Three-step iterative methods with optimal eighth-order convergence

Authors:
Alicia Cordero;Juan R. Torregrosa;María P. Vassileva
Affiliations:
Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022, Valencia, Spain;Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46022, Valencia, Spain;Instituto Tecnológico de Santo Domingo (INTEC), Avda. Los Próceres, Gala, Santo Domingo, République dominicaine
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

Citing 3
Cited 3

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Iterative methods for solving nonlinear equations with finitely many roots in an interval

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On improved three-step schemes with high efficiency index and their dynamics

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Abstract

In this paper, based on Ostrowski's method, a new family of eighth-order methods for solving nonlinear equations is derived. In terms of computational cost, each iteration of these methods requires three evaluations of the function and one evaluation of its first derivative, so that their efficiency indices are 1.682, which is optimal according to Kung and Traub's conjecture. Numerical comparisons are made to show the performance of the new family.