Some third-order families of iterative methods for solving nonlinear equations

摘要

In this paper, we present a convenient third-order iteration formula improving Newton's method for solving nonlinear equations. With any two iteration functions of order two the formula provides one-parameter third-order family of methods; each family member is free from second derivatives and per iteration it requires three evaluations of the given function and its derivative. Several numerical examples are given to illustrate the efficiency and performance of some of the presented methods. (C) 2006 Elsevier Inc. All rights reserved.