On unsymmetric block overrelaxation-type methods for saddle point problems

The unsymmetric block overrelaxation-type (UBOR-type) method is proposed to attack saddle point problems in this paper. The convergence and the optimal parameters for the method are studied when the iteration parameters satisfy some relationship. Theoretical analyses show that the UBOR-type method has faster asymptotic convergence rate than the SOR-like method and its convergence rate can reach the same as that of the GSOR method at least. Numerical experiments support our theoretical results. Moveover, the numerical results further reveal that the new method can be much more effective than the GSOR method in terms of iteration steps.