关于正实线性系统的一种新的迭代法  

New Iterative Method for Positive Real Linear System

作　　者：邵新慧[1] 李长军[1] 李岩[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）》2003年第10期1010-1013,共4页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(19871011);原国家教育委员会骨干教师基金资助项目.

摘　　要：针对系数矩阵A是大型稀疏非对称的且AT+A是对称正定的,或者等价地说A是正实矩阵的线性系统AU=b给出了一种新的迭代解法·该迭代法的构成是基于矩阵A的混合形式的分解A=M-S,其中M是对称正定矩阵及S是斜对称矩阵·迭代法需要选择一个对称正定矩阵D,通过适当选取矩阵D,新迭代法是收敛的,并且以定理的形式给出了两种选择D的方法,又通过例题给出了迭代法的计算过程·可以看出,对于用迭代法求解正实线性系统,新迭代方法要比其他的迭代方法如SOR法更容易实现·A new iterative method is given to the linear system of equations Au=b,where A is large,sparse and nonsymmetric and A^T+A is symmetric and positive definite(SPD) or equivalently A is positive real. The new method is constituted on a basis of mixed splitting of the matrix A,i.e. A=M-S,where M is a symmetric and positive definite matrix and S a skew symmetric matrix. The method needs to choose properly a matrix D which is symmetric and positive definite(SPD) so as to make sure its convergence. Two options of the matrix D are given in form of theorem,based on convergence analysis,with a computation of the method shown through an example. It is proved that the new iterative method is easier to solve the positive real linear system than other methods,e.g. the SOR method.

关 键 词：线性系统 迭代法 对称正定矩阵 斜对称矩阵 正定矩阵 矩阵混合形式的分解 

分 类 号：O242.26[理学—计算数学]