A modification of the Chebyshev method
-
1
Universidad de La Rioja
info
ISSN: 0272-4979
Año de publicación: 1997
Volumen: 17
Número: 4
Páginas: 511-525
Tipo: Artículo
Otras publicaciones en: IMA journal of numerical analysis
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.