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...
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| Published in | SIAM journal on matrix analysis and applications Vol. 35; no. 2; pp. 339 - 353 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Philadelphia
Society for Industrial and Applied Mathematics
01.01.2014
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| Abstract | 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. [PUBLICATION ABSTRACT] |
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| AbstractList | 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. [PUBLICATION ABSTRACT] 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. |
| Author | Pestana, J Wathen, A J |
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| CitedBy_id | crossref_primary_10_1016_j_camwa_2018_10_042 crossref_primary_10_1016_j_cma_2021_113997 crossref_primary_10_1007_s11075_015_9983_8 crossref_primary_10_1016_j_amc_2020_125263 crossref_primary_10_1016_j_laa_2018_01_034 crossref_primary_10_1016_j_apnum_2016_09_012 crossref_primary_10_1016_j_laa_2015_07_042 crossref_primary_10_1137_18M119063X crossref_primary_10_1002_nla_2103 |
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| Snippet | Mastronardi and Van Dooren [SIAM J. Matrix Anal. Appl., 34 (2013), pp. 173--196] recently introduced the block antitriangular (``Batman'') decomposition for... Mastronardi and Van Dooren [SIAM J. Matrix Anal. Appl. , 34 (2013), pp. 173--196] recently introduced the block antitriangular (``Batman'') decomposition for... |
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| SubjectTerms | Aldehydes Algorithms Blocking Eigenvalues Factorization Iterative methods Preconditioning Preserves Saddle points Simplification Transforms |
| Title | The Antitriangular Factorization of Saddle Point Matrices |
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