构造迭代算法研究了矩阵方程[]AXB, GXH =[C, D]，证明了该算法可经有限步得到方程的对称最小二乘解及其最佳逼近，并给出了相关性质。最后，通过数值例子表明该算法是有效的。%The matrix equation [ ]AXB,GXH =[C,D] is constructed in this paper with an iteration method. With this method, it is proven that the least⁃squares solutions for symmetric matrix and the nearness problem can be computed within finite iteration steps. And some properties of the iteration method are obtained. Finally, numerical examples are applied to prove the method efficient.
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