A filtered Lanczos procedure for extreme and interior eigenvalue problems

Haw Ren Fang, Yousef Saad

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

When combined with Krylov projection methods, polynomial filtering can provide a powerful method for extracting extreme or interior eigenvalues of large sparse matrices. This general approach can be quite efficient in the situation when a large number of eigenvalues is sought. However, its competitiveness depends critically on a good implementation. This paper presents a technique based on such a combination to compute a group of extreme or interior eigenvalues of a real symmetric (or complex Hermitian) matrix. The technique harnesses the effectiveness of the Lanczos algorithm with partial reorthogonalization and the power of polynomial filtering. Numerical experiments indicate that the method can be far superior to competing algorithms when a large number of eigenvalues and eigenvectors is to be computed.

Original languageEnglish (US)
Pages (from-to)A2220-A2246
JournalSIAM Journal on Scientific Computing
Volume34
Issue number4
DOIs
StatePublished - Sep 24 2012

Keywords

  • Interior eigenvalue problems
  • Lanczos algorithm
  • Partial reorthogonalization
  • Polynomial filtering

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