Browsing by Subject "Newton’s approximation method"

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    On the dynamics of a third order Newton's approximation method
    (Wiley, 2017) Gheondea, A.; Şamcı, M. E.
    We provide an answer to a question raised by S. Amat, S. Busquier, S. Plaza on the qualitative analysis of the dynamics of a certain third order Newton type approximation function Mf, by proving that for functions f twice continuously differentiable and such that both f and its derivative do not have multiple roots, with at least four roots and infinite limits of opposite signs at ±∞, Mf has periodic points of any prime period and that the set of points a at which the approximation sequence (Mn f(a))n ∈ ℕ does not converge is uncountable. In addition, we observe that in their Scaling Theorem analyticity can be replaced with differentiability. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim