A simply constructed third-order modifications of Newton's method

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:219

Article

Chun, Changbum

关键词: Newton's method;    iterative methods;    nonlinear equations;    order of convergence;    Chebyshev-Halley methods;    root-finding methods;   

DOI  :  10.1016/j.cam.2007.07.004

来源: Elsevier

【 摘 要 】

In this paper, we present a simple and easily applicable approach to construct some third-order modifications of Newton's method for solving nonlinear equations. It is shown by way of illustration that existing third-order methods can be employed to construct new third-order iterative methods. The proposed approach is applied to the classical Chebyshev-Halley methods to derive their second-derivative-free variants. Numerical examples are given to support that the methods thus obtained can compete with known third-order methods. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free