Scaling, Preconditioning, and Superlinear Convergence in GMRES-Type Iterations

A theoretical justification is found for several standard techniques related to ILU preconditioning, such as pre-scaling and pivot modification, with implications for practical implementation. An improved estimate for the reduction of the GMRES residual is obtained within the general framework of tw...

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Bibliographic Details
Published inMatrix Methods: Theory, Algorithms And Applications pp. 273 - 295
Main Author Kaporin, Igor
Format Book Chapter
LanguageEnglish
Published WORLD SCIENTIFIC 01.04.2010
Subjects
Matrices and Algorithms
two-side scaling
incomplete LU preconditioning
unsymmetric sparse matrix
superlinear convergence
two-stage preconditioning
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ISBN9812836020
9789812836014
9812836012
9814469556
9789812836021
9789814469555
DOI10.1142/9789812836021_0018

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Summary:A theoretical justification is found for several standard techniques related to ILU preconditioning, such as pre-scaling and pivot modification, with implications for practical implementation. An improved estimate for the reduction of the GMRES residual is obtained within the general framework of two-stage preconditioning. In particular, an estimate in terms of a conditioning measure of the scaled coefficient matrix and the Frobenius norm of the scaled ILU residual is presented.
ISBN:9812836020
9789812836014
9812836012
9814469556
9789812836021
9789814469555
DOI:10.1142/9789812836021_0018