Accelerated iterative methods for finding solutions of a system of nonlinear equations

In this paper, we present a technique to construct iterative methods to approximate the zeros of a nonlinear equation F(x)=0, where F is a function of several variables. This technique is based on the approximation of the inverse function of F and on the use of a fixed point iteration. Depending on the number of steps considered in the fixed point iteration, or in other words, the number of evaluations of the function F, we obtain some variants of classical iterative processes to solve nonlinear equations. These variants improve the order of convergence of classical methods. Finally, we show some numerical examples, where we use adaptive multi-precision arithmetic in the computation that show a smaller cost.