矩阵方程AX=B的可双对称化解及其最佳逼近

The dual-symmetric solution and its optimal approximation problem of matrix equation AX=B

给出了矩阵方程AX=B存在可双对称化解的充分必要条件及解的一般表达式,并提出了其最佳逼近问题,得到最佳逼近解。最后进行数值实验,得到的数值实验结果和理论结果相一致,数值实验表明该方法是行之有效的。

In this paper,the necessary and sufficient conditions for the existence of the matrix equation AX=B are given and the expressions for the solutions of this matrix equation are obtained.The best approximation problem associated is considered,and its optimal approximation solution is obtained.Finally,numerical experiments are carried out,and the results are consistent with the theoretical results,so the method is feasible and effective.