A unified framework for the design of efficient fourth order Newton-like methods.

Abstract

This paper deals with a unified approach for generating weighted-Newton algorithms designed for solving nonlinear systems of equations. We propose a method for calculating suitable weight functions using only the first Fr ´echet derivative of the considered nonlinear operator. The approach covers most of the known fourth order weighted-Newton algorithms, which illustrates the effectiveness of the weighting method. Moreover, it gives rise to a new efficient fourth order method, referred to as the polynomial weighting method (PM), which outperforms the classical Newton’s algorithm and a set of well-known Newtonlike methods including Jarratt’s method. Numerical comparison of the polynomial weighting method with some well-known fourth order methods is carried out on a set of benchmark problems.