Geodesic
On~approximations of compact sets of functions by piecewise polynomial surfaces
Izvestiya. Mathematics , Tome 31 (1988) no. 3, pp. 455-480.

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This article is concerned with approximations of certain concrete sets of functions of a single real (or complex) variable by families of functions that depend in a piecewise polynomial and smooth manner on several real parameters. A study is made of how the accuracy of such approximations is connected with the number of parameters, the degree, the number of “pieces”, and the smoothness of the approximating families of functions. Bibliography: 5 titles. 
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S. N. Kudryavtsev. On~approximations of compact sets of functions by piecewise polynomial surfaces. Izvestiya. Mathematics , Tome 31 (1988) no. 3, pp. 455-480. http://geodesic.mathdoc.fr/item/IM2_1988_31_3_a1/

[1] Vitushkin A. G., Otsenka slozhnosti zadachi tabulirovaniya, Fizmatgiz, M., 1959

[2] Ivanov L. D., Variatsii mnozhestv i funktsii, Nauka, M., 1975 | MR

[3] Kolmogorov A. N., Tikhomirov V. M., “$\varepsilon$-entropiya i $\varepsilon$-emkost mnozhestv v funktsionalnykh prostranstvakh”, Uspekhi matem. nauk, 14:2 (1959), 3–86 | MR

[4] Kudryavtsev S. N., “Ob approksimatsiyakh funktsionalnykh kompaktov algebraicheskimi poverkhnostyami”, Izv. AN SSSR. Ser. matem., 49:6 (1985), 1246–1259 | MR

[5] Warren H. E., “A construction of certain nonlinear approximating families”, Proc. Amer. Math. Soc., 21:2 (1969), 467–470 | DOI | MR | Zbl