Geodesic
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 
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/
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     title = {Construction of a single-step optimal stochastic algorithm for approximating {a~Lipschitz} function},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[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