Necessary and sufficient conditions for the existence of a positive definite solution of a nonlinear matrix equation

作     者：Wang, Xing Tao Li, Yuan Min 

作者机构：Harbin Inst Technol Dept Math Harbin 150006 Peoples R China 

出 版 物：《INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS》 (国际计算机数学杂志)

年 卷 期：2010年第87卷第11期

页      面：2542-2551页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Natural Science Foundation of China Science Research Foundation in Harbin Institute of Technology [HITC200708] 

主　　题：nonlinear matrix equation necessary and sufficient condition iterative algorithm positive definite solution 

摘      要：Some necessary and sufficient conditions for the existence of a positive definite solution of the nonlinear matrix equation X + A*X(-alpha)A = Q (0 alpha = 1) are given. By the way an iterative method is presented. Furthermore, the convergence and error estimation of the iterative algorithm are derived. The illustrative numerical examples due to Peng are worked out.