TITLE:
Generalized Shift-Splitting Preconditioner for Saddle Point Problems with Block Three-by-Three Structure
AUTHORS:
Linna Wang, Ke Zhang
KEYWORDS:
Saddle Point Problem, Generalized Shift-Splitting, Krylov Subspace, GMRES
JOURNAL NAME:
Open Access Library Journal,
Vol.6 No.12,
December
25,
2019
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.