On efficiency index of point-to-point iterative processes.
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Universidad de La Rioja
info
ISSN: 1017-1398
Ano de publicación: 2007
Volume: 46
Número: 1
Páxinas: 35-44
Tipo: Artigo
Outras publicacións en: Numerical Algorithms
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Resumo
In this paper, we analyze the index of efficiency of one-point iterative processes, which are in practice the most used methods to solve a nonlinear equation. We obtain the best situation for one-point iterative processes with cubic convergence: Chebyshev's method, Halley's method, the super-Halley method and many others classical iterative methods with order of convergence three. By means of a construction of particular multipoint iterations, we get to improve the best situation obtained for one-point methods. Moreover, these type of multipoint iterations, can be considered as quasi-one-point iterations, since they only depend on one initial approximation. Numerical examples are given and the computed results support this theory. © 2007 Springer Science+Business Media LLC.