14.21 References and Further Reading
Further information on the algorithms described in this section can be
found in the following book,
- G. H. Golub, C. F. Van Loan, Matrix Computations (3rd Ed, 1996),
Johns Hopkins University Press, ISBN 0-8018-5414-8.
The LAPACK library is described in the following manual,
The LAPACK source code can be found at the website above, along
with an online copy of the users guide.
The Modified Golub-Reinsch algorithm is described in the following paper,
- T.F. Chan, “An Improved Algorithm for Computing the Singular Value
Decomposition”, ACM Transactions on Mathematical Software, 8
(1982), pp 72–83.
The Jacobi algorithm for singular value decomposition is described in
the following papers,
- J.C. Nash, “A one-sided transformation method for the singular value
decomposition and algebraic eigenproblem”, Computer Journal,
Volume 18, Number 1 (1975), p 74–76
- J.C. Nash and S. Shlien “Simple algorithms for the partial singular
value decomposition”, Computer Journal, Volume 30 (1987), p
268–275.
- James Demmel, Krešimir Veselić, “Jacobi’s Method is more accurate than
QR”, Lapack Working Note 15 (LAWN-15), October 1989. Available
from netlib, http://www.netlib.org/lapack/ in the
lawns or
lawnspdf directories.
The algorithm for estimating a matrix condition number is described in
the following paper,
- 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., vol. 14, no. 4, pp. 381-396, December 1988.