New local generalized shift-splitting preconditioners for saddle point problems

Si-Tao Ling and Qing-Bing Liu

Applied Mathematics and Computation, 2017, vol. 302, issue C, 58-67

Abstract: Based on a local generalized shift-splitting of the saddle point matrix with symmetric positive definite (1, 1)-block and symmetric positive semidefinite (2, 2)-block, a new local generalized shift-splitting preconditioner with two shift parameters for solving saddle point problems is proposed. The preconditioner is extracted from a new local generalized shift-splitting iteration and can lead to the unconditional convergence of the iteration. In addition, we consider solving the saddle point systems by preconditioned Krylov subspace methods and discuss some properties of the preconditioned saddle point matrix with a deteriorated preconditioner, such as eigenvalues, eigenvectors, and degree of the minimal polynomial. Numerical experiments arising from a finite element discretization model of the Stokes problem are given to validate the effectiveness of the proposed preconditioner.

Keywords: Saddle point problem; Local generalized shift-splitting; Preconditioner; Convergence; Symmetric positive definite (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:302:y:2017:i:c:p:58-67

DOI: 10.1016/j.amc.2017.01.014

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