On a Steffensen-like method for solving nonlinear equations

  1. Amat, S. 1
  2. Ezquerro, J.A. 2
  3. Hernández-Verón, M.A. 2
  1. 1 Universidad Politécnica de Cartagena
    info

    Universidad Politécnica de Cartagena

    Cartagena, España

    ROR https://ror.org/02k5kx966

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Calcolo

ISSN: 0008-0624

Año de publicación: 2015

Volumen: 53

Número: 2

Páginas: 171

Tipo: Artículo

DOI: 10.1007/S10092-015-0142-3 SCOPUS: 2-s2.0-84927544664 WoS: WOS:000376417100003 GOOGLE SCHOLAR

Otras publicaciones en: Calcolo

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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

Procesos iteratios para resolver ecuaciones no lineales: construcción, convergencia, eficacia, análisis dinámico y aplicaciones

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Resumen

We study a generalization of Steffensen’s method in Banach spaces. Our main aim is to obtain similar convergence as Newton’s method, but without evaluating the first derivative of the operator involved. As motivation, we analyse numerical solutions of boundary-value problems approximated by the multiple shooting method that uses the proposed iterative scheme. Sufficient conditions for the semilocal convergence analysis of the method, including error estimates and the (Formula presented.)-order of convergence, are provided. Finally, the theoretical results are applied to a nonlinear system of equations related with the approximation of a Hammerstein-type integral equation. © 2015 Springer-Verlag Italia