Construction of a single-step optimal stochastic algorithm for approximating a Lipschitz function
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 5, pp. 652-662
The problem of approximating a function satisfying a Lipschitz condition in the interval $[a,b]$ is considered. A single-step optimal stochastic algorithm for selecting the data points is constructed.
@article{ZVMMF_1990_30_5_a1,
author = {M. A. Kokorev},
title = {Construction of a single-step optimal stochastic algorithm for approximating {a~Lipschitz} function},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {652--662},
year = {1990},
volume = {30},
number = {5},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_5_a1/}
}
TY - JOUR AU - M. A. Kokorev TI - Construction of a single-step optimal stochastic algorithm for approximating a Lipschitz function JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 1990 SP - 652 EP - 662 VL - 30 IS - 5 UR - http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_5_a1/ LA - ru ID - ZVMMF_1990_30_5_a1 ER -
%0 Journal Article %A M. A. Kokorev %T Construction of a single-step optimal stochastic algorithm for approximating a Lipschitz function %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 1990 %P 652-662 %V 30 %N 5 %U http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_5_a1/ %G ru %F ZVMMF_1990_30_5_a1
M. A. Kokorev. Construction of a single-step optimal stochastic algorithm for approximating a Lipschitz function. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 5, pp. 652-662. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_5_a1/
[1] Strongin R. G., Chislennye metody v mnogoekstremalnykh zadachakh, Nauka, M., 1978 | MR | Zbl
[2] Sukharev A. G., Minimaksnye algoritmy v zadachakh chislennogo analiza, Nauka, M., 1989 | MR | Zbl
[3] Chernousko F. L., “Ob optimalnom poiske minimuma vypuklykh funktsii”, Zh. vychisl. matem. i matem. fiz., 10:6 (1970), 1355–1366
[4] Zhilinskas A. G., “Odnoshagovyi baiesovskii metod poiska ekstremuma funktsii odnoi peremennoi”, Kibernetika, 1975, no. 1, 139–144 | Zbl
[5] Traub Dzh., Vozhnyakovskii Kh., Obschaya teoriya optimalnykh algoritmov, Mir, M., 1983 | MR | Zbl