Iterative Methods for Solving the Nonlinear Matrix Equation <i>X</i>-<i>A</i>*<i>X</i><sup>p</sup><i>A</i>-<i>B</i>*<i>X</i><sup>-q</sup><i>B</i>=<i>I</i>(0<<i>p</i>,<i>q</i><1)

• 作者: Dongjie Gao
• 来源期刊: 线性代数与矩阵理论研究进展(英文)
• 学科: 数学
• 关键词: Nonlinear Matrix Equation Positive Definite Solution Iterative Method Normal Cone
• 年，卷（期）: 2017,（3）
• 页码范围: 72-78
• 页数: 7页
• 分类号: O1

摘要

Consider the nonlinear matrix equation X-A*XpA-B*X-qB=I (0p,q1). By using the fixed point theorem for mixed monotone operator in a normal cone, we prove that the equation with 0p,q1 always has the unique positive definite solution. Two different iterative methods are given, including the basic fixed point iterative method and the multi-step stationary iterative method. Numerical examples show that the iterative methods are feasible and effective.