Bicubic partially blended rational fractal surface for a constrained interpolation problem. (English) Zbl 1393.28005
Summary: This paper investigates some univariate and bivariate constrained interpolation problems using fractal interpolation functions. First, we obtain rational cubic fractal interpolation functions lying above a prescribed straight line. Using a transfinite interpolation via blending functions, we extend the properties of the univariate rational cubic fractal interpolation function to generate surfaces that lie above a plane. In particular, the constrained bivariate interpolation discussed herein includes a method to construct fractal interpolation surfaces that preserve positivity inherent in a prescribed data set. Uniform convergence of the bivariate fractal interpolant to the original function which generates the data is proven.
MSC:
| 28A80 | Fractals |
| 26C15 | Real rational functions |
| 41A05 | Interpolation in approximation theory |
| 65D05 | Numerical interpolation |
Keywords:
blending functions; fractal interpolation; bicubic partially blended fractal surface; convergence; constrained interpolation; positivitySoftware:
pchipReferences:
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