A new family of multipoint methods of second order.

  1. Ezquerro, J.A. 1
  2. Hernández, M.A. 1
  3. Salanova, M.A. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Numerical Functional Analysis and Optimization

ISSN: 0163-0563

Año de publicación: 1998

Volumen: 19

Número: 5

Páginas: 499-512

Tipo: Artículo

SCOPUS: 2-s2.0-0032119062 WoS: WOS:000075252800004 GOOGLE SCHOLAR

Otras publicaciones en: Numerical Functional Analysis and Optimization

Resumen

We introduce a new family of multipoint methods of R-order two to approximate a solution of nonlinear operators equation in Banach spaces. An existence-uniqueness theorem and error estimates are provided for this family of iterations using Newton-Kantorovich-type assumptions and a technique based on a new system of recurrence relations. For a special choice of the parameter involved, we obtain the Midpoint method, whose order of convergence is three.