Geodesic
External estimation of a segment function by a polynomial strip
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 7, pp. 1175-1183 
I. Yu. Vygodchikova; S. I. Dudov; E. V. Sorina. External estimation of a segment function by a polynomial strip. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 7, pp. 1175-1183. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a4/
@article{ZVMMF_2009_49_7_a4,
     author = {I. Yu. Vygodchikova and S. I. Dudov and E. V. Sorina},
     title = {External estimation of a~segment function by a~polynomial strip},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1175--1183},
     year = {2009},
     volume = {49},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a4/}
}
TY  - JOUR
AU  - I. Yu. Vygodchikova
AU  - S. I. Dudov
AU  - E. V. Sorina
TI  - External estimation of a segment function by a polynomial strip
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 1175
EP  - 1183
VL  - 49
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a4/
LA  - ru
ID  - ZVMMF_2009_49_7_a4
ER  - 
%0 Journal Article
%A I. Yu. Vygodchikova
%A S. I. Dudov
%A E. V. Sorina
%T External estimation of a segment function by a polynomial strip
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 1175-1183
%V 49
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a4/
%G ru
%F ZVMMF_2009_49_7_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem is considered of constructing a least-width strip with a polynomial axis that contains the graph of a given continuous segment function. Convex analysis methods are used to obtain a criterion for solving the problem in a form comparable to the Chebyshev alternance. Sufficient conditions for the uniqueness of a solution are given, including those taking into account the differential properties of the segment function to be estimated.

[1] Pshenichnyi B. N., Vypuklyi analiz i ekstremalnye zadachi, Nauka, M., 1981 | MR

[2] Demyanov V. F., Vasilev L. V., Nedifferentsiruemaya optimizatsiya, Nauka, M., 1981 | MR

[3] Chernousko F. L., Otsenivanie fazovogo sostoyaniya dinamicheskikh sistem: metod ellipsoidov, Nauka, M., 1988 | MR

[4] Demyanov V. F., Rubinov A. M., Osnovy negladkogo analiza i kvazidifferentsialnoe ischislenie, Nauka, M., 1990 | MR

[5] Kurzhanski A. B., Valui I., Ellipsoidal calculus for estimation and control, Bürkhaüser, Boston, 1997 | MR

[6] Sendov B., Khausdorfovy priblizheniya, Sofiya, 1979

[7] Dzyadyk V. K., Vvedenie v teoriyu ravnomernogo priblizheniya funktsii polinomami, Nauka, M., 1977 | MR | Zbl

[8] Vygodchikova I. Yu., “O nailuchshem priblizhenii diskretnogo multiotobrazheniya algebraicheskim polinomom”, Matematika. Mekhanika: Sb. nauchn. tr., 3, Izd-vo Saratovskogo un-ta, Saratov, 2001, 25–27

[9] Vygodchikova I. Yu., “O edinstvennosti resheniya zadachi nailuchshego priblizheniya mnogoznachnogo otobrazheniya algebraicheskim polinomom”, Izv. Saratovskogo un-ta, 6:1/2 (2006), 11–19

[10] Demyanov V. F., Malozemov V. N., Vvedenie v minimaks, Nauka, M., 1972 | MR

[11] Dudov S. I., “O dvukh vspomogatelnykh faktakh dlya issledovaniya zadach polinomialnogo priblizheniya”, Matematika. Mekhanika: Sb. nauchn. tr., 9, Izd-vo Saratovskogo un-ta, Saratov, 2007, 22–26

[12] Vasilev F. P., Chislennye metody resheniya ekstremalnykh zadach, Nauka, M., 1988 | MR