The Antitriangular Factorization of Saddle Point Matrices

J. Pestana, A. J. Wathen

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


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. © 2014 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)339-353
Number of pages15
JournalSIAM Journal on Matrix Analysis and Applications
Issue number2
StatePublished - Jan 2014
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: This publication was based on work supported in part by award KUK-C1-013-04 from the King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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