A multi-point iterative method for solving nonlinear equations with optimal order of convergence
type: Item
instance of: scholarly article
title: A multi-point iterative method for solving nonlinear equations with optimal order of convergence
zbMATH Open document ID: 1406.65034
author: Mehdi Salimi
author: Nik Mohd Asri Nik Long
author: Somayeh Sharifi
author: Bruno Antonio Pansera
published in: Japan Journal of Industrial and Applied Mathematics
publication date: 2018-12-21T00:00:00Z
full work available at URL: KUNG.pdf
review text: The article is devoted to the classical problem of constructing efficient and higher-order of convergence iterative algorithms for solving nonlinear equations. In this area of numerical analysis, several iterative families with order of convergence \(\tau=8\) and optimal in the sense of Kung-Traub's conjecture are known. The authors construct a new three-stage method, free from second-order derivatives. The technique used for obtaining the new family includes weight functions technique and Newton interpolation. The numerical procedure has order of convergence \(\tau=2^3\) and the efficiency index \(EI=2^{\frac{3}{4}}\). The new algorithm requires only three function calculations and one derivative calculation at a point, that is, it is optimal in the sense of Kung-Traub considerations. As a result of the convergence theorem, some interesting choices of weight functions are listed. Some comparison of basin of attraction for popular methods are given.
reviewed by: Nikolay Kyurkchiev
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 6996759
zbMATH Keywords: multi-point iterative methods
zbMATH Keywords: simple root
zbMATH Keywords: order of convergence
zbMATH Keywords: Kung and Traub's conjecture
zbMATH Keywords: efficiency index
MaRDI profile type: Publication
OpenAlex ID: W2782282275
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DOI: 10.1007/S13160-017-0294-4
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description: scientific article; zbMATH DE number 6996759