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Smooth fractal interpolation


Fractal methodology provides a general frame for the understanding of real-world phenomena. In particular, the classical methods of real-data interpolation can be generalized by means of fractal techniques. In this paper, we describe a procedure for the construction of smooth fractal functions, with the help of Hermite osculatory polynomials. As a consequence of the process, we generalize any smooth interpolant by means of a family of fractal functions. In particular, the elements of the class can be defined so that the smoothness of the original is preserved. Under some hypotheses, bounds of the interpolation error for function and derivatives are obtained. A set of interpolating mappings associated to a cubic spline is defined and the density of fractal cubic splines in is proven.



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Correspondence to M. A. Navascués.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Navascués, M.A., Sebastián, M.V. Smooth fractal interpolation. J Inequal Appl 2006, 78734 (2006).

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