Accelerating the Induced Dimension Reduction method using spectral information
article
The Induced Dimension Reduction method (IDR(s)) (Sonneveld and van Gijzen, 2008) is a short-recurrences Krylov method to solve systems of linear equations. In this work, we accelerate this method using spectral information. We construct a Hessenberg relation from the IDR(s) residual recurrences formulas, from which we approximate the eigenvalues and eigenvectors. Using the Ritz values, we propose a self-contained variant of the Ritz-IDR(s) method (Simoncini and Szyld, 2010) for solving a system of linear equations. In addition, the Ritz vectors are used to speed-up IDR(s) for the solution of sequence of systems of linear equations. © 2018 Elsevier B.V.
Topics
Eigenvalues and eigenvectorsInduced Dimension Reduction methodSequence of systems of linear equationEigenvalues and eigenfunctionsInformation useDimension reduction methodEigenvalues and eigenvectorsKrylov methodRitz valuesShort recurrencesSpectral informationSystem of linear equationsLinear equations
TNO Identifier
820468
ISSN
03770427
Source
Journal of Computational and Applied Mathematics, 345, pp. 33-47.
Pages
33-47
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