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Smooth fractal interpolation

Journal of Inequalities and Applications volume 2006, Article number: 78734 (2006) Cite this article

Abstract

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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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad de Zaragoza, C/María de Luna 3, Zaragoza, 50018, Spain

    M. A. Navascués

  2. Departamento de Matemáticas, Universidad de Zaragoza, Campus Plaza de San Francisco s/n, Zaragoza, 50009, Spain

    M. V. Sebastián

Authors
  1. M. A. Navascués
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  2. M. V. Sebastián
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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 ( https://creativecommons.org/licenses/by/2.0 ), 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). https://doi.org/10.1155/JIA/2006/78734

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  • DOI: https://doi.org/10.1155/JIA/2006/78734

Keywords

  • Classical Method
  • Interpolation Error
  • Fractal Function
  • General Frame
  • Fractal Technique