Asymptotic expansion and extrapolation for Bernstein polynomials with applications

BIT Numerical Mathematics

Volumn 36, Issue 4, 1996, Pages 676-687

  Costabile, F ^a   Gualtieri, M I ^a   Serra, S ^b  

^a UNIVERSITY OF CALABRIA   (Italy)

^b UNIVERSITY OF MILAN   (Italy)

Author keywords

Bernstein polynomials; Chebyshev interpolation; Extrapolation

Indexed keywords

EID: 0000777758     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF01733787     Document Type: Article

References (14)

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2. P. L. Butzer, Linear combinations of Bernstein polynomials, Can. J. Math., 5 (1953), pp. 559-567.
3. R. De Vore and G. Lorentz, Constructive Approximation, Springer-Verlag, Berlin, 1991.
4. Z. Ditzian, A global inverse theorem for combinations of Bernstein polynomials, J. Approximation Theory, 26 (1979), pp. 277-292.
5. H. Engels, Numerical Quadrature and Cubature, Acad. Press, London, 1980.
6. M. Frentiu, Linear combinations of Bernstein polynomials and of Mirakjan operators, Studia Univ. Babes-Boljai Ser. Math. Mech., 15 (1970), pp. 63-68.
7. D. Jackson, The Theory of Approximation, Amer. Math. Soc. Coll. Publ., 11, New York, 1930.
8. G. C. Lorentz, Bernstein Polynomials, Univ. of Toronto Press, Toronto, 1953.
9. C. P. May, Saturation and inversed theorems for combinations of a class of exponential-type operators, Can. J. Math., 28 (1976), pp. 1224-1250.
10. M. J .D. Powell, On the maximum errors of polynomial approximation defined by interpolation and least squares criteria, Comput. J., 9 (1966), pp. 404-407.
11. E. J. Remez, Sur le calcul effectif des polynomes d'approximation de Tchebichef, C. R. Acad. Sci. Paris, 199 (1934), pp. 337-340.
12. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, Springer-Verlag, Berlin, 1970.
13. P. Tang, A fast algorithm for linear complex Chebyshev approximation. Math. Comp., 51 (1988), pp. 721-739.
14. E. Voronowskaja, Détermination de la forme asymptotique d'approximation des fonctions par les polynomes de M. Bernstein, C. R. Acad. Sci. U.R.S.S., (1932), pp. 79-85.