Cluster robustness of preconditioned gradient subspace iteration eigensolvers

Ovtchinnikov, E. 2006. Cluster robustness of preconditioned gradient subspace iteration eigensolvers. Linear Algebra and its Applications. 415 (1), pp. 140-166.

TitleCluster robustness of preconditioned gradient subspace iteration eigensolvers
AuthorsOvtchinnikov, E.
Abstract

The paper presents convergence estimates for a class of iterative methods for solving partial generalized symmetric eigenvalue problems whereby a sequence of subspaces containing approximations to eigenvectors is generated by combining the Rayleigh-Ritz and the preconditioned steepest descent/ascent methods. The paper uses a novel approach of studying the convergence of groups of eigenvalues, rather than individual ones, to obtain new convergence estimates for this class of methods that are cluster robust, i.e. do not involve distances between computed eigenvalues.

KeywordsSelf-adjoint eigenvalue problem, Steepest descent/ascent method, Conjugate gradient method, Preconditioning, Convergence estimates, Clustered eigenvalues
JournalLinear Algebra and its Applications
Journal citation415 (1), pp. 140-166
ISSN0024-3795
YearMay 2006
Digital Object Identifier (DOI)doi:10.1016/j.laa.2005.06.039
Publication dates
PublishedMay 2006

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