Backward Perturbation Analysis for the Matrix Equation A^TXA+B^TYB=D

作     者：Xing-dong Yang Xiu-hong Feng Qing-quan He 

作者机构：Department of Mathematics Nanjing University of Information Science and Technology Nanjing 210044 China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2011年第27卷第2期

页      面：281-288页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 070104[理学-应用数学] 071101[理学-系统理论] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(No.40975037) 

主　　题：matrix equation backward error approximate solution 

摘      要：Consider the linear matrix equation ATXA -k BTYB = D, where AB are n × n real matrices and D symmetric positive semi-definite matrix. In this paper, the normwise backward perturbation bounds for the solution of the equation are derived by applying the Brouwer fixed-point theorem and the singular value decomposition as well as the property of Kronecker product. The results are illustrated by two simple numerical examples.