14.16 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,

• LAPACK Users' Guide (Third Edition, 1999), Published by SIAM, ISBN 0-89871-447-8.

  http://www.netlib.org/lapack

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, Kres<imir Veseli´c, “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.