Geodesic
Generalized polynomial approximation providing the best reference
Matematičeskie zametki, Tome 60 (1996) no. 5, pp. 658-669 
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/
@article{MZM_1996_60_5_a1,
     author = {V. I. Berdyshev},
     title = {Generalized polynomial approximation providing the best reference},
     journal = {Matemati\v{c}eskie zametki},
     pages = {658--669},
     year = {1996},
     volume = {60},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a1/}
}
TY  - JOUR
AU  - V. I. Berdyshev
TI  - Generalized polynomial approximation providing the best reference
JO  - Matematičeskie zametki
PY  - 1996
SP  - 658
EP  - 669
VL  - 60
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a1/
LA  - ru
ID  - MZM_1996_60_5_a1
ER  - 
%0 Journal Article
%A V. I. Berdyshev
%T Generalized polynomial approximation providing the best reference
%J Matematičeskie zametki
%D 1996
%P 658-669
%V 60
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1996_60_5_a1/
%G ru
%F MZM_1996_60_5_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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