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: 0.73 Citations

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

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DOI: 10.4236/oalib.1105968 324 Downloads 900 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.

Cited by

[1]	A simplified relaxed alternating positive semi-definite splitting preconditioner for saddle point problems with three-by-three block structure
	Journal of Applied Mathematics and Computing, 2023

[2]	Lopsided shift-splitting preconditioner for saddle point problems with three-by-three structure
	Computational and Applied Mathematics, 2022

[3]	Semi-convergence of the APSS method for a class of nonsymmetric three-by-three singular saddle point problems
	arXiv preprint arXiv:2208.00814, 2022

[4]	An alternating positive semidefinite splitting preconditioner for the three-by-three block saddle point problems
	2021

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