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On Complete Bicubic Fractal Splines

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DOI: 10.4236/am.2010.13024    4,684 Downloads   8,869 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

A. 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.

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