Shift-splitting preconditioners for saddle point problems

Yang Cao*, Jun Du, Qiang Niu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

137 Citations (Scopus)

Abstract

In this paper, we first present a shift-splitting preconditioner for saddle point problems. The preconditioner is based on a shift-splitting of the saddle point matrix, resulting in an unconditional convergent fixed-point iteration. Based on the idea of the splitting, we further propose a local shift-splitting preconditioner. Some properties of the local shift-splitting preconditioned matrix are studied. These preconditioners extend those studied by Bai, Yin and Su for solving non-Hermitian positive definite linear systems (Bai et al., 2006). Finally, numerical experiments of a model Stokes problem are presented to show the effectiveness of the proposed preconditioners.

Original languageEnglish
Pages (from-to)239-250
Number of pages12
JournalJournal of Computational and Applied Mathematics
Volume272
DOIs
Publication statusPublished - 15 Dec 2014

Keywords

  • Convergence
  • Preconditioning
  • Saddle point problem
  • Shift-splitting

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