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Shape preserving \(\alpha\)-fractal rational cubic splines. (English) Zbl 1447.28005

Univariate polynomials, rational functions, splines and, in particular, cubic splines are all very helpful for interpolation and other approximants in one dimension. Also, rational functions formed from cubic and quadratic polynomials are useful, and a particular interest lies in recovering properties of data such as boundedness, monotonicity etc.
In this article, rational functions with cubic and quadratics are considered and analysed with respect to convergence, positivity, boundedness and monotonicity. Many of these highly relevant properties are established, and numerical examples prove the usefulness of this ansatz.

MSC:

28A80 Fractals
26C15 Real rational functions
41A05 Interpolation in approximation theory
41A29 Approximation with constraints

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References:

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