Title: Restrictions on implicit filtering techniques for orthogonal projection methods
Authors: De Samblanx, Gorik ×
Bultheel, Adhemar #
Issue Date: Jan-1999
Publisher: North Holland
Series Title: Linear Algebra and Its Applications vol:286 issue:1-3 pages:45-68
Abstract: We consider the class of the Orthogonal Projection Methods (OPM) to solve iteratively large eigenvalue problems. An OPM is a method that projects a large eigenvalue problem on a smaller subspace. In this subspace, an approximation of the eigenvalue spectrum can be computed from a small eigenvalue problem using a direct method. Examples of OPMs are the Arnoldi and the Davidson method. We show how an OPM can be restarted - implicitly and explicitly. This restart can be used to remove a specific subset of vectors from the approximation subspace. This is called explicit filtering. An implicit restart can also be combined with an implicit filtering step, i.e. the application of a polynomial or rational function on the subspace, even if inaccurate arithmetic is assumed. However, the condition for the implicit application of a tilter is that the rank of the residual matrix must be small. (C) 1999 Elsevier Science Inc. All rights reserved.
ISSN: 0024-3795
Publication status: published
KU Leuven publication type: IT
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
Technologiecluster ESAT Elektrotechnische Engineering
Electrical Engineering (ESAT) TC, Technology Campus De Nayer Sint-Katelijne-Waver
× corresponding author
# (joint) last author

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