矩阵方程AXB=C的中心对称最小二乘解的迭代解法

The iterative method for the centrosymmetric least-squares solutions and the optimal approximation to the matrix Eequation AXB = C

给出了求矩阵方程AXB=C的中心对称最小二乘解的一种迭代解法,即利用法方程变换,将求解最小二乘解转化为相容矩阵方程的求解问题,再利用迭代法求出新方程的直接解.使用该方法,对任意给定的初始中心对称矩阵都可在有限步内迭代求出它的中心对称最小二乘解.并且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.

An iterative method was presented to solve the centrosymmetric least-squares solutions of the matrix equation AXB-C. By applying the orthogonal method of matrix equation, the problem of solving the least-squares solutions to the matrix equation to another problem of solving a consistent matrix equation. Then the direct centrosymmetric solutions were obtained by applying the iterative method in finite steps an arbitrary initializing centrosymmelric matrix. Also, the optimal approximated problem can be coverted to an another problem to find the least-norm solutions of a new matrix equation, and the problem can be solved by using the iterative method.