Volume no :3, Issue no: 2, May (2010)

Journal of Pure and Applied Mathematics: Advances and Applications

A SECOND-DERIVATIVE-FREE VARIANT OF HALLEY'S METHOD WITH SIXTH-ORDER CONVERGENCE

Author's: Jiaqi Han, Huiqian He, Aimin Xu and Zhongdi Cen
Pages: [195] - [203]
Received Date: April 8, 2010
Submitted by:

Abstract

In recent years, the modified Halley’s methods have been one of the popular iterative methods to find approximate solutions to the roots of nonlinear equation. In this paper, we propose a new method without the second derivative to modify the Halley’s method. The present iterative method is of sixth-order convergence and can be viewed as an improvement of the recent works [9, 10]. Several numerical examples are given to illustrate the efficiency and performance of this method.

Keywords

Newton’s method, Halley’s method, convergence, nonlinear equation.