Iterative Algorithm for Solving a System of Nonlinear Matrix Equations
Copyright policy )Iterative Algorithm for Solving a System of Nonlinear Matrix Equations
We discuss the positive definite solutions for the system of nonlinear matrix equations X − A∗Y−nA = I and Y − B∗X−mB = I, where n, m are two positive integers. Some properties of solutions are studied, and the necessary and sufficient conditions for the existence of positive definite solutions are given. An iterative algorithm for obtaining positive definite solutions of the system is proposed. Moreover, the error estimations are found. Finally, some numerical examples are given to show the efficiency of the proposed iterative algorithm.
- Qassim University Saudi Arabia
Iterative numerical methods for linear systems, iterative algorithm, Numerical computation of solutions to systems of equations, Other matrix algorithms, Matrix equations and identities, positive definite solutions, system of nonlinear matrix equations, numerical example, error estimation, QA1-939, Mathematics
Iterative numerical methods for linear systems, iterative algorithm, Numerical computation of solutions to systems of equations, Other matrix algorithms, Matrix equations and identities, positive definite solutions, system of nonlinear matrix equations, numerical example, error estimation, QA1-939, Mathematics
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