. REID, FORTRAN 90/95 Explained, Oxford
University Press, Oxford, UK, second ed., 1996.
- 32
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C. B. MOLER AND G. W. STEWART, An Algorithm for Generalized
Matrix Eigenvalue Problems, SIAM J. Numer. Anal., 10 (1973),
pp. 241-256.
- 33
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C. PAIGE, Computing the generalized singular value decomposition,
SIAM J. Sci. Stat., 7 (1986), pp. 1126-1146.
- 34
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B. PARLETT AND F. V., Accurate Singular Values and
Differential QD Algorithms, Tech. Rep. CPAM-554, University of
California at Berkeley, Mathematics Department, July 1992.
- 35
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G. QUINTANA-ORTI, E. QUINTANA-ORTI, AND A. PETITET, Efficient
Solution of the Rank-Deficient Linear Least Squares Problem,
SIAM Journal on Scientific and Statistical Computing, 20 (1999),
pp. 1155-1163.
Also LAPACK Working Note # 113:
http://www.netlib.org/lapack/lawns/lawn113.ps or
http://www.netlib.org/lapack/lawns/lawn113.pdf.
- 36
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G. QUINTANA-ORTI, X. SUN, AND C. H. BISCHOF, BLAS-3 Version of
the QR Factorization with Column Pivoting.
http://www.netlib.org/lapack/lawns/lawn114.ps or
http://www.netlib.org/lapack/lawnspdf/lawn114.pdf, 1996.
PRISM Working Note # 26 and LAPACK Working Note # 114.
- 37
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B. T. SMITH, J. M. BOYLE, J. J. DONGARRA, B. S. GARBOW, Y. IKEBE, V. C.
KLEMA, AND C. B. MOLER, Matrix Eigensystem Routines - EISPACK
Guide, vol. 6 of Lecture Notes in Computer Science, Springer-Verlag,
Berlin, 1976.
- 38
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G. W. STEWART, On the sensitivity of the eigenvalue problem
, SIAM J. Num. Anal., 9 (1972), pp. 669-686.
- 39
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height 2pt depth -1.6pt width 23pt, Error and
perturbation bounds for subspaces associated with certain eigenvalue
problems, SIAM Review, 15 (1973), pp. 727-764.
- 40
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G. W. STEWART AND J.-G. SUN, Matrix Perturbation Theory, Academic
Press, New York, 1990.
- 41
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SUN MICROSYSTEMS INC., Sun Performance Library User's
Guide.
http://docs.sun.com/htmlcoll/coll.118.3/iso-8859-1/PERFLIBUG/plug_bookTOC.html.
- 42
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R. C. WARD, Balancing the Generalized Eigenvalue Problem,
SIAM J. Sci. Stat. Comp., 2 (1981), pp. 141-152.
- 43
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R. C. WHALEY, A. PETITET, AND J. J. DONGARRA, Automated empirical
optimization of software and the ATLAS project, To appear in Parallel
Computing, (2001).
Also available as University of Tennessee LAPACK Working Note #147,
UT-CS-00-448, 2000 (www.netlib.org/lapack/lawns/lawn147.ps).
- 44
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J. H. WILKINSON, Kronecker's canonical form and the QZ algorithm,
Lin. Alg. Appl., 28 (1979), pp. 285-303.
Susan Blackford
2001-08-19