Advances in Linear Algebra & Matrix Theory

Volume 7, Issue 3 (September 2017)

ISSN Print: 2165-333X   ISSN Online: 2165-3348

Google-based Impact Factor: 0.33  Citations  

Iterative Methods for Solving the Nonlinear Matrix Equation X-A*XpA-B*X-qB=I (0<p,q<1)

HTML  XML Download Download as PDF (Size: 271KB)  PP. 72-78  
DOI: 10.4236/alamt.2017.73007    1,200 Downloads   2,286 Views   Citations
Author(s)

ABSTRACT

Consider the nonlinear matrix equation X-A*XpA-B*X-qB=I (0<p,q<1). By using the fixed point theorem for mixed monotone operator in a normal cone, we prove that the equation with 0<p,q<1 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.

Cite this paper

Gao, D. (2017) Iterative Methods for Solving the Nonlinear Matrix Equation X-A*XpA-B*X-qB=I (0<p,q<1). Advances in Linear Algebra & Matrix Theory, 7, 72-78. doi: 10.4236/alamt.2017.73007.

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.