Inexact inverse subspace iteration for generalized eigenvalue problems

Qiang Ye, Ping Zhang

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


n this paper, we present an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax=λBx. We first formulate a version of inexact inverse subspace iteration in which the approximation from one step is used as an initial approximation for the next step. We then analyze the convergence property, which relates the accuracy in the inner iteration to the convergence rate of the outer iteration. In particular, the linear convergence property of the inverse subspace iteration is preserved. Numerical examples are given to demonstrate the theoretical results.

Original languageEnglish
Pages (from-to)1697-1715
Number of pages19
JournalLinear Algebra and Its Applications
Issue number7
StatePublished - Apr 1 2011

Bibliographical note

Funding Information:
URL:∼qye (Q. Ye). 1 Supported in part by NSF under Grant DMS-0915062. 2 Current Address: Microscape Technology Co., Ltd., No. 80, The 4th Avenue, TEDA, Tianjin 300457, China.


  • Eigenvalue problem
  • Inexact inverse iteration
  • Inner-outer iteration
  • Subspace iteration

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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