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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)

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)
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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. 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.
作者 Dongjie Gao
机构地区 Department of Mathematics
出处 《Advances in Linear Algebra & Matrix Theory》 2017年第3期72-78,共7页 线性代数与矩阵理论研究进展（英文）
关键词 Nonlinear Matrix Equation Positive Definite Solution Iterative Method Normal Cone Nonlinear Matrix Equation Positive Definite Solution Iterative Method Normal Cone
分类号 O1 [理学—基础数学]
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Advances in Linear Algebra & Matrix Theory
2017年 第3期

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