On a class of iterations containing the Chebyshev and the Halley methods.

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

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Publicationes mathematicae Debrecen

ISSN: 0033-3883

Año de publicación: 1999

Volumen: 54

Número: 3

Páginas: 403-415

Tipo: Artículo

SCOPUS: 2-s2.0-0040628187 WoS: WOS:000082234600015 GOOGLE SCHOLAR

Otras publicaciones en: Publicationes mathematicae Debrecen

Resumen

We investigate a parametrized set of cubically convergent iterative methods for solving nonlinear equations in a Banach space. The methods can be thought of as a weighted mean between the Chebyshev and the Halley methods, the weights being a and 1 - α, where α ∈ (-15, 2). A Kantorovich-type convergence theorem and corresponding error bounds are provided. Finally, we decide that Halley's method is more suitable for solving a nonlinear equation than Chebyshev's method. Even more, we can consider other iterations more suitable than Halley's one.