Numerical properties of different root-finding algorithms obtained for approximating continuous newton's method

  1. Gutiérrez, J.M. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Algorithms

ISSN: 1999-4893

Any de publicació: 2015

Volum: 8

Número: 4

Pàgines: 1210-1218

Tipus: Article

DOI: 10.3390/A8041210 SCOPUS: 2-s2.0-84952325297 WoS: WOS:000367618300024 GOOGLE SCHOLAR lock_openAccés obert editor

Altres publicacions en: Algorithms

Repositori institucional: lock_openAccés obert Editor

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Ecuaciones no lineales y métodos iterativos. Aplicaciones a problemas de optimización y ecuaciones matriciales. Nonlinear equations and iterative methods. Applications to optimization problems and matrix equations.

2015/00069/001

Resum

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. © 2015 by the authorlicensee MDPI, Basel, Switzerland.