On semi-convergence of a class of relaxation methods for singular saddle point problems

Recently, a class of efficient relaxation iterative methods has been proposed to solve the nonsingular saddle point problems. In this paper, we further prove the semi-convergence of these methods when it is applied to solve the singular saddle point problems. The semi-convergence properties of the relaxation iteration methods are carefully analyzed, which show that the iterative sequence generated by the relaxation iterative methods converges to a solution of the singular saddle point problem under suitable restrictions on the involved iteration parameters. In addition, numerical experiments are used to show the feasibility and effectiveness of the relaxation iterative methods for solving singular saddle point problems.