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An Iterative Technique for Construction of Invariant Subspaces
Author(s) -
Zítko Jan,
Ulrychová Iveta
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510374
Subject(s) - preconditioner , linear subspace , eigenvalues and eigenvectors , invariant subspace , invariant (physics) , generalized minimal residual method , mathematics , subspace topology , linear system , iterative method , polynomial , algebra over a field , pure mathematics , algorithm , mathematical analysis , physics , quantum mechanics , mathematical physics
The restarted GMRES( m ) method for solving linear systems Ax = b is attractive when a good preconditioner is available. The determining of efficient preconditioners is often connected to a construction of an A –invariant subspace corresponding to eigenvalues closest to zero. One class of methods for determination of invariant subspaces is based on the construction of polynomial filters. We study the usage of Tchebychev polynomials for constructing suitable filters. Applying filters on the initial restart vectors amplifies the components of eigenvectors belonging to the small (wanted) eigenvalues and damp the remaining (unwanted) components. The presented convergence theorem describes the repeated application of filters for the construction of the wanted eigenspace of the matrix A . (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)