An Inexact Inverse Iteration for Large Sparse Eigenvalue Problems

Yu Ling Lai*, Kun Yi Lin, Wen-Wei Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)425-437
Number of pages13
JournalNumerical Linear Algebra with Applications
Volume4
Issue number5
DOIs
StatePublished - 1 Jan 1997

Keywords

  • Inexact inverse iteration
  • Large eigenvalue problem
  • Linear convergence

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