耦合矩阵方程AX+XB=C,DX+XE=F的梯度迭代算法  

Gradient Iterative Algorithm for the Coupled Matrix Equations AX+XB=C,DX+XE=F

作　　者：殷红彩[1] 张华民[2] 段凯宇[1] 

机构地区：[1]安徽财经大学管理科学与工程学院,安徽蚌埠233030 [2]蚌埠学院理学院,安徽蚌埠233030

出　　处：《蚌埠学院学报》2016年第6期36-40,共5页Journal of Bengbu University

基　　金：安徽财经大学科研项目(ACKY1654);安徽省教育厅重点项目(KJ2016A458)

摘　　要：利用递阶辨识原理建立了一种耦合矩阵方程的梯度迭代算法,并给出了算法的收敛性证明。分析表明:在该耦合矩阵方程有唯一解的条件下,迭代解收敛到方程的唯一解,并通过一个数值例子验证了算法的有效性。By the hierarchical identification principle,a gradient-based iterative method for solving a class of coupled matrix equations was established,and the convergence proof of the suggested algorithm was given in this paper. It was proved that if the coupled matrix equations have a unique solution then the iterative solutions converge fast to the exact one for any initial value. A numerical example was given to illustrate the effectiveness of the proposed algorithm.

关 键 词：递阶辨识原理 梯度迭代算法 矩阵方程 

分 类 号：O241.6[理学—计算数学]