On semi-convergence of the generalized shift-splitting iteration method for singular nonsymmetric saddle point problems

Recently, a class of generalized shift-splitting iteration methods were proposed for solving nonsingular nonsymmetric saddle point problems (Cao et al., 2015). In this paper, the generalized shift-splitting iteration method is extended to solve singular nonsymmetric saddle point problems. Semi-convergence of the generalized shift-splitting iteration method is carefully analyzed, which shows that the iterative sequence generated by the generalized shift-splitting iteration method converges to a solution of the singular saddle point problem unconditionally. Numerical results verify the robustness and efficiency of the generalized shift-splitting iteration method.