矩阵方程AXB+CYD=E的中心对称解的递推算法

An Iterative Algorithm for the Centrosymmetric Solution of a Matrix Equation AXB + CYD = E

讨论了矩阵方程AXB+CYD=E中心对称解的迭代算法,该算法能够判断矩阵方程是否有中心对称解,在有解的条件下,能得到它的中心对称解,而且在选取特殊的初始矩阵时,该算法能够求出矩阵方程的极小范数中心对称解,以及对给定的矩阵进行最佳逼近的中心对称解.

The iterative method for the centrosymmetic solution of a matrix equation is presented, which can judge whether a linear matrix equation has the eentrosymmetric solution. When the matrix equation has centrosymmetric solution pair, then for an initial matrix pair, centrosymmetric solution can be obtained within finite iterative steps in the absence of roundoff errors, and minimum norm of the centrosymmetric solution can be obtained by choosing a special kind of initial pair matrices. In addition, the unique optimal approximation pair solution to the given matrices can also be obtained.