Further analysis of the Arnoldi process for eigenvalue problems

M. Bellalij, Y. Saad, H. Sadok

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

This paper takes another look at the convergence analysis of the Arnoldi procedure for solving non-Hermitian eigenvalue problems. Two main viewpoints are put in contrast. The.rst exploits the eigenbasis, when there is one, and relies on classical min-max approximation theory results. The second approach relies on the Schur factorization. Its aim is to link the convergence analysis of the Arnoldi process for eigenvalue problems to that of the generalized minimal residual iterations (GMRES), for which much is known.

Original languageEnglish (US)
Pages (from-to)393-407
Number of pages15
JournalSIAM Journal on Numerical Analysis
Volume48
Issue number2
DOIs
StatePublished - 2010

Keywords

  • Arnoldi's methods
  • Convergence analysis
  • Krylov subspaces

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