求解鞍点问题的修正SOR-like方法  

Modified SOR-like Method for Solution to Saddle Point Problem

作　　者：沈海龙[1] 邵新慧[1] 张铁[1] 李长军[1] 

机构地区：[1]东北大学理学院,辽宁沈阳110004

出　　处：《东北大学学报（自然科学版）》2009年第6期905-908,共4页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(10771031);教育部高校骨干教师基金资助项目

摘　　要：针对大型稀疏鞍点问题给出了一种含有待定参数的新迭代解法,称之为修正SOR-like方法,简记为MPSOR-like方法.该迭代法的构成是基于对系数矩阵进行的一种分裂.迭代法需要选择一个预处理矩阵和待定参数,通过适当选取预处理矩阵和待定参数,新迭代法是收敛的,并且以定理的形式给出了新迭代方法的迭代矩阵的特征值和参数之间的基本等式,从而也导出了迭代法收敛的充分和必要条件.理论结果表明新方法更具有广泛性,并且选择适当的参数可以使新方法较SOR-like方法具有更快的收敛速度.给出了迭代法的数值试验结果.A new iterative solution with undetermined parameters is proposed to solve the problem of large-scale sparse saddle point, i.e. the modified SOR-like method or MPSOR-like method. Based on a splitting for the matrix of coefficients, the iteration method needs the choices of a pretreated matrix and undetermined parameters. After the choices were done, the iteration method proposed becomes convergent in form of theorem, thus giving a basic equality between the eigenvalue of iterative matrix and the parameters, with the sufficient and necessary conditions deduced for the convergence of the iteration method. The new method shows theoretically that it is more extensive with quicker convergence rate than the SOR-like method if the parameters is chosen properly. An experimental result of the iteration method is given numerically.

关 键 词：鞍点 迭代法 对称正定矩阵 SOR—like方法 MPSOR—like方法 

分 类 号：O241[理学—计算数学]