Modified unsymmetric SOR method for saddle-point problems

In this paper, we propose a modified unsymmetric SOR (MUSOR) method for solving singular or nonsingular saddle-point problem, which is an extension of the SSOR iteration method. For the MUSOR method, we prove its convergence for solving nonsingular saddle-point problem and semi-convergence for solving singular saddle-point problem under suitable conditions. Moreover, we study the choices of the optimal parameters. Numerical experiments are presented, which support our theoretical results and reveal that the new method is effective and feasible for solving both singular and nonsingular saddle-point problems.