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A family of derivative-free methods with high order of convergence and its application to nonsmooth equations. (English) Zbl 1246.65079
Summary: A family of derivative-free methods of seventh-order convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the iteration. The efficiency indices of the members of this family are equal to $1.6266$. Also, numerical examples are used to show the performance of the presented methods, on smooth and nonsmooth equations, and to compare with other derivative-free methods, including some optimal fourth-order ones, in the sense of Kung-Traub’s conjecture.

65H05Single nonlinear equations (numerical methods)
Full Text: DOI
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