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A family of modified Ostrowski’s methods with optimal eighth order of convergence

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

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
214 KB
Volume
24
Category
Article
ISSN
0893-9659

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✦ Synopsis

In this paper, we derive a new family of eighth-order methods for obtaining simple roots of nonlinear equations by using the weight function method. 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 are optimal according to the Kung and Traub's conjecture (1974) [2]. Numerical comparisons are made to show the performance of the derived method, as is shown in the numerical section.

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