On Developing an Adaptive Free-Derivative Kung and Traub’s Method with Memory

Mohammad Javad Lalehchini, Taher Lotfi, Katayoun Mahdiani

Abstract


In this paper, there has been developed an adaptive method
with memory based on the on the first two steps of the general optimal
method without memory by Kung and Traub. Included is convergence
analysis along with numerical implementations. The proposed adaptive
method with memory can increase the efficiency index of the optimal
method without memory as high as possible while reusing all the available information of the functional evaluations in the previous iteration
for this purpose. Also, we discuss the numerical stability from the point
of basins of attraction.

Keywords


Nonlinear Equation, Method with and without Memory, Adaptive Method, Efficiency Index, Basins of Attraction.

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