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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| Published in | Matrix Methods: Theory, Algorithms And Applications pp. 273 - 295 |
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| Main Author | |
| Format | Book Chapter |
| Language | English |
| Published |
WORLD SCIENTIFIC
01.04.2010
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| Subjects | |
| Online Access | Get full text |
| ISBN | 9812836020 9789812836014 9812836012 9814469556 9789812836021 9789814469555 |
| DOI | 10.1142/9789812836021_0018 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Kaporin, Igor |
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| DOI | 10.1142/9789812836021_0018 |
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| Editor | Olshevsky, Vadim Tyrtyshnikov, Eugene |
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| Keywords | two-side scaling incomplete LU preconditioning unsymmetric sparse matrix superlinear convergence two-stage preconditioning |
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| Snippet | A theoretical justification is found for several standard techniques related to ILU preconditioning, such as pre-scaling and pivot modification, with... |
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| StartPage | 273 |
| SubjectTerms | Matrices and Algorithms |
| Title | Scaling, Preconditioning, and Superlinear Convergence in GMRES-Type Iterations |
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