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: Asmaa M. Al-Dubiban Salah M. El-Sayed
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: System of Nonlinear Matrix Equations Iterative Methods MONOTONIC Sequence Positive Definite MATRICES
• 年，卷（期）: 2014,（13）
• 页码范围: 1977-1987
• 页数: 11页
• 分类号: O1

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.