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Some variants of Ostrowski’s method with seventh-order convergence. (English) Zbl 1130.41006
Summary: 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.

41A25Rate of convergence, degree of approximation
65D99Numerical approximation
Full Text: DOI
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