Complexity of an homotopy method at the neighbourhood of a zero

  1. Yakoubsohn, J.-C. 3
  2. Gutiérrez, J.M. 1
  3. Magreñán, Á.A. 2
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

  2. 2 Universidad Internacional de La Rioja
    info

    Universidad Internacional de La Rioja

    Logroño, España

    ROR https://ror.org/029gnnp81

  3. 3 Paul Sabatier University
    info

    Paul Sabatier University

    Tolosa, Francia

    ROR https://ror.org/02v6kpv12

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Libro:
Advances in Iterative Methods for Nonlinear Equations

Editorial: Springer

ISBN: 978-3-319-39227-1

Año de publicación: 2016

Volumen: 10

Páginas: 147-171

Tipo: Capítulo de Libro

DOI: 10.1007/978-3-319-39228-8_7 SCOPUS: 2-s2.0-85031750534 WoS: WOS:000400343500007 GOOGLE SCHOLAR

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

This paper deals with the enlargement of the region of convergence of Newton’s method for solving nonlinear equations defined in Banach spaces. We have used an homotopy method to obtain approximate zeros of the considered function. The novelty in our approach is the establishment of new convergence results based on a Lipschitz condition with a L-average for the involved operator. In particular, semilocal convergence results (Kantorovich-type results), as well as local convergence results (γ-theory) are obtained. © Springer International Publishing Switzerland 2016.