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.
|Number of pages||14|
|Journal||BIT Numerical Mathematics|
|State||Published - Dec 2000|
Bibliographical noteFunding 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
ASJC Scopus subject areas
- Computer Networks and Communications
- Computational Mathematics
- Applied Mathematics