Backward perturbation analysis and residual-based error bounds for the linear response eigenvalue problem

Lei Hong Zhang, Wen-Wei Lin, Ren Cang Li*

*Corresponding author for this work

Research output: Contribution to journalArticle

8 Scopus citations

Abstract

The numerical solution of a large scale linear response eigenvalue problem is often accomplished by computing a pair of deflating subspaces associated with the interesting part of the spectrum. This paper is concerned with the backward perturbation analysis for a given pair of approximate deflating subspaces or an approximate eigenquadruple. Various optimal backward perturbation bounds are obtained, as well as bounds for approximate eigenvalues computed through the pair of approximate deflating subspaces or approximate eigenquadruple. These results are reminiscent of many existing classical ones for the standard eigenvalue problem.

Original languageEnglish
Pages (from-to)869-896
Number of pages28
JournalBIT Numerical Mathematics
Volume55
Issue number3
DOIs
StatePublished - 30 Sep 2015

Keywords

  • Backward perturbation
  • Deflating subspace
  • Eigenvalue approximation
  • Error bound
  • Linear response eigenvalue problem
  • Rayleigh–Ritz approximation

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