The antitriangular factorization of saddle point matrices

Journal article

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

Authors: Pestana, J; Wathen, A

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Society for Industrial and Applied Mathematics
• Journal: SIAM Journal on Matrix Analysis and Applications
• Volume: 35
• Issue: 2
• Pages: 339-353
• Publication date: 2014-04-01
• Acceptance date: 2014-01-28
• DOI: 10.1137/130934933
• EISSN: 1095-7162
• ISSN: 0895-4798
• Keywords: block triangular preconditioner; eigenvectors; iterative method; SBTMR; saddle point system; eigenvalues; convergence