A new family of fourth-order optimal iterative schemes and remark on Kung and Traub's conjecture
type: Item
instance of: scholarly article
title: A new family of fourth-order optimal iterative schemes and remark on Kung and Traub's conjecture
zbMATH Open document ID: 1477.65076
DOI: 10.1155/2021/5516694
author: Chein-Shan Liu
author: Tsung-Lin Lee
published in: Journal of Mathematics
publication date: 2021-06-23T00:00:00Z
review text: Summary: Kung and Traub conjectured that a multipoint iterative scheme without memory based on \(m\) evaluations of functions has an optimal convergence order \(p= 2^{m-1}\). In the paper, we first prove that the two-step fourth-order optimal iterative schemes of the same class have a common feature including a same term in the error equations, resorting on the conjecture of Kung and Traub. Based on the error equations, we derive a constantly weighting algorithm obtained from the combination of two iterative schemes, which converges faster than the departed ones. Then, a new family of fourth-order optimal iterative schemes is developed by using a new weight function technique, which needs three evaluations of functions and whose convergence order is proved to be \(p=2^{3-1} =4\).
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 7362402
Wikidata QID: Q113758357
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/5516694
OpenAlex ID: W3129256424
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description: scientific article; zbMATH DE number 7362402