Eigenvalue perturbation and generalized Krylov subspace method

Applied Numerical Mathematics

Volumn 27, Issue 2, 1998, Pages 185-202

  Zhang, T ^a   Golub, G H ^a   Law, K H ^a,b  

^a STANFORD UNIVERSITY   (United States)

^b Stanford University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; PERTURBATION TECHNIQUES;

KRYLOV SUBSPACE APPROXIMATION;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 0032090342     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(98)00002-6     Document Type: Article

References (15)

1. J.H. Bramble, A.V. Knyazev and J.E. Pasciak, A subspace preconditioning algorithm for eigenvector/eigenvalue computation, Adv. Comput. Math. 6 (1996) 159-189.
2. J.R. Bunch, C.P. Nielsen and D.C. Sorensen, Rank-one modification of the symmetric eigenproblem, Numer. Math. 31 (1978) 31-48.
3. 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 (1975) 87-94.
4. K. Gallivan, E. Grimme and P. Van Dooren, A rational Lanczos algorithm for model reduction, Numer. Algorithms 12 (1996) 33-63.
5. G.H. Golub, Some modified matrix eigenvalue problems, SIAM Rev. 15 (1973) 318-334.
6. G.H. Golub and C.F. Van Loan, Matrix Computations (Johns Hopkins University Press, Baltimore, MD, 1989).
7. T. Kato, Perturbation Theory for Linear Operators (Springer, New York, 1980).
8. A.V. Knyazev and A.L. Skorokhodov, Preconditioned gradient-type iterative methods in a subspace for partial generalized symmetric eigenvalue problems, SIAM J. Numer. Anal. 31 (1994) 1226-1239.
9. 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 (1986) 817-825.
10. F. Rellich, Perturbation Theory of Eigenvalue Problems (Gordon and Breach, New York, 1969).
11. B. Simon, Fifty years of eigenvalue perturbation theory, Bull. Amer. Math. Soc. (N.S.) 24 (2) (1991) 303-319.
12. G.L.G. Sleijpen and H.A. van der Vorst, A Jacobi-Davidson iteration method for linear eigenvalue problems, SIAM J. Matrix Anal. Appl. 17 (1996) 401-425.
13. G.W. Stewart and J.-G. Sun, Matrix Perturbation Theory (Academic Press, Boston, 1990).
14. J.H. Wilkinson, The Algebraic Eigenvalue Problem (Clarendon Press, Oxford, England, 1965).
15. T. Zhang, K.H. Law and G.H. Golub, On the homotopy method for perturbed symmetric generalized eigenvalue problem, SIAM J. Sci. Comput. (to appear).