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An inexact inverse iteration for large sparse eigenvalue problems
Author(s) -
Lai YuLing,
Lin KunYi,
Lin WenWei
Publication year - 1997
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/(sici)1099-1506(199709/10)4:5<425::aid-nla117>3.0.co;2-g
Subject(s) - inverse iteration , mathematics , eigenvalues and eigenvectors , power iteration , inverse , rayleigh quotient iteration , convergence (economics) , computation , preconditioner , matrix (chemical analysis) , iterative method , arnoldi iteration , eigendecomposition of a matrix , mathematical optimization , algorithm , physics , geometry , materials science , quantum mechanics , economics , composite material , economic growth
In this paper, we propose an inverse inexact 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. © 1997 John Wiley & Sons, Ltd.