矩阵方程AXB+CYD=E的双对称最小二乘解及其最佳逼近

An Least Squares Bisymmetric Solution and Optimal Approximation of the Matrix Equation AXB + CYD = E

利用本文提出的迭代算法可得到矩阵AXB+CYD=E的双对称最小二乘解,并对算法的收敛性给出了证明,当选取初始矩阵为零时能得到矩阵方程的极小范数双对称最小二乘解,利用此方法还可得到任意给定矩阵的最佳逼近双对称解.

An iterative method is presented to solve the least squares bisymmetric solution for the matrix equation AXB ＋ CYD = E, and the convergence of the method is proved. By this iterative method, the minimum norm of the least squares bisymmetric solution can be obtained by choosing a special kind of initial bisymmetrie matrices. In addition, the unique optimal approximation pair solution to the given matrices in Frobenius norm can be obtained.