Title of article
Positive definite solution of the matrix equation X = Q − A*X^−1A + B*X^−1B via Bhaskar-Lakshmikantham fixed point theorem
Author/Authors
Berzig, Maher University of Tunisia - Tunis College of Sciences and Techniques - Department of Mathematics, Tunisia , Duan, Xuefeng Guilin University of Electronic Technology - School of Mathematics and Computational Science - Department of Mathematics, China , Samet, Bessem University of Tunisia - Tunis College of Sciences and Techniques - Department of Mathematics, Tunisia
From page
1
To page
6
Abstract
Purpose: The purpose of this paper is to study the existence and uniqueness of a positive definite solution to the nonlinear matrix equation X = Q − A*X^−1A + B*X^−1B, which is a special stochastic rational Riccati equation arising in stochastic control theory.Methods: Our technique is based on the Bhaskar and Lakshmikantham coupled fixed point theorem.Results: A new result on the existence of a unique positive definite solution is derived. An iterative method is constructed to compute the unique positive definite solution. Finally, some numerical examples are used to show that the iterative method is feasible.Conclusion: Coupled fixed point theory on ordered metric spaces can be a useful tool to solve some classes of nonlinear matrix equations.
Keywords
Nonlinear matrix equation , Positive definite solution , Sufficient condition , Iterative method , Error estimation , Coupled fixed point
Journal title
Mathematical Sciences
Journal title
Mathematical Sciences
Record number
2568912
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