The antitriangular factorisation of saddle point matrices

Jennifer Pestana, Andrew Wathen

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Abstract

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.
Original languageEnglish
Pages (from-to)339–353
Number of pages15
JournalSIAM Journal on Matrix Analysis and Applications
Volume35
DOIs
Publication statusPublished - 1 Apr 2014

Keywords

  • block antitriangluar preconditioner
  • Batman
  • convergence
  • eigenvalues
  • eigenvectors
  • iterative method
  • saddle point system

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