Journal of Applied Mathematics
Volume 2006 (2006), Article ID 36829, 17 pages

Spline coalescence hidden variable fractal interpolation functions

A. K. B. Chand1 and G. P. Kapoor2

1Mathematics Group, Birla Institute of Technology and Science, Pilani, Goa Campus, Vasco da Gama, 403726, Goa, India
2Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur 208 016, India

Received 13 February 2006; Revised 13 July 2006; Accepted 8 August 2006

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.


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.