Bivariate Spline Interpolation with Optimal Approximation Order

Davydov, Oleg V. ; Nürnberger, Günther ; Zeilfelder, Frank

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URN: urn:nbn:de:bsz:180-madoc-20640
Document Type: Working paper
Year of publication: 1999
The title of a journal, publication series: None
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Classification: MSC: 65D07 65D05 41A15 41A05 41A63 41A25 ,
Subject headings (SWD): Bivariater Spline , Hermite-Interpolation , Interpolation , Approximation , Minimalbasis
Keywords (English): bivariate spline , interpolation , approximation order , minimally supported basis , locally linearly independent basis , Hermite-type interpolation
Abstract: Let Δ be a triangulation of some polygonal domain Δ ⊂ R² and let Srq(Δ) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to Δ. We present a Hermite type interpolation scheme for Srq(Δ), q ≥ 3r +2, that possesses optimal approximation order Ο(h q+1). Furthermore, the fundamental functions of our scheme form a locally linearly independent basis for a superspline subspace of Srq(Δ).
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