Abstract: Recently, some authors (Shen and Shi, 2016) studied the generalized shift- splitting (GSS) iteration method for singular saddle point problem with nonsymmetric positive definite (1,1)-block and symmetric positive semidefinite (2,2)-block. In this paper, we further apply the GSS iteration method to solve singular saddle point problem with nonsymmetric positive semidefinite (1,1)-block and symmetric positive semidefinite (2,2)-block, prove the semi-convergence of the GSS iteration method and analyze the spectral properties of the corresponding preconditioned matrix. Numerical experiment is given to indicate that the GSS iteration method with appropriate iteration parameters is effective and competitive for practical use.

Key words: Generalized shift-splitting, Semi-convergence, Positive definite matrix, Gen- eralized saddle point problems, Krylov subspace methods