Convexity Preserving Interpolatory Subdivision Schemes |
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Authors: | F Kuijt R van Damme |
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Institution: | (1) Faculty of Applied Mathematics University of Twente P.O. Box 217 NL-7500 AE Enschede The Netherlands http://www.math.utwente.nl/~kuijt f.kuijt@math.utwente.nl, NL;(2) Faculty of Applied Mathematics University of Twente P.O. Box 217 NL-7500 AE Enschede The Netherlands http://www.math.utwente.nl/~vandamme vandamme@math.utwente.nl, NL |
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Abstract: | We construct local subdivision schemes that interpolate functional univariate data and that preserve convexity. The resulting
limit function of these schemes is continuous and convex for arbitrary convex data. Moreover this class of schemes is restricted
to a subdivision scheme that generates a limit function that is convex and continuously differentiable for strictly convex
data. The approximation order of this scheme is four. Some generalizations, such as tension control and piecewise convexity
preservation, are briefly discussed.
November 29, 1996. Date revised: May 28, 1997. |
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Keywords: | , Subdivision schemes, Convexity preservation, Interpolation, AMS Classification, 41A05, 41A29, 65D05, 65D17, |
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