Ball comparison between two optimal eight-order methods under weak conditions
type: Item
instance of: scholarly article
title: Ball comparison between two optimal eight-order methods under weak conditions
zbMATH Open document ID: 1332.65066
author: Ioannis Konstantinos Argyros
author: Santhosh George
published in: S\(\vec{\text{e}}\)MA Journal
publication date: 2016-01-14T00:00:00Z
review text: A local convergence analysis of two families of optimal eighth-order methods in order to approximate a locally unique solution of a nonlinear equation is presented. In previous studies, the convergence order of these methods was given under hypotheses reaching up to the eighth derivative of the function. In this paper, the applicability of these methods by showing convergence using only the first derivative is expanded. The convergence radii and computable error estimates for these methods using Lipschitz constants are received.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 6530110
zbMATH Keywords: Kung-Traub method
zbMATH Keywords: eighth-order method
zbMATH Keywords: local convergence
zbMATH Keywords: optimal method
zbMATH Keywords: nonlinear equation
zbMATH Keywords: error estimates
reviewed by: Anton Iliev
MaRDI profile type: Publication
full work available at URL: s40324-015-0035-z
OpenAlex ID: W771506698
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DOI: 10.1007/S40324-015-0035-Z
description: scientific article; zbMATH DE number 6530110