对称半正定矩阵的二级多分裂  

Two-stage Multisplitting of Symmetric Positive Semidefinite Matrices

作　　者：张华隆[1] 

机构地区：[1]同济大学应用数学系,上海 200092

出　　处：《同济大学学报（自然科学版）》2003年第10期1232-1236,共5页Journal of Tongji University:Natural Science

摘　　要：考虑由二级多分裂迭代法求出大规模线性系统方程并行解的问题 .通过研究二级方法与多分裂方法两者之间的相互联系之后 ,借助于矩阵的对角补偿约化矩阵 ,较深入地讨论了对称半正定矩阵的二级多分裂方法 .首先分析一般矩阵的二级多分裂方法的特征与收敛性 ;然后给出对称半正定矩阵二级多分裂方法的构造过程 。This paper attempts to get the parallel solution of a large consistent linear system of equations by two?-stage multisplitting iterative method.After having studied the relationship between the two?-stage method and the multisplitting method,two?-stage multisplitting of symmetric positive semidefinite matrices are studied thoroughly by employing matrices of diagonally compensated reduced matrices.Firstly,the features and convergence of two?-stage multisplitting method of common matrices is analyzed.Secondly,constructing process of two?-stage multisplitting symmetric positive semidefinite matrices is obtained.Based on the above result,two?-state multisplitting iterative method is proved convergent for any initial vector if splitting is regular and weak regular.

关 键 词：对称半正定矩阵 二级多分裂 对角补偿约化矩阵 收敛性 

分 类 号：O241.6[理学—计算数学]