Semi-convergence analysis of the GSS iteration methods for singular saddle point problems

In this paper, we use the generalized shift-splitting (GSS) iteration method to solve nonsymmetric singular saddle point systems with the symmetric positive (semi-)definite (1,1) sub-block and symmetric positive semi-definite (2,2) sub-block, and prove the semi-convergence of the GSS iteration method. Numerical experiments are presented to investigate the correctness of the theoretical analyses and the feasibility of the GSS iteration method.