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

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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: 0.33 Citations

Open Access

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

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DOI: 10.4236/alamt.2017.73007 1,200 Downloads 2,286 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

Cite this paper

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.

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