Abstract
For best piecewise polynomial approximation ℰn=ℰn (f; [0, 1]) of a functionf, which is continuous on the interval [0, 1] and admits a bounded analytic continuation onto the disk K=z:¦z−1¦<, the relation ℰn=o[ω f (e −√n)] is valid.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
A. A. Gonchar, “On the speed of a rational approximation of continuous functions with characteristic singularities,” Matem. Sb.,73 (115), No. 4, 630–638 (1967).
D. J. Newman, “Rational approximation to ¦x¦, ” Mich. Math. J.,2, No. 1, 11–14 (1964).
N. I. Akhiezer, Vorlesungen über Approximationstheorie, Akademie Verlag, Berlin (1967).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 11, No. 2, pp. 129–134, February, 1972.
Rights and permissions
About this article
Cite this article
Gonchar, A.A. Piecewise polynomial approximation. Mathematical Notes of the Academy of Sciences of the USSR 11, 83–86 (1972). https://doi.org/10.1007/BF01097921
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01097921