Geodesic
Computational algorithms for the optimum covering of plane domains by a prescribed number of ellipses
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 35 (1995) no. 5, pp. 772-783 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{ZVMMF_1995_35_5_a10,
     author = {Sh. I. Galiev},
     title = {Computational algorithms for the optimum covering of plane domains by a prescribed number of ellipses},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {772--783},
     year = {1995},
     volume = {35},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1995_35_5_a10/}
}
TY  - JOUR
AU  - Sh. I. Galiev
TI  - Computational algorithms for the optimum covering of plane domains by a prescribed number of ellipses
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1995
SP  - 772
EP  - 783
VL  - 35
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1995_35_5_a10/
LA  - ru
ID  - ZVMMF_1995_35_5_a10
ER  - 
%0 Journal Article
%A Sh. I. Galiev
%T Computational algorithms for the optimum covering of plane domains by a prescribed number of ellipses
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1995
%P 772-783
%V 35
%N 5
%U http://geodesic.mathdoc.fr/item/ZVMMF_1995_35_5_a10/
%G ru
%F ZVMMF_1995_35_5_a10
Sh. I. Galiev. Computational algorithms for the optimum covering of plane domains by a prescribed number of ellipses. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 35 (1995) no. 5, pp. 772-783. http://geodesic.mathdoc.fr/item/ZVMMF_1995_35_5_a10/

[1] Tot L. F., Raspolozheniya na ploskosti, na sfere i v prostranstve, Fizmatgiz, M., 1958

[2] Fejes Toth L., Regular figures, Pergamon Press, N. Y., 1964 | Zbl

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

[4] Konvei Dzh., Sloen N., Upakovki sharov, reshetki i gruppy, v. I, II, Mir, M., 1990

[5] Fejes Toth G., “New results in the theory of packing and covering”, Convexity and its Appls., Birkhauser, Basel etc., 1983, 318–359 | MR

[6] Bezdek K., “Über einige Kreisüberdeckungen”, Beitrage zur Algebra und Geometrie, 14 (1983), 7–13 | MR | Zbl

[7] Bezdek A., Bezdek K., “Über einige duenuste Kreisueberdeckungen konvexer Bereiche durch endliche Anzahl von kongruente Kreisen”, Beitrage zur Algebra und Geometrie, 19 (1985), 159–168 | MR | Zbl

[8] Piyavskii S. A., “Ob optimizatsii setei”, Izv. AN SSSR. Tekhn. kibernetika, 1968, no. 1, 68–80

[9] Brusov V. S., Piyavskii S. A., “Vychislitelnyi algoritm optimalnogo pokrytiya oblastei ploskosti”, Zh. vychisl. matem. i matem. fiz., 11:2 (1971), 304–313

[10] Krotov V. F., Piyavskii S. A., “Dostatochnye usloviya optimalnosti v zadachakh ob optimalnykh pokrytiyakh”, Izv. AN SSSR. Tekhn. kibernetika, 1968, no. 2, 10–17 | MR

[11] Jandl H., Wieder K., “A continuous set covering problem as a quasidifferentiale optimization problem”, Optimizat. J. Math. Program. and Operat. Res., 19:6 (1988), 781–802 | MR | Zbl

[12] Galiev Sh. I., “Nakhozhdenie priblizhennogo resheniya maksimina so svyazannymi peremennymi i kratnogo maksimina”, Zh. vychisl. matem. i matem. fiz., 26:10 (1986), 1455–1467 | MR | Zbl

[13] Galiev Sh. I., “Chislennoe reshenie nekotorykh minimaksiminnykh zadach”, Zh. vychisl. matem. i matem. fiz., 28:7 (1988), 1000–1011 | MR

[14] Galiev Sh. I., “Napravlenie ubyvaniya dlya minimaksnykh zadach”, Zh. vychisl. matem. i matem. fiz., 33:1 (1993), 22–34 | MR | Zbl

[15] Galiev Sh. I., “Napravleniya ubyvaniya dlya minimaksiminnykh zadach”, Zh. vychisl. matem. i matem. fiz., 34:3 (1994), 323–343 | MR | Zbl

[16] Galiev Sh. I., “Suboptimalnye raspolozheniya tochek na ogranichennoi giperpoverkhnosti”, Issledovanie operatsii i analitich. proektirovanie v tekhn., KAI, Kazan, 1984, 7–13

[17] Bambah R. P., Rogers C. A., Zassenhaus H., “On coverings with convex domains”, Acta Arithmetica, 9 (1964), 191–207 | MR | Zbl

[18] Fejes Toth G., “Packing and covering with $r$-convex discs”, Stud. Sci. Math. Hungar., 18 (1983), 69–73 | MR | Zbl

[19] Fejes Toth G., “Covering the plane by convex discs”, Acta Math. Acad. Sci. Hungar., 23:1–2 (1972), 263–270 | MR | Zbl

[20] Kuperberg W., “An inequality link in packing and covering densities of plane convex bodies”, Geometriae Dedicata, 23 (1987), 59–66 | DOI | MR | Zbl

[21] Silverman B. W., Titterington D. M., “Minimum covering ellipses”, SIAM J. Sci. Statist. Comput., 1:4 (1980), 401–409 | DOI | MR | Zbl