An hybrid method that improves the accessibility of Steffensen's method

  1. Ezquerro, J.A. 1
  2. Hernández-Verón, M.A. 1
  3. Rubio, M.J. 1
  4. Velasco, A.I. 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: 2014

Volumen: 66

Número: 2

Páginas: 241-267

Tipo: Artículo

DOI: 10.1007/S11075-013-9732-9 SCOPUS: 2-s2.0-84901987441 WoS: WOS:000338336700003 GOOGLE SCHOLAR

Otras publicaciones en: Numerical Algorithms

Repositorio institucional: lockAcceso abierto Editor

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Resumen

Steffensen's method is known for its fast speed of convergence and its difficulty in applying it in Banach spaces. From the analysis of the accessibility of this method, we see that we can improve it by using the simplified secant method for predicting the initial approximation of Steffensen's method. So, from both methods, we construct an hybrid iterative method which guarantees the convergence of Steffensen's method from approximations given by the simplified secant method. We also emphasize that the study presented in this work is valid for equations with differentiable operators and non-differentiable operators. © 2013 Springer Science+Business Media New York.