Geodesic
On~approximations of compact sets of functions by algebraic surfaces
Izvestiya. Mathematics , Tome 27 (1986) no. 3, pp. 521-533.

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This article deals with approximations of certain compact sets of smooth and analytic functions by families of functions depending in a polynomial fashion on parameters. The connection between the accuracy of the approximations of the compact sets by such families and the number of parameters and their degree is studied. Bibliography: 3 titles. 
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S. N. Kudryavtsev. On~approximations of compact sets of functions by algebraic surfaces. Izvestiya. Mathematics , Tome 27 (1986) no. 3, pp. 521-533. http://geodesic.mathdoc.fr/item/IM2_1986_27_3_a4/

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

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

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