This article is cited in 2 papers

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.

UDC: 517.5

Received: 16.02.1976

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

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