Bernstein polynomials and learning theory

Journal of Approximation Theory

Volumn 128, Issue 2, 2004, Pages 187-206

  Braess, Dietrich ^a   Sauer, Thomas ^b  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b JUSTUS LIEBIG UNIVERSITY   (Germany)

Author keywords

Bernstein polynomials; Entropy function; Learning theory; Optimal encoding

Indexed keywords

EID: 3543139501     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jat.2004.04.010     Document Type: Article

References (14)

1. Aigner M. Diskrete Mathematik 1993 Vieweg Braunschweig
2. Amel'kovič V.G. A theorem converse to a theorem of Voronovskaya type Teor. Funkčiǐ, Funkcional Anal. i Prilozen, Vyp 2 1966 67-74
3. Berens H. Lorentz G.G. Inverse theorems for Bernstein polynomials Indiana Univ. Math. J. 21 1972 693-708
4. Berens H. Xu Y. K-moduli, moduli of smoothness, and Bernstein polynomials on a simplex Indag. Math. 2 1991 411-421
5. Braess D. Forster J. Sauer T. Simon H.U. How to achieve minimax expected Kullback-Leibler distance from an unknown finite distribution in: Cesa-Bianchi N. Numao N. Reischuk R. (Eds.). Algorithmic Learning Theory, Proceedings of the 13th International Conference ALT 2002 2002 380-394 Springer Heidelberg
6. Cover T.M. Admissibility properties of Gilbert's encoding for unknown source probabilities IEEE Trans. Inform. Theory 18 1971 216-217
7. Forster J. Warmuth M. Relative expected instantaneous loss bounds J. Comput. System Sci. 65 2002 612-625
8. Knoop H.-P. Zhou X. The lower estimate for linear positive operators. II Resultate Math. 25 1994 315-330
9. Krichevskiy R.E. Laplace's law of succession and universal encoding IEEE Trans. Inform. Theory 44 1 1998 296-303
10. G.G. Lorentz, Bernstein Polynomials, University of Toronto Press, 1953.
11. Popoviciu T. Sur l'approximation des fonctions convexes d'ordre superieur Mathematica 10 1935 49-54
12. Sauer T. The genuine Bernstein-Durrmeyer operator on a simplex Results Math. 26 1994 99-130
13. Shannon C.E. A mathematical theory of communication Bell System Tech. J. 27 1948 379-423, 623-656
14. Totik V. Approximation by Bernstein polynomials Amer. J. Math. 116 1994 995-1018