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Smooth fractal interpolation

Journal of Inequalities and Applications20062006:78734

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

©  M. A. Navascués and M. V. Sebastián 2006

Received: 12 December 2005

Accepted: 14 June 2006

Published: 4 September 2006

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’ Affiliations

(1)
Departamento de Matemática Aplicada, Universidad de Zaragoza
(2)
Departamento de Matemáticas, Universidad de Zaragoza

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Copyright

© M. A. Navascués and M. V. Sebastián 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.