%0 Journal Article
%T 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)
%A Dongjie Gao
%J Advances in Linear Algebra & Matrix Theory
%P 72-78
%@ 2165-3348
%D 2017
%I Scientific Research Publishing
%R 10.4236/alamt.2017.73007
%X Consider the nonlinear matrix equation <em>X</em>-<em>A*X</em><sup>p</sup><em>A</em>-<em>B*X</em><sup>-q</sup><em>B</em>=<em>I </em>(0&lt;<em>p</em>,<em>q&lt;</em><p,q>1). By using the fixed point theorem for mixed monotone operator in a normal cone, we prove that the equation with <span style=\"white-space:normal;\">0&lt;<em>p</em>,<em>q&lt;</em></span><p,q style=\"white-space: normal;\">1</p,q><p, q=\"\"> 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.</p,></p,q>
%K Nonlinear Matrix Equation
%K Positive Definite Solution
%K Iterative Method
%K Normal Cone
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=79339