On Complete Bicubic Fractal Splines

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.

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.

Keywords

Fractals, Iterated Function Systems, Fractal Interpolation Functions, Fractal Splines, Surface Approximation

Fractals, Iterated Function Systems, Fractal Interpolation Functions, Fractal Splines, Surface Approximation

Cite this paper

nullA. Chand and M. Navascués, "On Complete Bicubic Fractal Splines,"*Applied Mathematics*, Vol. 1 No. 3, 2010, pp. 200-210. doi: 10.4236/am.2010.13024.

nullA. Chand and M. Navascués, "On Complete Bicubic Fractal Splines,"

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