KAUST Grant NumberKUK-C1-013-04
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AbstractMastronardi 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. © 2014 Society for Industrial and Applied Mathematics.
CitationPestana J, Wathen AJ (2014) The Antitriangular Factorization of Saddle Point Matrices. SIAM Journal on Matrix Analysis and Applications 35: 339–353. Available: http://dx.doi.org/10.1137/130934933.
SponsorsThis publication was based on work supported in part by award KUK-C1-013-04 from the King Abdullah University of Science and Technology (KAUST).