矩阵方程AXA^T+BYB^T=C的对称最小二乘解

An Iterative Method for the Least Squares Symmetric Solution of the Linear Matrix Equation AXA^T+ BYB^T=C

建立了一种求矩阵方程AXAT+BYBT=C对称最小二乘解的递推算法,对任意的初始对称矩阵,经过有限步迭代得到它的对称最小二乘解.若选取特殊的初始矩阵,通过递推算法得到的解就是极小范数对称最小二乘解.而且,对给定的任意矩阵,通过对方程的变形能得到它的最佳逼近对称解.

In this paper, an iterative method is presented to solve the least squares symmetric solution pair of an linear matrix equation AXA T ＋ BYB T = C. By this iterative method, the least squares symmetric solution pair can be obtained, and minimum norm of the least squares solution pair can be obtained by choosing a special kind of initial matrix pair. In addition, the unique optimal approximation solution pair to the given matrices in Frobenius norm can be obtained.