Geodesic
Estimates of the complexity of approximation of continuous functions in some classes of determinate functions with delay
Diskretnaya Matematika, Tome 20 (2008) no. 4, pp. 147-156
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider determinate functions with delay which are generalisations of determinate functions and introduce the notion of complexity of an $\varepsilon$-approximation of a continuous real function by a function with delay. For some classes of continuous functions for which estimates of the number of elements in the $2\varepsilon$-distinguishable set of functions are known, upper and lower estimates are obtained. 
@article{DM_2008_20_4_a12,
     author = {A. N. Cherepov},
     title = {Estimates of the complexity of approximation of continuous functions in some classes of determinate functions with delay},
     journal = {Diskretnaya Matematika},
     pages = {147--156},
     year = {2008},
     volume = {20},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2008_20_4_a12/}
}
TY  - JOUR
AU  - A. N. Cherepov
TI  - Estimates of the complexity of approximation of continuous functions in some classes of determinate functions with delay
JO  - Diskretnaya Matematika
PY  - 2008
SP  - 147
EP  - 156
VL  - 20
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/DM_2008_20_4_a12/
LA  - ru
ID  - DM_2008_20_4_a12
ER  - 
%0 Journal Article
%A A. N. Cherepov
%T Estimates of the complexity of approximation of continuous functions in some classes of determinate functions with delay
%J Diskretnaya Matematika
%D 2008
%P 147-156
%V 20
%N 4
%U http://geodesic.mathdoc.fr/item/DM_2008_20_4_a12/
%G ru
%F DM_2008_20_4_a12
A. N. Cherepov. Estimates of the complexity of approximation of continuous functions in some classes of determinate functions with delay. Diskretnaya Matematika, Tome 20 (2008) no. 4, pp. 147-156. http://geodesic.mathdoc.fr/item/DM_2008_20_4_a12/

[1] Vitushkin A. G., Otsenka slozhnosti zadachi tabulyatsii, Fizmatgiz, Moskva, 1959

[2] Gashkov S. B., “O slozhnosti priblizhennoi realizatsii nepreryvnykh funktsii skhemami i formulami v polinomialnykh i nekotorykh drugikh bazisakh”, Matem. voprosy kibernetiki, 5 (1994), 144–207 | MR | Zbl

[3] Grekhem R., Knut D., Patashnik O., Konkretnaya matematika, Mir, Moskva, 1998

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

[5] Ofman Yu. P., “O priblizhennoi realizatsii nepreryvnykh funktsii na avtomatakh”, Doklady AN SSSR, 152:4 (1963), 823–825 | MR

[6] Tyulenev N. F., “Priblizhenie nepreryvnykh funktsii diskretnymi”, Sbornik trudov seminara po diskretnoi matematike i ee prilozheniyam, Mekh.-mat. f-t MGU, Moskva, 1997, 148–151

[7] Tyulenev N. F., “O priblizhenii nepreryvnykh funktsii diskretnymi”, Konstruktsii v algebre i logike, Tverskoi gosuniv., Tver, 1990, 110–116 | MR

[8] Cherepov I. A., “O priblizhenii nepreryvnykh funktsii determinirovannymi funktsiyami s zaderzhkoi”, Sbornik trudov seminara po diskretnoi matematike i ee prilozheniyam, Mekh.-mat. f-t MGU, Moskva, 2004, 163–166

[9] Cherepov A. N., Cherepov I. A., “O klassifikatsii nedeterminirovannykh funktsii”, Sbornik trudov seminara po diskretnoi matematike i ee prilozheniyam, Mekh.-mat. f-t MGU, Moskva, 2004, 160–163

[10] Cherepov A. N., “O slozhnosti priblizheniya nepreryvnykh funktsii nedeterminirovannymi funktsiyami s zaderzhkoi”, Materialy IX Mezhdunarodnoi konferentsii “Intellektualnye sistemy i kompyuternye nauki”, T. 1(2), Mekh.-mat. f-t MGU, Moskva, 2006, 307–310

[11] Cherepov A. N., “Otsenki slozhnosti priblizheniya nepreryvnykh funktsii nekotorykh klassov determinirovannymi funktsiyami s zaderzhkoi”, Materialy XVI Mezhdunarodnoi shkoly-seminara “Sintez i slozhnost upravlyayuschikh sistem”, Mekh.-mat. f-t MGU, Moskva, 2006, 118–122