Some variants of Ostrowski's method with seventh-order convergence

Authors:
Jisheng Kou;Yitian Li;Xiuhua Wang
Affiliations:
Department of Mathematics, Shanghai University, Shanghai 200444, China and State Key Laboratory of Water Resources and Hydropower Engineering Sciences, Wuhan University, Wuhan 430072, China;State Key Laboratory of Water Resources and Hydropower Engineering Sciences, Wuhan University, Wuhan 430072, China;Department of Mathematics, Xiaogan University, Xiaogan 432100, Hubei, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

In this paper, we present a class of new variants of Ostrowski's method with order of convergence seven. Per iteration the new methods require three evaluations of the function and one evaluation of its first derivative and therefore this class of methods has the efficiency index equal to 1.627. Numerical tests verifying the theory are given, and multistep iterations, based on the present methods, are developed.