Iterative Methods for Solving the _disibledevent=I (0p,q<1) - Advances in Linear Algebra & Matrix Theory

ALAMT > Vol.7 No.3, September 2017

Advances in Linear Algebra & Matrix Theory

Volume 7, Issue 3 (September 2017)

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

Google-based Impact Factor: 0.14 Citations

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

HTML XML

Download as PDF (Size: 271KB) PP. 72-78

DOI: 10.4236/alamt.2017.73007 1,622 Downloads 3,239 Views Citations

Author(s)

Dongjie Gao

Affiliation(s)

Department of Mathematics, Heze University, Heze, China.

ABSTRACT

Consider the nonlinear matrix equation X-A*X^pA-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.

KEYWORDS

Nonlinear Matrix Equation, Positive Definite Solution, Iterative Method, Normal Cone

Share and Cite:

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

Cited by

[1]	The maximal positive definite solution of the nonlinear matrix equation
	Mathematical Sciences, 2022

[2]	Gradient-Based Iterative Algorithm for a Coupled Complex Conjugate and Transpose Matrix Equations
	Advances in Linear Algebra & Matrix Theory, 2021

[3]	An Iterative Method for Solving the Matrix Equation XA^{} XA-B^{} X^{-1} B= I
	2020

[4]	ИТЕРАЦИОННИ МЕТОДИ ЗА РЕШАВАНЕ НА РАЦИОНАЛНИ МАТРИЧНИ УРАВНЕНИЯ
	2020

Journals Menu

Follow SCIRP

	+1 323-425-8868
	customer@scirp.org
	+86 18163351462(WhatsApp)
	1655362766

	Paper Publishing WeChat

Journals Menu

Home

About SCIRP

Service

Policies