2019
DOI: 10.1002/mma.6014
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On the choice of the best members of the Kim family and the improvement of its convergence

Abstract: The best members of the Kim family, in terms of stability, are obtained by using complex dynamics. From this elements, parametric iterative methods with memory are designed. A dynamical analysis of the methods with memory is presented in order to obtain information about the stability of them. Numerical experiments are shown for confirming the theoretical results. KEYWORDSbasin of attraction, iterative methods with memory, low-dimensional dynamical systems, nonlinear algebraic or transcendental equations, para… Show more

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Cited by 15 publications
(8 citation statements)
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“…The asymptotic behavior of the critical points is a key fact in analyzing the stability of the method. Previous results [25] state that at least one critical point appears in each immediate basin of attraction, that is, in the connected component of the basin of attraction containing the attractor. Let us also remark that superattracting fixed points are indeed critical points.…”
Section: Basic Dynamical Conceptsmentioning
confidence: 99%
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“…The asymptotic behavior of the critical points is a key fact in analyzing the stability of the method. Previous results [25] state that at least one critical point appears in each immediate basin of attraction, that is, in the connected component of the basin of attraction containing the attractor. Let us also remark that superattracting fixed points are indeed critical points.…”
Section: Basic Dynamical Conceptsmentioning
confidence: 99%
“…In this case, each point of the plane refers to a value of G3 ∈ Ĉ, that is, a member of Family (4). Instead of representing the 11 parameter planes, we just represent the unified parameter plane [25] for the sake of simplicity. White points represent convergence to any of the roots, whereas black points represent convergence to a different point or even divergence.…”
Section: Critical Points and Parameter Planesmentioning
confidence: 99%
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“…Cordero et al constructed a multi-step method based on Steffensen's method [18]. Also, in [19], some methods to find the solutions of nonlinear systems were investigated. Kanwar et al [20] presented a new method to compute the multiple roots of problems.…”
Section: Introductionmentioning
confidence: 99%
“…Using this technique, the stability of the fixed and critical points of secant, Steffensen' and Kurchatov's methods (among others) were studied in [19]. It was also used to analyze other procedures, such as those described in [20], the one defined by Choubey et al in [21] and those by Chicharro et al in [22][23][24].…”
Section: Introductionmentioning
confidence: 99%