On Parameterized Generalized Skew-Hermitian Triangular Splitting Iteration Method For Singular And Nonsingular Saddle Point Problems

In many computation science and engineering applications, we need to solve a class of large linear system, which are of the saddle point structure. To solve the saddle point problem effectively, Krukier et al.and Dou et al.have proposed a generalized skew-Hermitian triangular splitting (GSTS) iteration method for the nonsingular saddle point problems. In this paper, we further extend the GSTS method to a parameterized GSTS (PGSTS) method for solving the non-Hermitian nonsingular and singular saddle point problems. By using singular value decompo-sition 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 experi-ments are provided, which further confirm our theoretical results and show that the new method is feasible and effective for the non-Hermitian nonsingular and singular saddle point problems.