Geodesic
Optimal interpolation of differentiable periodic functions with bounded higher derivative
Matematičeskie zametki, Tome 22 (1977) no. 5, pp. 663-670 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{MZM_1977_22_5_a6,
     author = {V. L. Velikin},
     title = {Optimal interpolation of differentiable periodic functions with bounded higher derivative},
     journal = {Matemati\v{c}eskie zametki},
     pages = {663--670},
     year = {1977},
     volume = {22},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_5_a6/}
}
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AU  - V. L. Velikin
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JO  - Matematičeskie zametki
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EP  - 670
VL  - 22
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_1977_22_5_a6/
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ID  - MZM_1977_22_5_a6
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%A V. L. Velikin
%T Optimal interpolation of differentiable periodic functions with bounded higher derivative
%J Matematičeskie zametki
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%P 663-670
%V 22
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1977_22_5_a6/
%G ru
%F MZM_1977_22_5_a6
V. L. Velikin. Optimal interpolation of differentiable periodic functions with bounded higher derivative. Matematičeskie zametki, Tome 22 (1977) no. 5, pp. 663-670. http://geodesic.mathdoc.fr/item/MZM_1977_22_5_a6/