Spline coalescence hidden variable fractal interpolation functions

Chand, A. K. B.; Kapoor, G. P.

doi:https://doi.org/10.1155/JAM/2006/36829

Journal of Applied Mathematics

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Volume 2006 | Article ID 036829 | https://doi.org/10.1155/JAM/2006/36829

Spline coalescence hidden variable fractal interpolation functions

A. K. B. Chand¹and G. P. Kapoor²

Received13 Feb 2006

Revised13 Jul 2006

Accepted08 Aug 2006

Published02 Nov 2006

Abstract

This paper generalizes the classical spline using a new construction of spline coalescence hidden variable fractal interpolation function (CHFIF). The derivative of a spline CHFIF is a typical fractal function that is self-affine or non-self-affine depending on the parameters of a nondiagonal iterated function system. Our construction generalizes the construction of Barnsley and Harrington (1989), when the construction is not restricted to a particular type of boundary conditions. Spline CHFIFs are likely to be potentially useful in approximation theory due to effects of the hidden variables and these effects are demonstrated through suitable examples in the present work.

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Copyright

Copyright © 2006 A. K. B. Chand and G. P. Kapoor. 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.

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