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An inexact inverse iteration for large sparse eigenvalue problems

✍ Scribed by Yu-Ling Lai; Kun-Yi Lin; Wen-Wei Lin

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 111 KB
Volume: 4
Category: Article
ISSN: 1070-5325
DOI: 10.1002/(sici)1099-1506(199709/10)4:5<425::aid-nla117>3.0.co;2-g

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✦ Synopsis

In this paper, we propose an inexact inverse iteration method for the computation of the eigenvalue with the smallest modulus and its associated eigenvector for a large sparse matrix. The linear systems of the traditional inverse iteration are solved with accuracy that depends on the eigenvalue with the second smallest modulus and iteration numbers. We prove that this approach preserves the linear convergence of inverse iteration. We also propose two practical formulas for the accuracy bound which are used in actual implementation.

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