矩阵方程组A_1XB_1+C_1XD_1=F_1,A_2XB_2+C_1XD_2=F_2的反对称解及其最佳逼近  

The Anti-Symmetric Solution and Optimum Appromation of the Matrix Equations A_1XB_1+C_1XD_1=F_1,A_2XB_2+C_1XD_2=F_2

作　　者：梁开福[1] 王贵初[1] 

机构地区：[1]湘潭大学数学与计算科学学院

出　　处：《湘潭大学自然科学学报》2011年第3期18-21,共4页Natural Science Journal of Xiangtan University

基　　金：湖南省自然科学基金项目(10JJ2002)

摘　　要：利用迭代方法来解线性矩阵方程组A1XB1+C1XD1=F1,A2XB2+C2XD2=F2.若这个矩阵方程组是相容的,那么它的反对称解就能在有限步迭代中得到.如果选取一个特殊的初始矩阵,就能够求得其最小范数解.若任意给定一个矩阵,可在A1 X珘B1+C1 X珘D1=F1,A2 X珘B2+C2 X珘D2=F2中求得它的最佳逼近解.最后通过实例说明了这种迭代算法是有效的.In this paper,an iterative method is constructed to solve the linea matrix equations A1XB1＋C1XD1=F1,A2XB2＋C2XD2=F2.When this system of matrix equations is consistent,its solution can be obtained within finite iterative steps and its least-norm antisymmetric solution can be obtained by choosing a special kind of initial iterative matrix.Furthermore,its unique optimal approximation solution to a given matrix can be derived by finding the least-norm antisymmetric solution of a new system of matrix equations A1B1＋C1D1=F1,A2B2＋C2D2=F2.Given numerical examples are show the iterative method is quite efficient.

关 键 词：迭代方法 反对称解 最小范数解 最佳逼近解 

分 类 号：O151.21[理学—数学]