Geodesic
Uniform estimation of a segment function by a polynomial strip of fixed width
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 11, pp. 1981-1994 Cet article a éte moissonné depuis la source Math-Net.Ru

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The best uniform approximation of a segment function on an interval by a polynomial strip of fixed width (in ordinate) with respect to the Hausdorff measure at each point of the interval is considered. Ranges of strip widths are indicated for which this problem gives outer and inner estimates for the graph of the segment function in terms of the polynomial strip, and a range of strip widths is given for which the problem has an independent value. A necessary and sufficient condition for the existence of a solution and uniqueness conditions are obtained in a form comparable to the Chebyshev alternance. A range of strip widths is indicated for which the solution of the problem is always unique. Certain variational properties of the solution are examined. 
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S. I. Dudov; E. V. Sorina. Uniform estimation of a segment function by a polynomial strip of fixed width. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 11, pp. 1981-1994. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_11_a4/

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

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

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

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

[7] Polovinkin E. C., Elementy teorii mnogoznachnykh otobrazhenii, MFTI, M., 1982

[8] Nikolskii M. S., “Ob approksimatsii nepreryvnogo mnogoznachnogo otobrazheniya postoyannymi mnogoznachnymi otobrazheniyami”, Vestn. MGU. Ser. 15. Vychisl. matem. i kibernetika, 1990, no. 1, 76–80

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

[10] Dudov S. I., Konoplev A. B., “O priblizhenii mnogoznachnogo otobrazheniya postoyannymi mnogoznachnymi otobrazheniyami s sharovymi obrazami”, Matem. zametki, 82:4 (2007), 525–529 | MR | Zbl

[11] Vygodchikova I. Yu., Dudov S. I., Sorina E. V., “Vneshnyaya otsenka segmentnoi funktsii polinomialnoi polosoi”, Zh. vychisl. matem. i matem. fiz., 49:7 (2009), 1175–1183 | MR | Zbl

[12] Dudov S. I., “Vzaimosvyaz nekotorykh zadach po otsenke vypuklogo kompakta sharom”, Matem. sb., 198:1 (2007), 43–58 | MR | Zbl

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

[14] Karlin S., Stadden V., Chebyshevskie sistemy i ikh primenenie v analize i statistike, Nauka, M., 1976 | MR

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

[16] Dudov S. I., “O dvukh vspomogatelnykh faktakh dlya issledovaniya zadach polinomialnogo priblizheniya”, Sb. nauchn. trudov. Matematika. Mekhanika, 9, Saratovskii un-t, Saratov, 2007, 22–26