An improvement to double-step Newton method and its multi-step version for solving system of nonlinear equations and its applications
type: Item
instance of: scholarly article
title: An improvement to double-step Newton method and its multi-step version for solving system of nonlinear equations and its applications
zbMATH Open document ID: 1359.65078
author: Kalyanasundaram Madhu
author: J. Jayaraman
author: D. K. R. Babajee
published in: Numerical Algorithms
publication date: 2017-02-17T00:00:00Z
review text: The two-step fifth-order method, which is an improvement to the double-step Newton method as well as to the multi-step version of the two-step fifth-order method are proposed. The main advantages of the proposed schemes are the following: (i) they do not use second-order Fréchet derivatives and (ii) evaluate only one inverse of first-order Fréchet derivatives. It is verified that the root \(\alpha\) is a point of attraction for the proposed schemes in the sense of Ostrowski. The performances of the new methods are compared with Newton's method and some existing methods.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 6686470
zbMATH Keywords: system of nonlinear equations
zbMATH Keywords: Newton's method
zbMATH Keywords: order of convergence
zbMATH Keywords: multi-step method
zbMATH Keywords: Fréchet derivatives
zbMATH Keywords: point of attraction
reviewed by: Anton Iliev
MaRDI profile type: Publication
full work available at URL: s11075-016-0163-2
OpenAlex ID: W2470868123
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DOI: 10.1007/S11075-016-0163-2
description: scientific article; zbMATH DE number 6686470