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

ALAMT > Vol.7 No.3, September 2017

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 1,582 Downloads 3,252 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.

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