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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Bibliographic Details
Published inSIAM journal on matrix analysis and applications Vol. 35; no. 2; pp. 339 - 353
Main Authors Pestana, J, Wathen, A J
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2014
Subjects
Aldehydes
Algorithms
Blocking
Eigenvalues
Factorization
Iterative methods
Preconditioning
Preserves
Saddle points
Simplification
Transforms
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Summary: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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ISSN:0895-4798
1095-7162
DOI:10.1137/130934933