Gradient based and least squares based iterative algorithms for matrix equations AXB + CXTD = F
Gradient based and least squares based iterative algorithms for matrix equations AXB + CXTD = F
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DOI：
10.1016/j.amc.2010.07.019
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发表时间：
2010-11
期刊：
影响因子：
--
通讯作者：
Li Xie;Yanjun Liu;Huizhong Yang
中科院分区：
文献类型：
--
作者：
Li Xie;Yanjun Liu;Huizhong Yang
本文给出了求解矩阵方程AXB+CXTD=F的一种基于梯度的迭代算法和一种基于最小二乘的迭代算法。其基本思想是应用递阶辨识原理将所考虑的矩阵方程（系统）分解为两个子系统，并通过对求解Ax=B和AX B =F的迭代方法的推广，导出迭代算法。分析表明，当矩阵方程有唯一解时（在最小二乘意义下），对任意初值，迭代解收敛于精确解。数值例子验证了所提出的定理。
This paper develops a gradient based and a least squares based iterative algorithms for solving matrix equation AXB+CXTD=F. The basic idea is to decompose the matrix equation (system) under consideration into two subsystems by applying the hierarchical identification principle and to derive the iterative algorithms by extending the iterative methods for solving Ax=b and AXB=F. The analysis shows that when the matrix equation has a unique solution (under the sense of least squares), the iterative solution converges to the exact solution for any initial values. A numerical example verifies the proposed theorems.