Convergence for a class of multi-point modified Chebyshev-Halley methods under the relaxed conditions
type: Item
instance of: scholarly article
title: Convergence for a class of multi-point modified Chebyshev-Halley methods under the relaxed conditions
zbMATH Open document ID: 1335.65052
author: Xiu-Hua Wang
author: Jisheng Kou
published in: Numerical Algorithms
publication date: 2015-03-23T00:00:00Z
review text: The authors consider semilocal convergence for a class of multi-point modified Chebyshev-Halley methods for solving equations \(F(x)=0\), where \(X,Y\) are Banach spaces and \(F: \Omega \subseteq X \rightarrow Y\) is a nonlinear operator on a non-empty open convex subset \(\Omega\). The methods are more general than the methods presented in their previous works (see [ibid. 64, No. 1, 105--126 (2013; Zbl 1279.65065)]). Moreover, the convergence conditions are also relaxed. They prove a convergence theorem to show the existence and uniqueness of the solution. The results of numerical experiments are also presented and discussed.
Mathematics Subject Classification ID: 65J15
Mathematics Subject Classification ID: 47J25
zbMATH DE Number: 6418191
zbMATH Keywords: recurrence relations
zbMATH Keywords: R-order of convergence
zbMATH Keywords: semilocal convergence
zbMATH Keywords: Chebyshev-Halley method
zbMATH Keywords: convergence condition
zbMATH Keywords: nonlinear operator equation
zbMATH Keywords: Banach space
zbMATH Keywords: numerical experiment
reviewed by: Przemysław Stpiczyński
MaRDI profile type: Publication
full work available at URL: s11075-014-9861-9
OpenAlex ID: W1984005925
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DOI: 10.1007/S11075-014-9861-9
description: scientific article; zbMATH DE number 6418191