An identity for multivariate Bernstein polynomials

Computer Aided Geometric Design

Volumn 20, Issue 8-9, 2003, Pages 563-577

  Jetter, Kurt ^a   Stöckler, Joachim ^b  

^a UNIVERSITY OF HOHENHEIM   (Germany)

^b TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Bernstein polynomial; Dual; Quasi interpolation; Simplex

Indexed keywords

INTEGRATION; INTERPOLATION; MATHEMATICAL OPERATORS; THEOREM PROVING;

QUASI-INTERPOLANTS;

POLYNOMIALS;

EID: 0344465816     PISSN: 01678396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cagd.2003.06.005     Document Type: Article

References (13)

1. Berens H., Schmidt H.J., Xu Y. Bernstein-Durrmeyer polynomials on a simplex. J. Approx. Theory. 68:1992;247-261.
2. Braess D., Schwab C. Approximation on simplices with respect to weighted Sobolev norms. J. Approx. Theory. 103:2000;329-337.
3. Chen W., Ditzian Z. Multivariate Durrmeyer-Bernstein operators. Israel Math. Conf. Proc. 4:1991;109-119.
4. 2(S) . J. Approx. Theory. 72:1993;234-236.
5. Chui, C.K., He, W., Stöckler, J., 2003. Nonstationary tight spline frames on bounded intervals, Preprint 230, Department of Mathematics, University of Dortmund.
6. Ciesielski Z. The basis of B -splines in the space of algebraic polynomials. Ukrainian Math. J. 38:1986;311-315.
7. Derriennic M.-M. On multivariate approximation by Bernstein-type polynomials. J. Approx. Theory. 45:1985;155-166.
8. Derriennic M.-M. Linear combinations of derivatives of Bernstein-type polynomials on a simplex. Coll. Math. Soc. Janos Bolyai. 58:1990;197-220.
9. Gould H.W. Combinatorial Identities. 1972;Henry W. Gould, Morgantown, VA.
10. Jüttler B. The dual basis functions for the Bernstein polynomials. Adv. Comput. Math. 8:1998;345-352.
11. Sablonnière P. Bernstein-type quasi-interpolants. Laurent P.-J., Le Méhauté A., Schumaker L.L. Curves and Surfaces. 1991;421-426 Academic Press, Boston.
12. Sablonnière P. Representation of quasi-interpolants as differential operators and applications. Müller M.W., Buhmann M.D., Mache D.H., Felten M. New Developments in Approximation Theory. 1999;233-253 Birkhäuser-Verlag, Basel.
13. Zhao K., Sun J. Dual basis of multivariate Bernstein-Bézier polynomials. Computer Aided Geometric Design. 5:1988;119-125.