E. ANDERSON, Z. BAI, C. BISCHOF, J. W. DEMMEL, J. J. DONGARRA, J. DU CROZ,
A. GREENBAUM, S. HAMMARLING, A. MCKENNEY, AND D. SORENSEN, LAPACK: A
portable linear algebra library for high-performance computers, Computer
Science Dept. Technical Report CS-90-105, University of Tennessee,
Knoxville, 1990.
(LAPACK Working Note 20).
E. ANDERSON, Z. BAI, AND J. J. DONGARRA,
Generalized QR Factorization and its Applications,
Computer Science Dept. Technical Report CS-91-131,
University of Tennessee, Knoxville, 1991.
(LAPACK Working Note 31).
E. ANDERSON, J. J. DONGARRA, AND S. OSTROUCHOV, Installation guide
for LAPACK, Computer Science Dept. Technical Report CS-92-151,
University of Tennessee, Knoxville, 1992.
(LAPACK Working Note 41).
Z. BAI AND J. W. DEMMEL, On a block implementation of Hessenberg
multishift QR iteration, Int. J. of High Speed Comput., 1
(1989), pp. 97-112.
(LAPACK Working Note 8).
Z. BAI AND J. W. DEMMEL,
Design of a parallel nonsymmetric eigenroutine toolbox, Part I,
Proceedings of the Sixth SIAM Conference on Parallel Proceesing for Scientific
Computing, SIAM (1993), pp. 391-398.
Z. BAI AND J. W. DEMMEL,
Computing the generalized singular value decomposition,
SIAM J. Sci. Comp., 14 (1993), pp. 1464-1486.
(LAPACK Working Note 46).
Z. BAI, J. W. DEMMEL, AND A. MCKENNEY, On computing condition
numbers for the nonsymmetric eigenproblem, ACM Trans. Math. Soft. 19
(1993), pp. 202-223.
(LAPACK Working Note 13).
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.
J. BARLOW AND J. DEMMEL, Computing accurate eigensystems of scaled
diagonally dominant matrices, SIAM J. Num. Anal., 27 (1990), pp. 762-791.
(LAPACK Working Note 7).
P. DEIFT, J. W. DEMMEL, L.-C. LI, AND C. TOMEI, The bidiagonal
singular value decomposition and Hamiltonian mechanics, SIAM J. Num.
Anal., 28 (1991), pp. 1463-1516.
(LAPACK Working Note 11).
J. W. DEMMEL AND N. J. HIGHAM, Stability of block
algorithms with fast level 3 BLAS, ACM Trans. Math. Soft., 18 (1992),
pp. 274-291.
(LAPACK Working Note 22).
J. W. DEMMEL AND W. KAHAN, Accurate singular values of bidiagonal
matrices, SIAM J. Sci. Stat. Comput., 11 (1990), pp. 873-912.
(LAPACK Working Note 3).
J. J. DONGARRA, J. DU CROZ, I. S. DUFF, AND S. HAMMARLING, Algorithm
679: A set of Level 3 Basic Linear Algebra Subprograms, ACM
Trans. Math. Soft., 16 (1990), pp. 18-28.
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.
J. J. DONGARRA, J. DU CROZ, S. HAMMARLING, AND R. J. HANSON, Algorithm 656: An extended set of FORTRAN Basic Linear Algebra
Subprograms, ACM Trans. Math. Soft., 14 (1988), pp. 18-32.
J. J. DONGARRA, J. DU CROZ, S. HAMMARLING, AND R. J. HANSON, An extended set of
FORTRAN Basic Linear Algebra Subprograms, ACM Trans. Math. Soft., 14
(1988), pp. 1-17.
J. J. DONGARRA, I. S. DUFF, D. C. SORENSEN, AND H. A. VAN DER VORST, Solving Linear Systems on Vector and Shared Memory Computers, SIAM
Publications, 1991.
J. J. DONGARRA, F. G. GUSTAFSON, AND A. KARP, Implementing linear
algebra algorithms for dense matrices on a vector pipeline machine, SIAM
Review, 26 (1984), pp. 91-112.
