Convergence of Steffensen’s method for non-differentiable operators

  1. Argyros, I.K. 2
  2. Hernández-Verón, M.A. 1
  3. Rubio, M.J. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Cameron University
    info

    Cameron University

    Lawton, Estados Unidos

    ROR https://ror.org/00rgv0036

Revista:
Numerical Algorithms

ISSN: 1017-1398

Año de publicación: 2017

Volumen: 75

Número: 1

Páginas: 229-244

Tipo: Artículo

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DOI: 10.1007/S11075-016-0203-Y SCOPUS: 2-s2.0-84987668192 WoS: WOS:000399741400010 GOOGLE SCHOLAR

Otras publicaciones en: Numerical Algorithms

Objetivos de desarrollo sostenible

Proyectos relacionados

Ecuaciones no lineales y métodos iterativos. Aplicaciones a problemas de optimización y ecuaciones matriciales. Nonlinear equations and iterative methods. Applications to optimization problems and matrix equations.

2015/00069/001

Resumen

We present a semilocal as well as a local convergence analysis of Steffensen’s method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The novelty of this paper is twofold. On the one hand, we show convergence under general conditions including earlier ones as special cases. In particular, these conditions allow the important study when the operator involved is not differentiable. On the other hand, we use a combination of conditions that allow a more precise computation of the upper bounds on the norms of the inverses involved leading to a tighter convergence analysis. Finally, we provide numerical examples involving nonlinear integral equations on mixed Hammerstein type that appear in chemistry, vehicular traffic theory, biology, and queuing theory. © 2016 Springer Science+Business Media New York