The bisymmetric solutions of the matrix equation AXB = C are too difficult to be obtained by applying matrices decomposition. In this paper, an iterative method is applied to solve this problem. By this, the solvability of the equation AXB = C over bisymmetric X can be determined automatically, and its solution can be obtained in finite iterative steps when it is consistent, its least-norm solution can be obtained by choosing a special kind of starting iterative matrix, furthermore, its optimal approximation solution to a given matrix can be derived by finding the leastnorm solution of a new equation AtildeX B = tildeC.
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机译：矩阵方程AXB = C的双对称解太难了，无法通过应用矩阵分解来获得。在本文中，迭代方法被用来解决这个问题。这样，就可以自动确定方程AXB = C在双对称X上的可解性，并且当它是一致的时，可以以有限的迭代步骤来获得其解，可以通过选择一种特殊的起始迭代来获得其最小范数解。此外，通过找到新方程AtildeX B = tildeC的最小范数解，可以得出其对给定矩阵的最佳逼近解。
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