关键词: 鞍点问题, 迭代法, HS分裂, SOR方法, 收敛

Abstract: Saddle point problems exist in many engineering research areas such as fluid mechanics， electromagnetism， optimization problems， the least squares problems， elliptic partial differential equations， and etc. Based on SOR-Like methods in combination of the concept of HS splitting， a new iteration splitting improvement method was presented so as to apply the classic saddle point solutions to special saddle point problems. Then， the MSOR-Like method was proposed to handle the above special saddle point system containing asymmetric blocks， and the convergence analysis as well as the selection of optimal relaxation parameters were also given. Finally， a numerical example was given to verify different optimal matrix of the modified SOR method， and it was found that the only difference is in the convergence rate while there is no difference in the convergence effect. Furthermore， under the same calculation accuracy， the modified SOR method for solving the special saddle point problems is better than the conventional methods in solving the classical saddle point problems.

Key words: saddle point problem, iterative method, Hermitian and Skew-Hermitian (HS) splitting, SOR method, convergence