迭代法求矩阵方程AXB=C的双对称最小二乘解及其最佳逼近  

An Iterative Method for the Bisymmetric Least-squares Solutions and the Optimal Approximation of the Matrix Equation AXB=C

作　　者：张艳燕[1] 

机构地区：[1]湖南文理学院数学系,常德415000

出　　处：《工程数学学报》2009年第4期753-756,共4页Chinese Journal of Engineering Mathematics

摘　　要：本文给出了求矩阵方程AXB=C的双对称最小二乘解的一种迭代解法。即利用法方程变换,将求最小二乘解转化为相容矩阵方程的求解问题,则对任意给定的初始双对称矩阵,利用迭代法通过有限步求出新方程的双对称解即可。并将求最佳逼近的问题转化为求一个新方程的极小范数解的问题,同样可用迭代法求解。In this paper an iterative method is presented to find the bisymmetric least-squares solutions of the matrix equation AXB = C. By applying the orthogonal method to the matrix equation, we can convert the problem of finding the least-squares solutions to another problem of solving a consistent matrix equation. Then as for an arbitrary initializing bisymmetric matrix, we just need to get the bisymmetric solutions of the new equation in finite steps by applying the iterative method. We also can convert the optimal approximated problem to another problem that is to find the least-norm solutions of a new matrix equation, and the problem can also be solved by applying the iterative method.

关 键 词：迭代法 FROBENIUS范数 最小二乘解 最佳逼近解 极小范数解 

分 类 号：O241.6[理学—计算数学]