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Three-step iterative methods with optimal eighth-order convergence. (English) Zbl 1215.65091
Authors’ abstract: 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.
MSC:
65H05Single nonlinear equations (numerical methods)
References:
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[8]Ostrowski, A. M.: Solutions of equations and systems of equations, (1966)
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