A Family of Optimal Methods for Solving Nonlinear Equations
نویسندگان
چکیده
In this paper we show a family of iterative schemes for solving nonlinear equations with order of convergence 2, by using n+ 1 functional evaluations per step, so these methods are optimal in the sense of the Kung-Traub’s conjecture. The family is obtained by composing n Newton’s steps and approximating the derivative by using Hermite’s interpolation polynomial. Some numerical examples are provided to confirm the theoretical results and to show the good performance of the new methods, comparing them with a well known family of similar characteristics.
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