中文摘要：

鉴于用矩阵分解的方法求解多变量矩阵方程的复杂性，本文提出了一类迭代算法用于求解多变量矩阵方程的对称最小二乘解并证明了其收敛性，而且在选取特殊的初始对称矩阵组时，能得到它的极小范数解组。另外，给定任意矩阵组，利用此方法可得到它的最佳逼近对称解组。数值试验表明，这种方法相当有效。

英文摘要：

The least squares symmetric solutions of the matrix equation with several variables are too difficult to be obtained by applying matrices decomposition.An iterative method is presented to solve the least squares symmetric solutions of the linear matrix equation and its convergence is proved. And minimum norm of the least squares symmetric solutions can be obtained by choosing a special kind of initial symmetric matrices.In addition, the unique optimal approximation solutions to the given matrices in Frobenius norm can be obtained.The given numerical examples demonstrate that the iterative methods are quite efficient.