Numerical properties of different root-finding algorithms obtained for approximating continuous Newton's method
type: Item
instance of: scholarly article
title: Numerical properties of different root-finding algorithms obtained for approximating continuous Newton's method
zbMATH Open document ID: 1461.65076
author: Xianqiang Yang
published in: Algorithms
publication date: 2019-03-26T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 7042309
zbMATH Keywords: continuous Newton's method
zbMATH Keywords: Newton's method
zbMATH Keywords: nonlinear equations
zbMATH Keywords: iterative methods
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a8041210
OpenAlex ID: W2218281265
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DOI: 10.3390/A8041210
description: scientific article; zbMATH DE number 7042309