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 Mat. Zametki, 1977, Volume 22, Issue 5, Pages 663–670 (Mi mz8090)

Optimal interpolation of differentiable periodic functions with bounded higher derivative

V. L. Velikin

Dnepropetrovsk State University

Abstract: The problem of the optimal recovery of functions from the set $W_M^r$ is considered. It is shown, in particular, that for such recovery the use of information about the values of the function at $2n$ points gives the error in the norm of the space $C$ two times, and $\pi K_r/(2K_{r+1})$ times ($K_r$ is the Favard constant) in the norm of the space $L$, less than that by the use of the information about the values of the function and its derivatives at $n$ points.

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English version:
Mathematical Notes, 1977, 22:5, 860–865

Bibliographic databases:

UDC: 517.5

Citation: V. L. Velikin, “Optimal interpolation of differentiable periodic functions with bounded higher derivative”, Mat. Zametki, 22:5 (1977), 663–670; Math. Notes, 22:5 (1977), 860–865

Citation in format AMSBIB
\Bibitem{Vel77} \by V.~L.~Velikin \paper Optimal interpolation of differentiable periodic functions with bounded higher derivative \jour Mat. Zametki \yr 1977 \vol 22 \issue 5 \pages 663--670 \mathnet{http://mi.mathnet.ru/mz8090} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=467085} \zmath{https://zbmath.org/?q=an:0364.41003} \transl \jour Math. Notes \yr 1977 \vol 22 \issue 5 \pages 860--865 \crossref{https://doi.org/10.1007/BF01098350} 

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This publication is cited in the following articles:
1. B. D. Boyanov, “The optimal recovery of smooth functions”, Math. USSR-Sb., 69:2 (1991), 357–377
2. S. P. Sidorov, “Optimal Recovery of Linear Functionals on Sets of Finite Dimension”, Math. Notes, 84:4 (2008), 561–567
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