一类矩阵方程组的对称解及其最佳逼近  

Symmetric Solution of a Class of Matrix Equations and its Optimal Approximation Solution

作　　者：陈世军[1] 张凯院[1] 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《工程数学学报》2009年第4期711-715,共5页Chinese Journal of Engineering Mathematics

基　　金：陕西省自然科学基金(2006A05)

摘　　要：本文建立了求矩阵方程组AiXBi+CiXDi=Fi(i=1,2)对称解的迭代算法。使用该算法可以判断矩阵方程组是否有对称解。在有对称解时,能在有限步迭代后得到矩阵方程组的对称解;当选取特殊初始矩阵时,可得极小范数对称解。另外,在上述解集合中可得到给定矩阵的最佳逼近矩阵表达式。In this paper, an iterative method is presented to find the symmetric solution of the matrix equations AiXBi ＋ CiXDi = Fi （i = 1, 2）. By this iterative method, the solvability of the matrix equations can be determined automatically. A symmetric solution can be obtained within finite iterative steps when the matrix equations is consistent, and the symmetric solution with least norm can be obtained by choosing a special kind of initial symmetric matrices. In addition, the optimal approximation solution to a given symmetric matrix can be obtained.

关 键 词：矩阵方程组 对称解 迭代算法 最佳逼近 

分 类 号：O241.6[理学—计算数学]