Geodesic
Polygonal approximation of functions of two variables
Sbornik. Mathematics, Tome 35 (1979) no. 6, pp. 851-861 
K. I. Oskolkov. Polygonal approximation of functions of two variables. Sbornik. Mathematics, Tome 35 (1979) no. 6, pp. 851-861. http://geodesic.mathdoc.fr/item/SM_1979_35_6_a4/
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     author = {K. I. Oskolkov},
     title = {Polygonal approximation of functions of two variables},
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     volume = {35},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1979_35_6_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper studies the approximation of functions of two variables by functions whose graphs in $3$-space are continuous surfaces which are piecewise flat. By analogy with the case of functions of one variable, we naturally call such approximating functions polygonal. Bibliography: 8 titles.

[1] N. P. Korneichuk i A. I. Polovina, “O priblizhenii nepreryvnykh i differentsiruemykh funktsii algebraicheskimi mnogochlenami na otrezke”, DAN SSSR, 166:2 (1966), 281–283 | MR

[2] S. M. Nikolskii, “Neravenstva dlya tselykh funktsii konechnoi stepeni i ikh primenenie v teorii differentsiruemykh funktsii mnogikh peremennykh”, Trudy Matem. in-ta im. V. A. Steklsva AN SSSR, XXXVIII, 1951, 244–278 | MR | Zbl

[3] V. A. Popov, “Ob approksimatsii absolyutno nepreryvnykh funktsii splain-funktsiyami”, S. r. Acad. bulg. scienc., 28:10 (1975), 1299–1301 | MR | Zbl

[4] Yu. A. Brudnyi, “O nekotorykh nelineinykh metodakh approksimatsii, Teoriya priblizheniya funktsii”, Trudy Mezhdunarodnoi konferentsii po teorii priblizheniya funktsii (Kaluga, 24-28 iyulya 1975 g.), izd-vo “Nauka”, Moskva, 1977, 41–46 | MR

[5] J. R. Rice, “Remarks on picewise polynomial approximation”, Trudy Mezhdunarodnoi konferentsii po teorii priblizheniya funktsii (Kaluga, 24-28 iyulya 1975 g.), izd-vo “Nauka”, Moskva, 1977, 305–311 | MR

[6] M. Sh. Birman, M. 3. Solomyak, “Kusochno-polinomialnye priblizheniya funktsii klassov $W_p^\alpha$”, Matem. sb., 73(115) (1967), 331–355 | MR | Zbl

[7] V. E. Maiorov, “O nailuchshem priblizhenii klassov $W_1^r(I^s)$ v prostranstve $L_\infty(I^s)$”, Matem. zametki, 19:5 (1976), 699–706 | MR | Zbl

[8] K. I. Oskolkov, “Approksimativnye svoistva summiruemykh funktsii na mnozhestvakh polnoi mery”, Matem. sb., 103(145) (1977), 563–589 | MR | Zbl