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Three-step iterative methods with optimal eighth-order convergence

✍ Scribed by Alicia Cordero; Juan R. Torregrosa; María P. Vassileva

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
206 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

order a b s t r a c t

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.

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