Inexact inverse iteration for generalized eigenvalue problems

Gene H. Golub, Qiang Ye

Research output: Contribution to journalArticlepeer-review

56 Scopus citations


In this paper, we study an inexact inverse iteration with inner-outer iterations for solving the generalized eigenvalue problem Ax = λBx, and analyze how the accuracy in the inner iterations affects the convergence of the outer iterations. By considering a special stopping criterion depending on a threshold parameter, we show that the outer iteration converges linearly with the inner threshold parameter as the convergence rate. We also discuss the total amount of work and asymptotic equivalence between this stopping criterion and a more standard one. Numerical examples are given to illustrate the theoretical results.

Original languageEnglish
Pages (from-to)671-684
Number of pages14
JournalBIT Numerical Mathematics
Issue number4
StatePublished - Dec 2000

Bibliographical note

Funding Information:
∗Received March 1999. Communicated by Lars Eldén. †Research supported in part by National Science Foundation Grant DMS-9403899. ‡Research supported by Natural Sciences and Engineering Research Council of Canada while this author was with University of Manitoba, Winnipeg, Canada.


  • Inner-outer iterations
  • Inverse iteration
  • Shift-and-invert

ASJC Scopus subject areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics


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