A modification of the Chebyshev method

  1. Ezquerro, J.A. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
IMA journal of numerical analysis

ISSN: 0272-4979

Año de publicación: 1997

Volumen: 17

Número: 4

Páginas: 511-525

Tipo: Artículo

DOI: 10.1093/IMANUM/17.4.511 SCOPUS: 2-s2.0-0031480750 WoS: WOS:A1997YD74300002 GOOGLE SCHOLAR

Otras publicaciones en: IMA journal of numerical analysis

Repositorio institucional: lock_openAcceso abierto Editor

Resumen

In this paper we use a one-parametric family of second-order iterations to solve a nonlinear operator equation in a Banach space. Two different analyses of convergence are shown. First, under standard Newton-Kantorovich conditions, we establish a Kantorovich-type convergence theorem. Second, another Kantorovich-type convergence theorem is proved, when the first Fréchet-derivative of the operator satisfies a Lipschitz condition. We also give an explicit expression for the error bound of the family of methods in terms of a real parameter a α ≥ 0.