One-point Newton-type iterative methods: A unified point of view

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:275

Article

Cordero, Alicia¹  Jordan, Cristina¹  Torregrosa, Juan R.¹ 

[1] Univ Politecn Valencia, Inst Matemat Multidisciplinar, Valencia 46022, Spain

关键词: Nonlinear equation;    One-point method;    Newton's method;    Order of convergence;    Efficiency index;    Optimal order;   

DOI  :  10.1016/j.cam.2014.07.009

来源: Elsevier

【 摘 要 】

In this paper, a unified point of view that includes the most of one-point Newton-type iterative methods for solving nonlinear equations is introduced. A simple idea to design iterative methods with quadratic or cubic convergence is also described. This idea is extended to construct one-point iterative methods of order four. In addition, several numerical examples are given to illustrate and compare different known methods and some introduced by using this unifying idea. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free