求解线性系统的广义二阶段多分裂迭代法的收敛性  

Convergence of generalized two-stage multisplitting iteration methods for linear systems

作　　者：温瑞萍[1] 任孚鲛[1] 闫喜红[1] 

机构地区：[1]太原师范学院数学系,太原030012

出　　处：《应用数学与计算数学学报》2013年第3期382-393,共12页Communication on Applied Mathematics and Computation

基　　金：Project supported by the National Natural Science Foundation of China(11071184);the National Natural Science Foundation of Shanxi Province of China(2012011015-6)

摘　　要：一般二阶段多分裂迭代法的权矩阵都是预先给出的,在迭代过程中并不知道它的优劣.提出了广义的二阶段多分裂迭代法,它的加权矩阵不必预先给出,而是在迭代过程中通过求超平面上的最优解而得出的随迭代步数变化的动态的权矩阵.这样,动态的权矩阵能使得第k步的近似解更加逼近问题的真解.文中建立了新方法的收敛性理论,并以数值实验验证新方法的有效性.The weighting matrices in a standard multisplitting two-stage itera- tion method are determined previously in general. They are not known to be good or bad. In this paper, some generalized two-stage multisplitting iterative meth- ods are presented, whose weighting matrices are not necessarily known or given in advance. Instead, the variable weighting matrices can be obtained by finding the optimal point on the hyperplane at each step. Thus, the variable weighting matrices enable more approximate to the exact solution for the k-step iteration. The convergence theories of these generalized methods are established. Finally, the numerical comparison of several generalized two-stage parallel multisplitting methods are shown.

关 键 词：二阶段多分裂 迭代法 收敛性 加权矩阵 线性系统 

分 类 号：O241.6[理学—计算数学]