广义鞍点问题的改进的类SOR算法

AN IMPROVED SOR-TYPE ALGORITHM FOR SLOVING GENERALIZED SADDLE-POINT PROBLEMS

针对广义鞍点问题,本文提出了一个改进的类逐次超松弛迭代算法,在较弱的条件下,分析了算法的收敛性及线性收敛率.新算法的每步计算量与已有的算法类似,都是需要(近似)求解线性方程组,但新算法有更好的灵活度通过合适地选取参数矩阵,每一步子问题可以容易地求解,甚至可以有闭式解(closed-form solution).数值实验结果显示了新算法的有效性.

For the generalized saddle point problem,we develop an improved class of successive over relaxation algorithms.Under mild conditions,we prove its convergence and establish its linear rate of convergence.While,as the classical methods,it needs to solve some linear system of equations approximately to get the next iterate,the flexibility in choosing the involved matrices makes the subproblems easy or even to have closed form solutions,which leads the algorithm to be an efficient one.Preliminary numerical results show the effectiveness of the new method.