求解Sylvester方程的正交迭代算法  

Orthogonal Iterative Algorithm for Sylvester Equations

作　　者：殷霞[1] 章里程[1] 廖祖华[1] 

机构地区：[1]江南大学理学院,江苏无锡214122

出　　处：《江南大学学报（自然科学版）》2014年第6期731-735,共5页Joural of Jiangnan University (Natural Science Edition)　

基　　金：国家自然科学基金项目(11301227)

摘　　要：对于任意初始矩阵,运用求解Sylvester矩阵方程的正交迭代算法可以在有限步内得到方程的最小二乘解,而且通过选择初始矩阵还可以得到方程的极小范数最小二乘解,这种算法还能用于解决最佳逼近问题,数值例子表明了所提出算法的有效性。In this paper ,an orthogonal iterative algorithm for solving Sylvester matrix equations is proposed. Using the iterative algorithm,a/east-square solution of Sylvester matrix equations for any initial matrix can be obtained within finite iteration steps. Furthermore,the least-square solution with the minimum norm can be obtained by choosing a special initial matrix. The algorithm can also be applied to solve optimal approximation problems, Finally, the algorithms is tested on computer and the results verify the theoretical findings.

关 键 词：Sylvester矩阵方程 正交迭代算法 最小二乘解 极小范数解 最佳逼近问题 

分 类 号：O241[理学—计算数学] TP301.6[理学—数学]