Geodesic
An a priori estimate for the efficiency of adaptive algorithms for the polyhedral approximation of convex bodies
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 1, pp. 149-160 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{ZVMMF_2003_43_1_a11,
     author = {R. V. Efremov},
     title = {An a priori estimate for the efficiency of adaptive algorithms for the polyhedral approximation of convex bodies},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {149--160},
     year = {2003},
     volume = {43},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_1_a11/}
}
TY  - JOUR
AU  - R. V. Efremov
TI  - An a priori estimate for the efficiency of adaptive algorithms for the polyhedral approximation of convex bodies
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2003
SP  - 149
EP  - 160
VL  - 43
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_1_a11/
LA  - ru
ID  - ZVMMF_2003_43_1_a11
ER  - 
%0 Journal Article
%A R. V. Efremov
%T An a priori estimate for the efficiency of adaptive algorithms for the polyhedral approximation of convex bodies
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2003
%P 149-160
%V 43
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_1_a11/
%G ru
%F ZVMMF_2003_43_1_a11
R. V. Efremov. An a priori estimate for the efficiency of adaptive algorithms for the polyhedral approximation of convex bodies. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 43 (2003) no. 1, pp. 149-160. http://geodesic.mathdoc.fr/item/ZVMMF_2003_43_1_a11/

[1] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F., Matematicheskaya teoriya optimalnykh protsessov, Fizmatgiz, M., 1961

[2] Lotov A. V., Bushenkov V. A., Kamenev G. K., Metod dostizhimykh tselei. Matematicheskie osnovy i ekologicheskie prilozheniya, Nauka, M., 1997

[3] Gruber P. M., “Approximation of convex bodies”, Convexity and its Applics, Birkhäuser, Basel etc., 1983, 131–162 | MR

[4] Kamenev G. K., “Ob odnom klasse adaptivnykh algoritmov approksimatsii vypuklykh tel mnogogrannikami”, Zh. vychisl. matem. i matem. fiz., 32:1 (1992), 136–152 | MR

[5] Kamenev G. K., “Ob effektivnosti khausdorfovykh algoritmov poliedralnoi approksimatsii vypuklykh tel”, Zh. vychisl. matem. i matem. fiz., 33:5 (1993), 796–805 | MR | Zbl

[6] Dzholdybaeva S. M., Kamenev G. K., Eksperimentalnoe issledovanie approksimatsii vypuklykh tel mnogogrannikami, VTs AN SSSR, M., 1991

[7] Dzholdybaeva S. M., Kamenev G. K., “Chislennoe issledovanie effektivnosti algoritma approksimatsii vypuklykh tel mnogogrannikami”, Zh. vychisl. matem. i matem. fiz., 32:6 (1992), 857–866 | MR | Zbl

[8] Efremov R. V., “Tochnaya otsenka asimptoticheskoi effektivnosti adaptivnogo algoritma approksimatsii vypuklykh gladkikh tel mnogogrannikami v dvumernom sluchae”, Vestn. MGU. Ser. 15. Vychisl. matem. i kibernetika, 2000, no. 2, 29–34 | MR

[9] Bushenkov V. A., Lotov A. V., Metody postroeniya i ispolzovaniya obobschennykh mnozhestv dostizhimosti, VTs AN SSSR, M., 1982

[10] Bushenkov V. A., “Iteratsionnyi metod postroeniya ortogonalnykh proektsii vypuklykh mnogogrannykh mnozhestv”, Zh. vychisl. matem. i matem. fiz., 25:9 (1985), 1285–1292 | MR | Zbl

[11] Efremov R. V., Kamenev G. K., “Klass algoritmov poliedralnoi approksimatsii vypuklykh tel s apriornoi otsenkoi asimptoticheskoi effektivnosti”, Zh. vychisl. matem. i matem. fiz., 42:1 (2002), 23–32 | MR | Zbl

[12] Schneider S., Wieaker J. A., “Approximation of convex bodies by polytopes”, Bull. London Math. Soc., 13:2(41) (1981), 149–156 | DOI | MR | Zbl

[13] Gruber P. M., “Asymptotic estimates for best and stepwise approximation of convex bodies, I”, Forum Math., 5 (1993), 281–297 | DOI | MR | Zbl

[14] Schneider R., “Zur optimalen Approximation konvexer Hyperflächen durch Polyeder”, Math. Ann., 256:3 (1983), 289–301 | DOI | MR

[15] Schneider R., “Polyhedral approximation of smooth convex bodies”, J. Math. Anal. Appl., 128 (1987), 470–474 | DOI | MR | Zbl

[16] Kamenev G. K., “Sopryazhennye adaptivnye algoritmy poliedralnoi approksimatsii vypuklykh tel”, Zh. vychisl. matem. i matem. fiz., 42:9 (2002), 1351–1367 | MR | Zbl

[17] Leikhtveis K., Vypuklye mnozhestva, Nauka, M., 1985 | MR