Some variants of the Chebyshev-Halley family of methods with fifth-order of convergence

  1. Grau-Sánchez, M. 1
  2. Gutierrez, 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:
International Journal of Computer Mathematics

ISSN: 0020-7160

Año de publicación: 2010

Volumen: 87

Número: 4

Páginas: 818-833

Tipo: Artículo

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DOI: 10.1080/00207160802208358 SCOPUS: 2-s2.0-77951140632 WoS: WOS:000275825000010 GOOGLE SCHOLAR

Otras publicaciones en: International Journal of Computer Mathematics

Resumen

In this paper we present some techniques for constructing high-order iterative methods in order to approximate the zeros of a non-linear equation f(x)=0, starting from a well-known family of cubic iterative processes. The first technique is based on an additional functional evaluation that allows us to increase the order of convergence from three to five. With the second technique, we make some changes aimed at minimizing the calculus of inverses. Finally, looking for a better efficiency, we eliminate terms that contribute to the error equation from sixth order onwards. The paper contains a comparative study of the asymptotic error constants of the methods and some theoretical and numerical examples that illustrate the given results. We also analyse the efficiency of the aforementioned methods, by showing some numerical examples with a set of test functions and by using adaptive multi-precision arithmetic in the computation. © 2010 Taylor & Francis.