TITLE:
On Complete Bicubic Fractal Splines
AUTHORS:
Arya Kumar Bedabrata Chand, María A. Navascués
KEYWORDS:
Fractals, Iterated Function Systems, Fractal Interpolation Functions, Fractal Splines, Surface Approximation
JOURNAL NAME:
Applied Mathematics,
Vol.1 No.3,
September
29,
2010
ABSTRACT: Fractal geometry provides a new insight to the approximation and modelling of experimental data. We give the construction of complete cubic fractal splines from a suitable basis and their error bounds with the original function. These univariate properties are then used to investigate complete bicubic fractal splines over a rectangle Bicubic fractal splines are invariant in all scales and they generalize classical bicubic splines. Finally, for an original function , upper bounds of the error for the complete bicubic fractal splines and derivatives are deduced. The effect of equal and non-equal scaling vectors on complete bicubic fractal splines were illustrated with suitably chosen examples.