Rayleigh quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves

M A Freitag, Alastair Spence

Research output: Contribution to journalArticle

19 Citations (Scopus)
57 Downloads (Pure)

Abstract

We show that for the non-Hermitian eigenvalue problem simplified Jacobi-Davidson with preconditioned Galerkin-Krylov solves is equivalent to inexact Rayleigh quotient iteration where the preconditioner is altered by a simple rank one change. This extends existing equivalence results to the case of preconditioned iterative solves. Numerical experiments are shown to agree with the theory.
Original languageEnglish
Pages (from-to)2049-2060
Number of pages12
JournalLinear Algebra and its Applications
Volume428
Issue number8-9
Early online date27 Dec 2007
DOIs
Publication statusPublished - 15 Apr 2008

Fingerprint

Jacobi-Davidson Method
Rayleigh Quotient Iteration
Jacobi-Davidson
Preconditioner
Galerkin
Eigenvalue Problem
Experiments
Numerical Experiment
Equivalence

Keywords

  • Inexact Rayleigh quotient iteration
  • Nonsymmetric eigenproblem
  • Eigenvalue approximation
  • Preconditioning
  • Iterative methods

Cite this

Rayleigh quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves. / Freitag, M A; Spence, Alastair.

In: Linear Algebra and its Applications, Vol. 428, No. 8-9, 15.04.2008, p. 2049-2060.

Research output: Contribution to journalArticle

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