鞍点问题的修正对称超松弛迭代算法

为了提高求解鞍点问题的迭代算法的速度,通过设置合适的加速变量,对修正超松弛迭代算法（简记作MSOR-like算法）和广义对称超松弛迭代算法（简记作GSSOR-like算法）进行了修正,给出了修正对称超松弛迭代算法,即MSSOR-like （modified symmetric successiveover-relaxation）算法,并研究了该算法收敛的充分必要条件.最后,通过数值例子表明,选择合适的参数后,新算法的迭代速度和迭代次数均优于MSOR-like （modified successive overrelaxation）和GSSOR-like （generalized symmetric successive over-relaxation）算法,因此,它是一种较好的解决鞍点问题的算法.

MSSOR-like method for saddle point problems

In order to speed up iterative methods for solving the saddle point problems, the modified successive over-relaxation （MSOR-like） method and the generalized symmetric successive over-relaxation （GSSOR-like） method are modi- fied by setting up appropriate accelerating parameters, and a new iterative method which is called as the modified symmetric successive over-relaxation （MSSOR-like） method is presented. Then, the convergence conditions of this method are dis- cussed. Numerical results show that the iteration speed of the MSSOR-like method is improved significantly with the other proposed methods, and the new method needs less iterations, which indicates that the MSSOR-like method is much more effective than the MSOR-like and GSSOR-like methods.