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A note on Inverse Iteration
Author(s) -
Neymeyr Klaus
Publication year - 2005
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/nla.388
Subject(s) - rayleigh quotient iteration , mathematics , iterated function , inverse , quotient , rayleigh quotient , power iteration , sequence (biology) , descent (aeronautics) , matrix (chemical analysis) , convergence (economics) , positive definite matrix , iterative method , combinatorics , mathematical optimization , mathematical analysis , geometry , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , biology , economic growth , engineering , economics , composite material , genetics , aerospace engineering
Inverse iteration, if applied to a symmetric positive definite matrix, is shown to generate a sequence of iterates with monotonously decreasing Rayleigh quotients. We present sharp bounds from above and from below which highlight inverse iteration as a descent scheme for the Rayleigh quotient. Such estimates provide the background for the analysis of the behaviour of the Rayleigh quotient in certain approximate variants of inverse iteration. Copyright © 2004 John Wiley & Sons, Ltd.