Computation of the fundamental singular subspace of a large matrix

Linear Algebra and Its Applications

Volumn 257, Issue 1-3, 1997, Pages 77-104

  Philippe, B ^a   Sadkane, M ^a  

^a CAMPUS DE BEAULIEU   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040514637     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(96)00040-7     Document Type: Article

References (16)

1. M. Berry and G. Golub, Estimating the largest singular values of large sparse matrices via modified moments, Numer. Algorithms 1:353-374 (1991).
2. M. W. Berry, Multiprocessor sparse SVD algorithms and applications, Ph.D. Thesis, CSRD - Univ. of Illinois, Nov. 1990.
3. S. Chauveau, Mise en Oeuvre des Factorisations QR et de Choleski Incomplètes de Matrices Creuses, Tech. Rep., Stage de DEA, IRISA, 1994.
4. M. Crouzeix, B. Philippe, and M. Sadkane, The Davidson method, SIAM J. Sci. Comput. 15:62-76 (1994).
5. J. K. Cullum and R. A. Willoughby, Lanczos Algorithm for Large Symmetric Eigenvalue Computations. Vol I. Theory, Birkhaüser, Boston, 1985.
6. E. R. Davidson, The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real symmetric matrices, J. Comput. Phys. 17:87-94 (1975).
7. I. S. Duff, R. G. Grimes, and J. G. Lewis, Sparse matrix test problems, ACM Trans. Math. Software 15:1-14 (1989).
8. G. H. Golub, F. T. Luk, and M. L. Overton, A block Lanczos method for computing the singular values and corresponding singular vectors of a matrix, ACM Trans. Math. Software 7:149-169 (1981).
9. G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd ed., Johns Hopkins U.P., Baltimore, 1989.
10. R. B. Morgan and D. S. Scott, Generalizations of Davidson's method for computing eigenvalues of sparse symmetric matrices, SIAM J. Sci. Statist. Comput. 7:817-825 (1986).
11. B. N. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, N.J., 1980.
12. B. N. Parlett and D. S. Scott, The Lanczos algorithm with selective orthogonalization, Math. Comp. 33:217-238 (1979).
13. Y. Saad, On the rates of convergence of the Lanczos and block Lanczos methods, SIAM J. Numer. Anal. 17:687-706 (1980).
14. Y. Saad, Preconditioning techniques for nonsymmetric and indefinite linear systems, J. Comput. Appl. Math. 24:89-105 (1988).
15. R. R. Underwood, An Iterative Block Lanczos Method for the Solution of Large Sparse Symmetric Eigenproblems, Ph.D. Thesis, Stanford Univ., May 1975.
16. S. Van Huffel, Iterative algorithms for computing the singular subspace of a matrix associated with its smallest singular values, Linear Algebra Appl. 154-156:675-709 (1991).