Geodesic
Generalized polynomial approximation providing the best reference
Matematičeskie zametki, Tome 60 (1996) no. 5, pp. 658-669 Cet article a éte moissonné depuis la source Math-Net.Ru

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We pose the extremum problem of finding a polynomial approximation for a function of several variables so that this approximation by a fragment of the function provides the best reference. We obtain an upper bound for the modulus of informativity of polynomials and rational functions. 
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     author = {V. I. Berdyshev},
     title = {Generalized polynomial approximation providing the best reference},
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     pages = {658--669},
     year = {1996},
     volume = {60},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a1/}
}
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V. I. Berdyshev. Generalized polynomial approximation providing the best reference. Matematičeskie zametki, Tome 60 (1996) no. 5, pp. 658-669. http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a1/

[1] Beloglazov I. N., Dzhanzhgava G. I., Chigin G. P., Osnovy navigatsii po geofizicheskim polyam, Nauka, M., 1985

[2] Krasovskii A. A., Beloglazov I. N., Chigin G. P., Teoriya korrelyatsionno-ekstremalnykh navigatsionnykh sistem, Nauka, M., 1979

[3] Berdyshev V. I., “Polinomialnaya approksimatsiya, svyazannaya s navigatsiei po geofizicheskim polyam”, Dokl. RAN, 6 (1992), 1099–1102 | Zbl

[4] Berdyshev V. I., “Polynomial approximation and geophysical-field navigation problem”, Russian J. Numer. Anal. Math. Modelling, 8:2 (1993), 83–100 | MR | Zbl

[5] Nikolskii S. M., Priblizhenie funktsii mnogikh peremennykh i teoremy vlozheniya, Nauka, M., 1969

[6] Natanson I. P., Konstruktivnaya teoriya funktsii, GITTL, M.–L., 1949