On the local convergence of a third order family of iterative processes

  1. Hernández-Verón, M.A. 1
  2. Romero, N. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Algorithms

ISSN: 1999-4893

Año de publicación: 2015

Volumen: 8

Número: 4

Páginas: 1121-1128

Tipo: Artículo

DOI: 10.3390/A8041121 SCOPUS: 2-s2.0-84952314711 WoS: WOS:000367618300019 GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Algorithms

Repositorio institucional: lock_openAcceso abierto Editor

Proyectos relacionados

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

Resumen

Efficiency is generally the most important aspect to take into account when choosing an iterative method to approximate a solution of an equation, but is not the only aspect to consider in the iterative process. Another important aspect toconsider is the accessibility of the iterative process, which shows the domain of starting points from which the iterativeprocess converges to a solution of the equation. So, we consider a family of iterative processes with a higher efficiency index than Newton's method. However, this family of proecsses presents problems of accessibility to the solution x*. Froma local study of the convergence of this family, we perform an optimization study of the accessibility and obtain iterative processes with better accessibility than Newton's method. © 2015 by the authors; licensee MDPI, Basel, Switzerland.