BIT Numerical Mathematics

, Volume 40, Issue 4, pp 671–684

Inexact Inverse Iteration for Generalized Eigenvalue Problems

  • Gene H. Golub
  • Qiang Ye

DOI: 10.1023/A:1022388317839

Cite this article as:
Golub, G.H. & Ye, Q. BIT Numerical Mathematics (2000) 40: 671. doi:10.1023/A:1022388317839


In this paper, we study an inexact inverse iteration with inner-outer iterations for solving the generalized eigenvalu 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.

Inverse iterationshift-and-invertinner-outer iterations

Copyright information

© Swets & Zeitlinger 2000

Authors and Affiliations

  • Gene H. Golub
    • 1
  • Qiang Ye
    • 2
  1. 1.Department of Computer ScienceStanford UniversityStanfordUSA.
  2. 2.Department of MathematicsUniversity of KentuckyLexingtonUSA.