A note on some quadrature based three-step iterative methods for non-linear equations
type: Item
instance of: scholarly article
title: A note on some quadrature based three-step iterative methods for non-linear equations
zbMATH Open document ID: 1194.65072
author: Hengfei Ding
author: Yu-Xin Zhang
author: San-Fu Wang
author: Xiaoya Yang
published in: Applied Mathematics and Computation
publication date: 2009-10-09T00:00:00Z
review text: In a recent paper [\textit{N. A. Mir} and \textit{T. Zaman}, Some quadrature based three-step iterative methods for nonlinear equations, Appl. Math. Comput. 193, 366--373 (2007; Zbl 1193.65068)], some view three-step iterative methods for nonlinear equations have been proposed. In this note it's shown that the Algorithm 2.2 and Algorithm 2.3 given by the authors have twelfth-order and ninth-order convergence respectively, not seventh-order one as claimed in their work.
reviewed by: Juri M. Rappoport
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 5612873
zbMATH Keywords: non-linear equations
zbMATH Keywords: three-step iterative methods
zbMATH Keywords: efficiency index
zbMATH Keywords: order of convergence
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.amc.2009.04.036
OpenAlex ID: W2088129149
cites work: New family of seventh-order methods for nonlinear equations
cites work: Some fourth-order iterative methods for solving nonlinear equations
cites work: Some sixth-order variants of Ostrowski root-finding methods
cites work: A note on modified Householder iterative method free from second derivatives for nonlinear equations
cites work: A family of combined iterative methods for solving nonlinear equation
cites work: Some variants of Ostrowski's method with seventh-order convergence
cites work: Some quadrature based three-step iterative methods for non-linear equations
cites work: Iterative methods with fourth-order convergence for nonlinear equations
cites work: A sixth order method for nonlinear equations
cites work: A note on three-step iterative method for nonlinear equations
cites work: Modified Chebyshev-Halley methods free from second derivative
DOI: 10.1016/J.AMC.2009.04.036
description: scientific article; zbMATH DE number 5612873