Zero-finder methods derived from Obreshkov's techniques

  1. Grau-Sánchez, M. 1
  2. Gutiérrez, J.M. 2
  1. 1 Universitat Politècnica de Catalunya
    info

    Universitat Politècnica de Catalunya

    Barcelona, España

    ROR https://ror.org/03mb6wj31

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Applied Mathematics and Computation

ISSN: 0096-3003

Año de publicación: 2009

Volumen: 215

Número: 8

Páginas: 2992-3001

Tipo: Artículo

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DOI: 10.1016/J.AMC.2009.09.046 SCOPUS: 2-s2.0-70449531459 WoS: WOS:000271936400022 GOOGLE SCHOLAR

Otras publicaciones en: Applied Mathematics and Computation

Proyectos relacionados

Regiones de accesibilidad y optimización de procesos iterativos para resolver ecuaciones no lineales. Aplicaciones

2009/00009/001

Resumen

In this paper two families of zero-finding iterative methods for solving nonlinear equations f (x) = 0 are presented. The key idea to derive them is to solve an initial value problem applying Obreshkov-like techniques. More explicitly, Obreshkov's methods have been used to numerically solve an initial value problem that involves the inverse of the function f that defines the equation. Carrying out this procedure, several methods with different orders of local convergence have been obtained. An analysis of the efficiency of these methods is given. Finally we introduce the concept of extrapolated computational order of convergence with the aim of numerically test the given methods. A procedure for the implementation of an iterative method with an adaptive multi-precision arithmetic is also presented. © 2009 Elsevier Inc. All rights reserved.