J. J. DONGARRA, S. HAMMARLING, AND D. C. SORENSEN, Block reduction
of matrices to condensed forms for eigenvalue computations, JCAM, 27
(1989), pp. 215-227.
(LAPACK Working Note 2).
J. J. DONGARRA AND S. OSTROUCHOV, Quick installation guide
for LAPACK on unix systems, Computer Science Dept. Technical
Report CS-94-249, University of Tennessee, Knoxville, 1994.
(LAPACK Working Note 81).
J. J. DONGARRA, R. POZO, AND D. WALKER,
An object oriented design for high performance linear algebra on
distributed memory architectures, Computer Science Dept. Technical
Report CS-93-200, University of Tennessee, Knoxville, 1993.
(LAPACK Working Note 61).
J. DU CROZ, P. J. D. MAYES, AND G. RADICATI DI BROZOLO, Factorizations of band matrices using Level 3 BLAS, Computer Science
Dept. Technical Report CS-90-109, University of Tennessee, Knoxville,
1990.
(LAPACK Working Note 21).
S. I. FELDMAN, D. M. GAY, M. W. MAIMONE, AND N. L. SCHRYER,
A Fortran-to-C Converter, Computing Science Technical
Report No. 149, AT & T Bell Laboratories, Murray Hill, NJ, 1990.
B. S. GARBOW, J. M. BOYLE, J. J. DONGARRA, AND C. B. MOLER, Matrix
Eigensystem Routines - EISPACK Guide Extension, vol. 51 of Lecture Notes
in Computer Science, Springer-Verlag, Berlin, 1977.
A. GREENBAUM AND J. J. DONGARRA, Experiments with QL/QR methods
for the symmetric tridiagonal eigenproblem, Computer Science Dept.
Technical Report CS-89-92, University of Tennessee, Knoxville, 1989.
(LAPACK Working Note 17).
M. GU AND S. EISENSTAT,
A stable algorithm for the rank-1 modification of the symmetric
eigenproblem, Yale University, Computer Science Department Report
YALEU/DCS/RR-916, New Haven, CT (1992).
S. HAMMARLING,
The numerical solution of the general Gauss-Markov
linear model, in Mathematics in Signal Processing,
eds. T. S. Durrani et al., Clarendon Press, Oxford
(1986).
N. J. HIGHAM, FORTRAN codes for
estimating the one-norm of a real or complex matrix, with applications to
condition estimation, ACM Trans. Math. Soft., 14 (1988), pp. 381-396.
S. HUSS-LEDERMAN, A. TSAO AND G. ZHANG,
A parallel implementation of the invariant subspace
decomposition algorithm for dense symmetric matrices,
in Proceedings of the Sixth SIAM Conference on Parallel Processing for
Scientific Computing, SIAM (1993), pp. 367-374.
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.
R. LEHOUCQ, The computation of elementary unitary matrices,
Computer Science Dept. Technical Report CS-94-233, University
of Tennessee, Knoxville, 1994.
(LAPACK Working Note 72).
C. PAIGE,
Some aspects of generalized QR factorization,
in Reliable Numerical Computations, eds. M. Cox and S. Hammarling,
Clarendon Press, Oxford (1990).
M. PAYNE AND B. WICHMANN,
Language Independent Arithmetic (LIA) - Part 1:
Integer and floating point arithmetic,
International Standards Organization, ISO/IEC 10967-1:1994, 1994.
J. RUTTER,
A serial implementation of Cuppen's Divide and Conquer Algorithm for
the Symmetric Tridiagonal Eigenproblem,
University of California, Computer Science Division Report
UCB/CSD 94/799, Berkeley CA (1994).
(LAPACK Working Note 69).
R. SCHREIBER AND C. F. VAN LOAN, A storage efficient WY
representation for products of Householder transformations, SIAM J. Sci.
Stat. Comput., 10 (1989), pp. 53-57.
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,
2 ed., 1976.
J. H. WILKINSON,
Some recent advances in numerical linear algebra,
in: D. A. H. JACOBS, ed., The State of the Art in Numerical
Analysis, Academic Press, New York, 1977.