A family of iterative methods that uses divided differences of first and second orders
type: Item
instance of: scholarly article
title: A family of iterative methods that uses divided differences of first and second orders
zbMATH Open document ID: 1329.65105
author: Miquel Noguera
author: J. A. Ezquerro
author: Miquel Grau-Sánchez
author: Miguel A. Hernández Verón
published in: Numerical Algorithms
publication date: 2015-11-17T00:00:00Z
full work available at URL: http://hdl.handle.net/2117/80873
review text: This paper extends a biparametric family of fourth-order Steffensen-type derviative-free iterative methods that uses multidimensional divided differences of first and second orders for solving systems of nonlinear equations. In considering the computational efficiency, two optimal methods are identified. The semilocal convergence of one of these optimal methods is studied by using a technique based on recurrence relations. A numerical example of a system of nonlinear equations that arises from a process of discretization of a nonlinear integral equation of mixed Hammerstein type is used to demonstrate the theoretical results.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 65Y20
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 6510061
zbMATH Keywords: divided difference
zbMATH Keywords: order of convergence
zbMATH Keywords: efficiency
zbMATH Keywords: fourth-order Steffensen-type derviative-free iterative methods
zbMATH Keywords: systems of nonlinear equations
zbMATH Keywords: numerical example
zbMATH Keywords: nonlinear integral equation of mixed Hammerstein type
describes a project that uses: MPFR
MaRDI profile type: Publication
OpenAlex ID: W2056197860
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DOI: 10.1007/S11075-015-9962-0
description: scientific article; zbMATH DE number 6510061