A Traub type result for one-point iterative methods with memory

  1. Ezquerro, J.A. 2
  2. Grau-Sánchez, M. 1
  3. Hernández-Verón, M.A. 2
  4. Noguera, M. 1
  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:
Analysis and Applications

ISSN: 0219-5305

Año de publicación: 2014

Volumen: 12

Número: 3

Páginas: 323-340

Tipo: Artículo

DOI: 10.1142/S021953051450016X SCOPUS: 2-s2.0-84898885027 WoS: WOS:000334733200005 GOOGLE SCHOLAR

Otras publicaciones en: Analysis and Applications

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Resumen

We present an extension of a well-known result of Traub to increase the R-order of convergence of one-point iterative methods by a simple modification of this type of methods. We consider the extension to one-point iterative methods with memory and present a particular case where Kurchatov's method is used. Moreover, we analyze the efficiency and the semilocal convergence of this method. Finally, two applications are presented, where differentiable and nondifferentiable equations are considered, that illustrate the above-mentioned. © 2014 World Scientific Publishing Company.