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
Authors’ Affiliations
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