Abstract
The inverse-free preconditioned Krylov subspace method of Golub and Ye [G.H. Golub, Q. Ye, An inverse free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems, SIAM J. Sci. Comp. 24 (2002) 312-334] is an efficient algorithm for computing a few extreme eigenvalues of the symmetric generalized eigenvalue problem. In this paper, we first present an analysis of the preconditioning strategy based on incomplete factorizations. We then extend the method by developing a block generalization for computing multiple or severely clustered eigenvalues and develop a robust black-box implementation. Numerical examples are given to illustrate the analysis and the efficiency of the block algorithm.
Original language | English |
---|---|
Pages (from-to) | 1298-1313 |
Number of pages | 16 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 233 |
Issue number | 5 |
DOIs | |
State | Published - Jan 1 2010 |
Bibliographical note
Funding Information:The two authors were supported in part by National Science Foundation grant DMS-0411502.
Keywords
- Arnoldi algorithm
- Block Krylov subspace method
- Eigenvalue problem
- Preconditioning
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics