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Media type:
E-Article
Title:
A GEOMETRIC CONVERGENCE THEORY FOR THE PRECONDITIONED STEEPEST DESCENT ITERATION
Contributor:
NEYMEYR, KLAUS
Published:
Society for Industrial and Applied Mathematics, 2012
Published in:
SIAM Journal on Numerical Analysis, 50 (2012) 6, Seite 3188-3207
Language:
English
DOI:
10.1137/11084488X
ISSN:
0036-1429
Origination:
Footnote:
Description:
Preconditioned gradient iterations for very large eigenvalue problems are efficient solvers with growing popularity. However, only for the simplest preconditioned eigensolver, namely the preconditioned gradient iteration (or preconditioned inverse iteration) with fixed step size, are sharp nonasymptotic convergence estimates known. These estimates require a properly scaled preconditioner. In this paper a new sharp convergence estimate is derived for the preconditioned steepest descent iteration which combines the preconditioned gradient iteration with the Rayleigh-Ritz procedure for optimal line search convergence acceleration. The new estimate always improves that of the fixed-step-size iteration. The practical importance of this new estimate is that arbitrarily scaled preconditioned can be used. The Rayleigh-Ritz procedure implicitly computes the optimal scaling constant.