On the convergence of derivatives of Bernstein approximation

Journal of Approximation Theory

Volumn 134, Issue 1, 2005, Pages 130-135

  Floater, Michael S ^a  

^a UNIVERSITY OF OSLO   (Norway)

Author keywords

Asymptotic formula; Bernstein approximation; Divided difference; Error bound

Indexed keywords

EID: 17844389391     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jat.2004.02.009     Document Type: Article

References (9)

1. S.N. Bernstein Démonstration du théorème de Weierstrass fondée sur le calcul de probabilités Comm. Kharkov Math. Soc. 13 1912 1-2
2. S.D. Conte C. de Boor Elementary Numerical Analysis 1980 McGraw-Hill New York
3. P.J. Davis Interpolation and Approximation 1975 Dover New York
4. R.A. DeVore G.G. Lorentz Constructive Approximation 1993 Springer Berlin
5. T.N.T. Goodman Shape preserving representations in: T. Lyche L.L. Schumaker (Eds.) Mathematical Methods in Computer Aided Geometric Design 1989 Academic Press New York 333-357
6. A.J. López-Moreno J. Martínez-Moreno F.J. Muñoz-Delgado Asymptotic expression of derivatives of Bernstein type operators Rend. Circ. Mat. Palermo. Ser. II 68 2002 615-624
7. G.G. Lorentz Zur theorie der polynome von S. Bernstein Mate. Sbornik 2 1937 543-556
8. D.D. Stancu The remainder of certain linear approximation formulas in two variables SIAM J. Num. Anal. 1 1964 137-163
9. E. Voronovskaya, Détermination de la forme asymptotique d'approximation des fonctions par les polynômes de M. Bernstein, Dokl. Akad. Nauk SSSR (1932) 79-85.