Geodesic
The efficiency of Hausdorff algorithms for approximating convex bodies
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 33 (1993) no. 5, pp. 796-805 Cet article a éte moissonné depuis la source Math-Net.Ru

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     title = {The efficiency of {Hausdorff} algorithms for approximating convex bodies},
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G. K. Kamenev. The efficiency of Hausdorff algorithms for approximating convex bodies. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 33 (1993) no. 5, pp. 796-805. http://geodesic.mathdoc.fr/item/ZVMMF_1993_33_5_a10/

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

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

[3] Gruber P. M., Kendrov P., “Approximation of convex bodies by polytopes”, Rendiconti Circolo mat. Palermo. Ser. 2, 31:2 (1982), 195–225 | DOI | MR | Zbl

[4] Sonnevend Gy., “Asymptotically optimal, sequential methods for the approximation of convex, compact sets in $\mathbb{R}^d$ in the Hausdorff metrics”, Colloquia Math. Soc. Janos Bolyai, 35(2), 1980, 1075–1089 | MR

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

[6] Kamenev G. K., Metody approksimatsii vypuklykh tel mnogogrannikami i ikh primenenie dlya postroeniya i analiza obobschennykh mnozhestv dostizhimosti, Dis. ...kand. fiz.-matem. nauk, MFTI, M., 1986

[7] McClure D. E., Vitale R. A., “Polygonal approximation of plane convex bodies”, J. Math. Analys. and Appl., 51:2 (1975), 326–358 | DOI | MR | Zbl

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

[9] Rodzhers K., Ukladki i pokrytiya, Mir, M., 1968 | MR

[10] Schneider R., “Polyhedral approximation of smooth convex bodies”, J. Math. Analys. and Appl., 128:2 (1987), 470–474 | DOI | MR | Zbl

[11] Gruber P. M., “Volume approximation of convex bodies by inscribed polytopes”, Math. Ann., 281:2 (1988), 229–245 | DOI | MR | Zbl

[12] Yudin D. B., Nemirovskii A. S., “Otsenka informatsionnoi slozhnosti zadach matematicheskogo programmirovaniya”, Ekonomika i matem. metody, 12:1 (1976), 128–142 | MR | Zbl

[13] Tarasov S. P., Khachiyan L. G., Erlikh I. I., “Metod vpisannykh ellipsoidov”, Dokl. AN SSSR, 298:5 (1988), 1081–1092 | MR

[14] Sonnevend G., “An optimal sequential algorithm for uniform approximation of convex functions on $[0, 1]^2$”, Appl. Math. and Optimizat., 1983, no. 10, 127–142 | DOI | MR | Zbl

[15] Brooks J. N., Strantzen J. B., Blaschke's rolling theorem in $\mathbb{R}^n$, Mem. Amer. Math. Soc., 80, no. 405, Providence, 1980 | MR

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

[17] 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