Low-complexity root-finding iteration functions with no derivatives of any order of convergence

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:275

Article

Cordero, Alicia¹  Torregrosa, Juan R.¹ 

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

关键词: Nonlinear equation;    Iterative method;    Derivative-free scheme;    Divided difference;    Efficiency index;    Optimal order;   

DOI  :  10.1016/j.cam.2014.01.024

来源: Elsevier

【 摘 要 】

In this paper, a procedure to design Steffensen-type methods of different orders for solving nonlinear equations is suggested. By using a particular divided difference of first order we can transform many iterative methods into derivative-free iterative schemes, holding the order of convergence of the departure original method. Numerical examples and the study of the dynamics are made to show the performance of the presented schemes and to compare them with another ones. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free