On Single Precision Preconditioners for Krylov Subspace Iterative Methods

Large sparse linear systems Ax= b arise in many scientific applications. Krylov subspace iterative methods are often used for solving such linear systems. Preconditioning techniques are efficient to reduce the number of iterations of Krylov subspace methods. The coefficient matrix of the linear syst...

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Bibliographic Details
Published inLarge-Scale Scientific Computing pp. 721 - 728
Main Authors Tadano, Hiroto, Sakurai, Tetsuya
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 2008
SeriesLecture Notes in Computer Science
Subjects
Double Precision Arithmetic
Krylov Subspace
Krylov Subspace Method
Single Precision
Sparse Approximate Inverse
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Summary:Large sparse linear systems Ax= b arise in many scientific applications. Krylov subspace iterative methods are often used for solving such linear systems. Preconditioning techniques are efficient to reduce the number of iterations of Krylov subspace methods. The coefficient matrix of the linear system is transformed into MA or AM in the left or right preconditioning, where M is a preconditioning matrix. In this paper, we analyze the influence of perturbation in the computation of preconditioning of Krylov subspace methods. We show that the perturbation of preconditioner does not affect the accuracy of the approximate solution when the right preconditioning is used. Some numerical experiments illustrate the influence of preconditioners with single precision arithmetic.
ISBN:9783540788256
3540788255
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-540-78827-0_83