On choice of preconditioner for minimum residual methods for nonsymmetric matrices
Existing convergence bounds for Krylov subspace methods such as GMRES for nonsymmetric linear systems give little mathematical guidance for the choice of preconditioner. Here, we establish a desirable mathematical property of a preconditioner which indicates when convergence of a minimum residual me...
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| Format: | Report |
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SIMAX
2011
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| _version_ | 1826267906655125504 |
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| author | Pestana, J Wathen, A |
| author_facet | Pestana, J Wathen, A |
| author_sort | Pestana, J |
| collection | OXFORD |
| description | Existing convergence bounds for Krylov subspace methods such as GMRES for nonsymmetric linear systems give little mathematical guidance for the choice of preconditioner. Here, we establish a desirable mathematical property of a preconditioner which indicates when convergence of a minimum residual method will essentially depend only on the eigenvalues of the preconditioned system, as is true in the symmetric case. Our theory covers the generic case of nonsymmetric coefficient matrices which are diagonalisable over C; it does not cover matrices with nontrivial Jordan form. |
| first_indexed | 2024-03-06T21:01:27Z |
| format | Report |
| id | oxford-uuid:3b0185c0-63ba-47c7-9aad-5b03d19d54cc |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:01:27Z |
| publishDate | 2011 |
| publisher | SIMAX |
| record_format | dspace |
| spelling | oxford-uuid:3b0185c0-63ba-47c7-9aad-5b03d19d54cc2022-03-26T14:05:02ZOn choice of preconditioner for minimum residual methods for nonsymmetric matricesReporthttp://purl.org/coar/resource_type/c_93fcuuid:3b0185c0-63ba-47c7-9aad-5b03d19d54ccMathematical Institute - ePrintsSIMAX2011Pestana, JWathen, AExisting convergence bounds for Krylov subspace methods such as GMRES for nonsymmetric linear systems give little mathematical guidance for the choice of preconditioner. Here, we establish a desirable mathematical property of a preconditioner which indicates when convergence of a minimum residual method will essentially depend only on the eigenvalues of the preconditioned system, as is true in the symmetric case. Our theory covers the generic case of nonsymmetric coefficient matrices which are diagonalisable over C; it does not cover matrices with nontrivial Jordan form. |
| spellingShingle | Pestana, J Wathen, A On choice of preconditioner for minimum residual methods for nonsymmetric matrices |
| title | On choice of preconditioner for minimum residual methods for nonsymmetric matrices |
| title_full | On choice of preconditioner for minimum residual methods for nonsymmetric matrices |
| title_fullStr | On choice of preconditioner for minimum residual methods for nonsymmetric matrices |
| title_full_unstemmed | On choice of preconditioner for minimum residual methods for nonsymmetric matrices |
| title_short | On choice of preconditioner for minimum residual methods for nonsymmetric matrices |
| title_sort | on choice of preconditioner for minimum residual methods for nonsymmetric matrices |
| work_keys_str_mv | AT pestanaj onchoiceofpreconditionerforminimumresidualmethodsfornonsymmetricmatrices AT wathena onchoiceofpreconditionerforminimumresidualmethodsfornonsymmetricmatrices |