GNU Scientific Library – Reference Manual: Linear Algebra References and Further Reading

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### 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,

- 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, 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.

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