An effective iterative method for computing real and complex roots of systems of nonlinear equations

A simple and flexible iterative method is proposed to determine the real or complex roots of any system of nonlinear equations F(x)=0. The idea is based on passing defined functions G_j(x_j),j=1,…,n tangent to F_i(x_j),i,j=1,…,n at an arbitrary starting point. Choosing G_j(x_j) in the form of or or any other reversible function compatible to F_i(x_j), where k is obtained for the best correlation with the function F_i(x_j), gives an added freedom, which in contrast with all existing methods, accelerates the convergence.The method that was first proposed for computing the roots of any single function is now adopted for a system of nonlinear equations. This method is compared to some classical and famous methods such as Newton’s method and Newton-Simpson’s method. The results show the effectiveness and robustness of this new method.