Abstract
Using a baseb and an even number of knots, we define a symmetric iterative interpolation process. The main properties of this process come from an associated functionF. The basic functional equation forF is thatF(t/b)=σn F(n/b)F(t-n). We prove thatF is a continuous positive definite function. We find almost precisely in which Lipschitz classes derivatives ofF belong. If a functiony is defined only on integers, this process extendsy continuously to the real axis asy(t=∑ n y(n)F(t−n). Error bounds for this iterative interpolation are given.
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Communicated by Michael F. Barnsley.
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Deslauriers, G., Dubuc, S. Symmetric iterative interpolation processes. Constr. Approx 5, 49–68 (1989). https://doi.org/10.1007/BF01889598
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DOI: https://doi.org/10.1007/BF01889598