线性矩阵方程AXB+CXD=F的斜埃尔米特迭代解  

The skew Hermitian iterative solutions of the linear matrix equation AXB+CXD=F

作　　者：杨吉 黄光鑫[1,3] 尹凤 YANG Ji;HUANG Guangxin;YIN Feng(Sichuan Key Laboratory of Geomathematics, Chengdu University of Technology, Chengdu 610059, China;College of Mathematics and Physics, Chengdu University of Technology, Chengdu 610059, China;College of Computer and Cyber Security (Oxford Brookes College), Chengdu University of Technology, Chengdu 610059, China)

机构地区：[1]成都理工大学数学地质四川省重点实验室,成都610059 [2]成都理工大学数理学院,成都610059 [3]成都理工大学计算机与网络安全学院(牛津布鲁克斯学院),成都610059

出　　处：《成都理工大学学报（自然科学版）》2022年第3期378-384,共7页Journal of Chengdu University of Technology: Science & Technology Edition

基　　金：桥梁无损检测与工程计算四川省重点实验室开放基金项目(2020QZJ03)。

摘　　要：若矩阵P∈C^(n×n)满足P^(H)=-P,则称P为斜埃尔米特矩阵。S^(n×n)表示所有复数域上n×n的斜埃尔米特矩阵构成的集合,即S^(n×n)={P_(S)|P_(S)^(H)=-P_(S)}。本文给出了2种求解线性矩阵方程AXB+CXD=F的梯度形松弛算法,证明了算法的收敛性,并且给出了算法收敛的一个充分条件。对于任意一个给定的初始斜埃尔米特矩阵,利用所提出的梯度形松弛算法,可以得到线性矩阵方程AXB+CXD=F的斜埃尔米特数值解。最后用2个数值实例说明所提出的算法的有效性。If the matrix P∈C^(n×n) satisfies P^(H)=-P,then P is called an skew Hermitian matrix.Sn×n represents the set of all skew Hermitian matrices of n×n in complex field,i.e.,S^(n×n)={P_(S)|P_(S)^(H)=-P_(S)}.Two gradient relaxation algorithms for solving linear matrix equations AXB+CXD=F are proposed in the present paper.The convergence of the algorithm is proved and a sufficient condition for the convergence of the algorithm is also given.For any given initial skew Hermite matrix,the numerical skew Hermitian solutions of the linear matrix equations AXB+CXD=F can be obtained by using the proposed gradient relaxation algorithms.Finally,two numerical examples are provided to illustrate the effectiveness of the proposed methods.

关 键 词：梯度算法 迭代解 斜埃尔米特矩阵 收敛因子 

分 类 号：O151.21[理学—数学]