On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations

Abstract

We consider a system of nonlinear equations $F(\mathbf{x})=0$. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.