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Fractal approximation of jackson type for periodic phenomena
Published in World Scientific Publishing Co. Pte Ltd
2018
Volume: 26
   
Issue: 5
Abstract
The reconstruction of an unknown function providing a set of Lagrange data can be approached by means of fractal interpolation. The power of that methodology allows us to generalize any other interpolant, both smooth and nonsmooth, but the important fact is that this technique provides one of the few methods of nondifferentiable interpolation. In this way, it constitutes a functional model for chaotic processes. This paper studies a generalization of an approximation formula proposed by Dunham Jackson, where a wider range of values of an exponent of the basic trigonometric functions is considered. The trigonometric polynomials are then transformed in close fractal functions that, in general, are not smooth. For suitable election of this parameter, one obtains better conditions of convergence than in the classical case: the hypothesis of continuity alone is enough to ensure the convergence when the sampling frequency is increased. Finally, bounds of discrete fractal Jackson operators and their classical counterparts are proposed. © 2018 World Scientific Publishing Company.
About the journal
JournalFractals
PublisherWorld Scientific Publishing Co. Pte Ltd
ISSN0218348X
Open AccessNo
Concepts (11)
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    Curve fitting
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    Interpolation
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    CLASSICAL COUNTERPART
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    Convergence
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    FRACTAL APPROXIMATION
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    FRACTAL INTERPOLATION
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    Smoothing
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    TRIGONOMETRIC APPROXIMATION
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    Trigonometric functions
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    TRIGONOMETRIC POLYNOMIAL
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    Fractals