Block Krylov-Schur method for large symmetric eigenvalue problems

Yunkai Zhou, Yousef Saad

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

Stewart's Krylov-Schur algorithm offers two advantages over Sorensen's implicitly restarted Arnoldi (IRA) algorithm. The first is ease of deflation of converged Ritz vectors, the second is the avoidance of the potential forward instability of the QR algorithm. In this paper we develop a block version of the Krylov-Schur algorithm for symmetric eigenproblems. Details of this block algorithm are discussed, including how to handle rank deficient cases and how to use varying block sizes. Numerical results on the efficiency of the block Krylov-Schur method are reported.

Original languageEnglish (US)
Pages (from-to)341-359
Number of pages19
JournalNumerical Algorithms
Volume47
Issue number4
DOIs
StatePublished - Apr 2008

Bibliographical note

Funding Information:
Work supported by US Department of Energy under contract DE-FG02-03ER25585, by NSF grants ITR-0428774 and CMMI-0727194, and by the Minnesota Supercomputing Institute.

Keywords

  • Block method
  • Implicit restart
  • Krylov-Schur
  • Lanczos

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