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Successive eigenvalue relaxation: a new method for the generalized eigenvalue problem and convergence estimates

Ovtchinnikov, Evgueni and Xanthis, Leonidas (2001) Successive eigenvalue relaxation: a new method for the generalized eigenvalue problem and convergence estimates. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 457 (2006). pp. 441-451. ISSN 1364-5021

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Official URL: http://dx.doi.org/10.1098/rspa.2000.0674

Abstract

We present a new subspace iteration method for the efficient computation of several smallest eigenvalues of the generalized eigenvalue problem Au = lambda Bu for symmetric positive definite operators A and B. We call this method successive eigenvalue relaxation, or the SER method (homoechon of the classical successive over-relaxation, or SOR method for linear systems). In particular, there are two significant features of SER which render it computationally attractive: (i) it can effectively deal with preconditioned large-scale eigenvalue problems, and (ii) its practical implementation does not require any information about the preconditioner used: it can routinely accommodate sophisticated preconditioners designed to meet more exacting requirements (e.g. three-dimensional elasticity problems with small thickness parameters). We endow SER with theoretical convergence estimates allowing for multiple and clusters of eigenvalues and illustrate their usefulness in a numerical example for a discretized partial differential equation exhibiting clusters of eigenvalues.

Item Type:Article
Additional Information:Online ISSN 1471-2946
Uncontrolled Keywords:large-scale eigenvalue problems, eigensolvers with preconditioning, subspace iteration, convergence rate, multiple and clustered eigenvalues
Research Community:University of Westminster > Electronics and Computer Science, School of
ID Code:529
Deposited On:26 Sep 2005
Last Modified:11 Aug 2010 15:29

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