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An identity for multivariate Bernstein polynomials |
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| Authors: | Kurt Jetter,Joachim St ckler |
| Affiliation: | a Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, D-70593, Stuttgart, Germany b Fachbereich Mathematik, Universität Dortmund, D-44221, Dortmund, Germany |
| Abstract: | We prove an identity for multivariate Bernstein polynomials on simplices, which may be considered a pointwise orthogonality relation. Its integrated version provides a new representation for the polynomial dual basis of Bernstein polynomials. An identity for the reproducing kernel is used to define quasi-interpolants of arbitrary order. |
| Keywords: | Bernstein polynomial Dual Quasi-interpolation Simplex |
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