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中文摘要：
1 引言矩阵反问题和矩阵特征值反问题在科学和工程技术中具有广泛的应用,有关研究已取得了许多进展(见[1])．而中心对称矩阵与反中心对称矩阵在信息论、线性系统理论、线性估计理论及数值分析等领域中应用广泛(见[2])．本文研究矩阵方程XAY=B(X,Y,B 已知)的中心对称与反中心对称解及其最佳逼近．
英文摘要：
Given matrices X, Y and B, the centrosymmetric and anti-centrosymmetric solutions to the matrix equation XAY=B as well as the corresponding optimal approximation problems are studied. The general forms of such solutions are given and the expressions of the optimal approximation solutions to a given matrix are derived. A numerical algorithm for solving the optimal approximation solution is described and one example is used to illustrate the effectiveness of the proposed method.
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