The antitriangular factorization of saddle point matrices
Mastronardi and Van Dooren [SIAM J. Matrix Anal. Appl., 34 (2013), pp. 173–196] recently introduced the block antitriangular (“Batman”) decomposition for symmetric indefinite matrices. Here we show the simplification of this factorization for saddle point matrices and demonstrate how it represents t...
| Egile Nagusiak: | , |
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| Formatua: | Journal article |
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Society for Industrial and Applied Mathematics
2014
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| _version_ | 1826268197810077696 |
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| author | Pestana, J Wathen, A |
| author_facet | Pestana, J Wathen, A |
| author_sort | Pestana, J |
| collection | OXFORD |
| description | Mastronardi and Van Dooren [SIAM J. Matrix Anal. Appl., 34 (2013), pp. 173–196] recently introduced the block antitriangular (“Batman”) decomposition for symmetric indefinite matrices. Here we show the simplification of this factorization for saddle point matrices and demonstrate how it represents the common nullspace method. We show that rank-1 updates to the saddle point matrix can be easily incorporated into the factorization and give bounds on the eigenvalues of matrices important in saddle point theory. We show the relation of this factorization to constraint preconditioning and how it transforms but preserves the structure of block diagonal and block triangular preconditioners |
| first_indexed | 2024-03-06T21:05:58Z |
| format | Journal article |
| id | oxford-uuid:3c76a726-19e8-402f-a25b-95ec2ac8cce2 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:05:58Z |
| publishDate | 2014 |
| publisher | Society for Industrial and Applied Mathematics |
| record_format | dspace |
| spelling | oxford-uuid:3c76a726-19e8-402f-a25b-95ec2ac8cce22022-03-26T14:13:46ZThe antitriangular factorization of saddle point matricesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3c76a726-19e8-402f-a25b-95ec2ac8cce2Symplectic Elements at OxfordSociety for Industrial and Applied Mathematics2014Pestana, JWathen, AMastronardi and Van Dooren [SIAM J. Matrix Anal. Appl., 34 (2013), pp. 173–196] recently introduced the block antitriangular (“Batman”) decomposition for symmetric indefinite matrices. Here we show the simplification of this factorization for saddle point matrices and demonstrate how it represents the common nullspace method. We show that rank-1 updates to the saddle point matrix can be easily incorporated into the factorization and give bounds on the eigenvalues of matrices important in saddle point theory. We show the relation of this factorization to constraint preconditioning and how it transforms but preserves the structure of block diagonal and block triangular preconditioners |
| spellingShingle | Pestana, J Wathen, A The antitriangular factorization of saddle point matrices |
| title | The antitriangular factorization of saddle point matrices |
| title_full | The antitriangular factorization of saddle point matrices |
| title_fullStr | The antitriangular factorization of saddle point matrices |
| title_full_unstemmed | The antitriangular factorization of saddle point matrices |
| title_short | The antitriangular factorization of saddle point matrices |
| title_sort | antitriangular factorization of saddle point matrices |
| work_keys_str_mv | AT pestanaj theantitriangularfactorizationofsaddlepointmatrices AT wathena theantitriangularfactorizationofsaddlepointmatrices AT pestanaj antitriangularfactorizationofsaddlepointmatrices AT wathena antitriangularfactorizationofsaddlepointmatrices |