Introduction to a Newton-type method for solving nonlinear equations

摘要

In this paper we shall introduce a new Newton-type method, namely rational Newton, for solving a nonlinear equation. This new method is shown to converge cubically. We shall examine the effectiveness of the rational Newton method by comparing the performance with the well established methods, namely the classical Newton method, the Halley rational method, the Kou et al. and the Weerakoon and Fernando method for approximating the root of a given nonlinear equation. The approximate solution of the rational Newton method is found to be substantially more accurate than the well established methods.