Sylvester矩阵方程极小范数最小二乘解的迭代解法  

An Iterative Method for the Least Squares Solution with the Minimum Norm of Sylvester Matrix Equation

作　　者：殷霞[1] 章里程[1] 朱晓英[1] 

机构地区：[1]江南大学理学院,江苏无锡214122

出　　处：《数学的实践与认识》2013年第11期239-243,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11001109)

摘　　要：研究了Sylvester矩阵方程最小二乘解以及极小范数最小二乘解的迭代解法,首先利用递阶辨识原理,得到了求解矩阵方程AX+YB=C的极小范数最小二乘解的一种迭代算法,进而,将这种算法推广到一般线性矩阵方程A_iX_iB_i=C的情形,最后,数值例子验证了算法的有效性.In this paper, Sylvester matrix equation AX ~ YB = C with two unknown matrices X, Y is discussed. By applying a hierarchical identification principle, we propose an iterative algorithm for solving the least norm problem of the equation. We prove that the iterative solution converges to the least-squares solution and the least-squares solution with the minimum norm for some initial value. Furthermore, the iterative method is extended to solve the least Frobenius norm problem of general matrix equation. Finally, the algorithms are tested on computer and the results verify the theoretical findings.

关 键 词：Sylvester矩阵方程 迭代解法 最小二乘解 极小范数解 

分 类 号：O241.5[理学—计算数学]