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...

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Autors principals: Pestana, J, Wathen, A
Format: Journal article
Publicat: Society for Industrial and Applied Mathematics 2014
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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
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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
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AT wathena theantitriangularfactorizationofsaddlepointmatrices
AT pestanaj antitriangularfactorizationofsaddlepointmatrices
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