- Research Article
- Open Access
Smooth fractal interpolation
- M. A. Navascués1Email author and
- M. V. Sebastián2
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.
Keywords
- Classical Method
- Interpolation Error
- Fractal Function
- General Frame
- Fractal Technique
Authors’ Affiliations
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Copyright
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.
