On a characterization of some Newton-like methods of R-order at least three

Authors:
M. A. Hernández;N. Romero
Affiliations:
Department of Mathematics and Computation, University of La Rioja, C/Luis de Ulloa s/n, 26004 Logroño, Spain;Department of Mathematics and Computation, University of La Rioja, C/Luis de Ulloa s/n, 26004 Logroño, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

In this paper, we extend to Banach spaces the result given by Gander in (Amer. Math. Monthly 92 (1985) 131) to obtain a characterization of Newton-like iterative process with R-order of convergence at least three. To do this, we consider the construction and the study of the semilocal convergence of a multiparametric family of iterative processes in Banach spaces for solving the nonlinear equation F(x)=0.