On parameterized generalized skew-Hermitian triangular splitting iteration method for singular and nonsingular saddle point problems

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摘要

Recently, Krukier et al. (2014) and Dou et al. (2014) have studied the generalized skew-Hermitian triangular splitting (GSTS) iteration method for nonsingular and singular saddle point problems, respectively. In this paper, we further extend the GSTS method to a parameterized GSTS (PGSTS) method for solving non-Hermitian nonsingular and singular saddle point problems. By singular value decomposition technique, we derive conditions of the new iterative method for guaranteeing the convergence for non-Hermitian nonsingular saddle point problems and its semi-convergence for singular saddle point problems, respectively. In addition, the choice of the acceleration parameters in a practical manner is studied. Numerical experiments are provided, which further confirm our theoretical results and show the new method is feasible and effective for non-Hermitian nonsingular or singular saddle point problems.

论文关键词:Saddle point problems,Semi-convergence,Convergence,GSTS iteration method,Matrix splitting

论文评审过程:Available online 22 January 2015.

论文官网地址:https://doi.org/10.1016/j.amc.2014.12.120