A block inverse-free preconditioned Krylov subspace method for symmetric generalized eigenvalue problems

Patrick Quillen, Qiang Ye

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

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 languageEnglish
Pages (from-to)1298-1313
Number of pages16
JournalJournal of Computational and Applied Mathematics
Volume233
Issue number5
DOIs
StatePublished - 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

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