An identity for multivariate Bernstein polynomials

Authors:
Kurt Jetter;Joachim Stöckler
Affiliations:
Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, D-70593 Stuttgart, Germany;Fachbereich Mathematik, Universität Dortmund, D-44221 Dortmund, Germany
Venue:
Computer Aided Geometric Design
Year:
2003

Citing 5
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A new proof of an identity of Jetter and Stöckler for multivariate Bernstein polynomials

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An identity for a general class of approximation operators

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A new proof of an identity of Jetter and Stöckler for multivariate Bernstein polynomials

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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.