On efficiency index of point-to-point iterative processes.

  1. Hernández, 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:
Numerical Algorithms

ISSN: 1017-1398

Año de publicación: 2007

Volumen: 46

Número: 1

Páginas: 35-44

Tipo: Artículo

DOI: 10.1007/S11075-007-9125-Z SCOPUS: 2-s2.0-35648985134 WoS: WOS:000250539300003 GOOGLE SCHOLAR

Otras publicaciones en: Numerical Algorithms

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Resumen

In this paper, we analyze the index of efficiency of one-point iterative processes, which are in practice the most used methods to solve a nonlinear equation. We obtain the best situation for one-point iterative processes with cubic convergence: Chebyshev's method, Halley's method, the super-Halley method and many others classical iterative methods with order of convergence three. By means of a construction of particular multipoint iterations, we get to improve the best situation obtained for one-point methods. Moreover, these type of multipoint iterations, can be considered as quasi-one-point iterations, since they only depend on one initial approximation. Numerical examples are given and the computed results support this theory. © 2007 Springer Science+Business Media LLC.