Positive Definite Solutions for the System of Nonlinear Matrix Equations <i>X</i>+ <i>A<sup>*</sup>Y<sup>-n</sup>A</i>= <i>I</i>, <i>Y</i>+ <i>B<sup>*</sup>X<sup>-m</sup>B</i>= <i>I</i>

作     者：Salah M. El-Sayed Asmaa M. Al-Dubiban 

作者机构：Department of Scientific Computing Faculty of Computers and Informatics Benha University Benha Egypt Faculty of Science and Arts Qassim University Qassim KSA 

出 版 物：《Applied Mathematics》 (应用数学（英文）)

年 卷 期：2014年第5卷第13期

页      面：1977-1987页

学科分类：07[理学] 0701[理学-数学] 

主　　题：System of Nonlinear Matrix Equations Iterative Methods Monotonic Sequence Positive Definite Matrices 

摘      要：In this paper, some properties of the positive definite solutions for the nonlinear system of matrix equations X + A*Y-nA = I, Y + B*X-mB = I are derived. As a matter of fact, an effective iterative method to obtain the positive definite solutions of the system is established. These solutions are based on the convergence of monotone sequences of positive definite matrices. Moreover, the necessary and sufficient conditions for the existence of the positive definite solutions are obtained. Finally, some numerical results are given.