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Algorithms 2015, 8(4), 1210-1218; doi:10.3390/a8041210

Numerical Properties of Different Root-Finding Algorithms Obtained for Approximating Continuous Newton’s Method

Department of Mathematics and Computer Sciences, University of La Rioja, Logroño 26004, Spain
Academic Editors: Alicia Cordero, Juan R. Torregrosa and Francisco I. Chicharro
Received: 28 October 2015 / Revised: 10 December 2015 / Accepted: 14 December 2015 / Published: 17 December 2015
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems)
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Abstract

This paper is dedicated to the study of continuous Newton’s method, which is a generic differential equation whose associated flow tends to the zeros of a given polynomial. Firstly, we analyze some numerical features related to the root-finding methods obtained after applying different numerical methods for solving initial value problems. The relationship between the step size and the order of convergence is particularly considered. We have analyzed both the cases of a constant and non-constant step size in the procedure of integration. We show that working with a non-constant step, the well-known Chebyshev-Halley family of iterative methods for solving nonlinear scalar equations is obtained. View Full-Text
Keywords: continuous Newton’s method; Newton’s method; nonlinear equations; iterative methods continuous Newton’s method; Newton’s method; nonlinear equations; iterative methods
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Gutiérrez, J.M. Numerical Properties of Different Root-Finding Algorithms Obtained for Approximating Continuous Newton’s Method. Algorithms 2015, 8, 1210-1218.

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