Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration

Melina A. Freitag, Patrick Kürschner

Research output: Contribution to journalArticle

1 Citation (Scopus)
138 Downloads (Pure)

Abstract

Convergence results are provided for inexact two-sided inverse and Rayleigh quotient iteration, which extend the previously established results to the generalized non-Hermitian eigenproblem and inexact solves with a decreasing solve tolerance. Moreover, the simultaneous solution of the forward and adjoint problem arising in two-sided methods is considered, and the successful tuning strategy for preconditioners is extended to two-sided methods, creating a novel way of preconditioning two-sided algorithms. Furthermore, it is shown that inexact two-sided Rayleigh quotient iteration and the inexact two-sided Jacobi-Davidson method (without subspace expansion) applied to the generalized preconditioned eigenvalue problem are equivalent when a certain number of steps of a Petrov-Galerkin-Krylov method is used and when this specific tuning strategy is applied.

Original languageEnglish
Pages (from-to)175-196
Number of pages22
JournalNumerical Linear Algebra with Applications
Volume22
Issue number1
Early online date14 Aug 2014
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • Bi-conjugated gradients
  • Convergence rate
  • Inexact inverse iteration
  • Krylov subspace methods
  • Preconditioning
  • Two-sided (in)exact Rayleigh quotient iteration
  • Two-sided Jacobi-Davidson method

Fingerprint Dive into the research topics of 'Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration'. Together they form a unique fingerprint.

  • Cite this