On iterative methods and implicit-factorization preconditioners for regularized saddle-point systems
We consider conjugate-gradient like methods for solving block symmetric indefinite linear systems that arise from saddle point problems or, in particular, regularizations thereof. Such methods require preconditioners that preserve certain sub-blocks from the original systems but allow considerable f...
| Auteurs principaux: | , , , |
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| Format: | Report |
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Unspecified
2005
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| _version_ | 1826269816705515520 |
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| author | Dollar, H Gould, N Schilders, W Wathen, A |
| author_facet | Dollar, H Gould, N Schilders, W Wathen, A |
| author_sort | Dollar, H |
| collection | OXFORD |
| description | We consider conjugate-gradient like methods for solving block symmetric indefinite linear systems that arise from saddle point problems or, in particular, regularizations thereof. Such methods require preconditioners that preserve certain sub-blocks from the original systems but allow considerable flexibility for the remaining blocks. We construct fourteen families of implicit factorizations that are capable of reproducing the required sub-blocks and (some) of the remainder. These generalize known implicit factorizations for the unregularized case. Improved eigenvalue clustering is possible if additionally some of the non-crucial blocks are reproduced. Numerical experiments confirm that these implicit-factorization preconditioners can be very effective in practice. |
| first_indexed | 2024-03-06T21:31:04Z |
| format | Report |
| id | oxford-uuid:44b2c52a-0fa2-4a0d-b485-f4affd4d18f1 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:31:04Z |
| publishDate | 2005 |
| publisher | Unspecified |
| record_format | dspace |
| spelling | oxford-uuid:44b2c52a-0fa2-4a0d-b485-f4affd4d18f12022-03-26T15:03:14ZOn iterative methods and implicit-factorization preconditioners for regularized saddle-point systemsReporthttp://purl.org/coar/resource_type/c_93fcuuid:44b2c52a-0fa2-4a0d-b485-f4affd4d18f1Mathematical Institute - ePrintsUnspecified2005Dollar, HGould, NSchilders, WWathen, AWe consider conjugate-gradient like methods for solving block symmetric indefinite linear systems that arise from saddle point problems or, in particular, regularizations thereof. Such methods require preconditioners that preserve certain sub-blocks from the original systems but allow considerable flexibility for the remaining blocks. We construct fourteen families of implicit factorizations that are capable of reproducing the required sub-blocks and (some) of the remainder. These generalize known implicit factorizations for the unregularized case. Improved eigenvalue clustering is possible if additionally some of the non-crucial blocks are reproduced. Numerical experiments confirm that these implicit-factorization preconditioners can be very effective in practice. |
| spellingShingle | Dollar, H Gould, N Schilders, W Wathen, A On iterative methods and implicit-factorization preconditioners for regularized saddle-point systems |
| title | On iterative methods and implicit-factorization preconditioners for regularized saddle-point systems |
| title_full | On iterative methods and implicit-factorization preconditioners for regularized saddle-point systems |
| title_fullStr | On iterative methods and implicit-factorization preconditioners for regularized saddle-point systems |
| title_full_unstemmed | On iterative methods and implicit-factorization preconditioners for regularized saddle-point systems |
| title_short | On iterative methods and implicit-factorization preconditioners for regularized saddle-point systems |
| title_sort | on iterative methods and implicit factorization preconditioners for regularized saddle point systems |
| work_keys_str_mv | AT dollarh oniterativemethodsandimplicitfactorizationpreconditionersforregularizedsaddlepointsystems AT gouldn oniterativemethodsandimplicitfactorizationpreconditionersforregularizedsaddlepointsystems AT schildersw oniterativemethodsandimplicitfactorizationpreconditionersforregularizedsaddlepointsystems AT wathena oniterativemethodsandimplicitfactorizationpreconditionersforregularizedsaddlepointsystems |