Generalized Shift-Splitting Preconditioner for Saddle Point Problems with Block Three-by-Three Structure - Open Access Library Journal

OALibJ > Vol.6 No.12, December 2019

Open Access Library Journal

Volume 6, Issue 12 (December 2019)

ISSN Print: 2333-9705 ISSN Online: 2333-9721

Google-based Impact Factor: 1.18 Citations

Generalized Shift-Splitting Preconditioner for Saddle Point Problems with Block Three-by-Three Structure ()

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DOI: 10.4236/oalib.1105968 398 Downloads 1,043 Views Citations

Author(s)

Linna Wang, Ke Zhang^*

Affiliation(s)

Department of Mathematics, Shanghai Maritime University, Shanghai, China.

ABSTRACT

We propose a generalized shift-splitting iteration method for saddle point problems with block three-by-three structure. As a new iteration method, the method converges to the unique solution of the saddle point problem unconditionally. When exploited as a preconditioner, the spectral distribu-tion of the preconditioned matrix is investigated. Numerical experiments show that the new variant is efficient in speeding up GMRES for solving the block three-by-three saddle point problem.

KEYWORDS

Saddle Point Problem, Generalized Shift-Splitting, Krylov Subspace, GMRES

Share and Cite:

Wang, L. and Zhang, K. (2019) Generalized Shift-Splitting Preconditioner for Saddle Point Problems with Block Three-by-Three Structure. Open Access Library Journal, 6, 1-14. doi: 10.4236/oalib.1105968.

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