Numerical Algorithm For Solving A Nonlinear Matrix Equation

Nonlinear matrix equations have many applications in engineering, nano research, control theory, communication system, dynamic programming, signal processing, statistics etc. In this paper, we propose an iterative algorithm for obtaining positive de nite solutions of a nonlinear matrix equation. Necessary and su cient conditions for the existence of solutions are derived. The rate of convergence of the iterative sequence and perturbation bound for the solution are obtained. We give numerical examples to ensure the e ectiveness of the suggested iterative algorithm. Keywords- Nonlinear matrix equation; Positive de nite solution; Iterative algorithm.