Construction of the polynomial of least deviation for approximations with a sign-sensitive weight
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 42 (2002) no. 2, pp. 142-154 Cet article a éte moissonné depuis la source Math-Net.Ru

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A. A. Chumak. Construction of the polynomial of least deviation for approximations with a sign-sensitive weight. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 42 (2002) no. 2, pp. 142-154. http://geodesic.mathdoc.fr/item/ZVMMF_2002_42_2_a1/

[1] Dolzhenko E. P., Sevastyanov E. A., “Znakochuvstvitelnye approksimatsii. Voprosy edinstvennosti i ustoichivosti”, Dokl. RAN, 333:1 (1993), 5–7 | MR | Zbl

[2] Dolzhenko E. P., Sevastyanov E. A., “Approksimatsiya so znakochuvstvitelnym vesom (teoremy suschestvovaniya i edinstvennosti)”, Izv. RAN. Ser. matem., 62:6 (1998), 59–102 | MR | Zbl

[3] Vallèe-Poussin Ch.-J., “Sur les polynomes d'approximation et la représentation approchée d'un angle”, Bull. Acad. Belgique, 1910, 808–844 | Zbl

[4] Vallèe-Poussin Ch.-J., Leçons sur l'approximation des fonctions d'une variable réelle, Gauthier-Villars, Paris, 1919 | Zbl

[5] Remez E. J., “Sur le calcul effectif des polynomes d'approximation de Tchebycheff”, Compt. Rend., 199 (1934), 337–339

[6] Remez E. Ya., Osnovy chislennykh metodov chebyshevskogo priblizheniya, Nauk. dumka, Kiev, 1969 | MR | Zbl

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

[8] V. F. Demyanov i V. N. Malozemov (red.), Voprosy teorii i elementy programmnogo obespecheniya minimaksnykh zadach, Izd-vo LGU, L., 1977

[9] Berdyshev V. I., Petrak L. V., Approksimatsiya funktsii, szhatie chislennoi informatsii, prilozheniya, UrO RAN, Ekaterinburg, 1999 | MR

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

[11] Bogatyrev A. B., “O postroenii mnogochlenov, naimenee uklonyayuschikhsya ot nulya na sisteme otrezkov. Teoriya priblizhenii i garmonicheskii analiz”, Tezisy dokl. mezhdunar. konf., TulGU, Tula, 1998, 52–53

[12] Chebyshev P. L., “Teoriya mekhanizmov, izvestnykh pod nazvaniem parallelogrammov”, Sobr. soch., v. 2, Izd-vo AN SSSR, M.-L., 1947, 23–51

[13] Chebyshev P. L., “O funktsiyakh, naimenee otklonyayuschikhsya ot nulya”, Sobr. soch., v. 3, Izd-vo AN SSSR, M.-L., 1948, 24–29

[14] Lebedev V. I., “Chebyshevskie iteratsionnye metody”, Dob. k kn.: Pashkovskii S., Vychislenie primeneniya mnogochlenov i ryadov Chebysheva, Nauka, M., 1983, 369–375 | MR

[15] Lokutsievskii O. V., Gavrikov M. B., Nachala chislennogo analiza, TOO “Yanus”, M., 1995 | MR

[16] Dzyadik V. K., Kovtunets' V. V., “Zbizhnist algoritmu pobudovi vyzhiv”, Ukr. matem. zhurnal, 46:6 (1994), 825–832 | MR | Zbl

[17] Shevchuk L. B., Postroenie teorii uzhei i nekotorye ee primeneniya, Avtoref. dis. $\dots$ kand. fiz.-matem. nauk AN USSR, In-t matem., Kiev, 1990, 11 | Zbl

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

[19] Dolzhenko E. P., Sevastyanov E. A., “Approksimatsii so znakochuvstvitelnym vesom (ustoichivost, prilozheniya k teorii uzhei i khausdorfovym approksimatsiyam)”, Izv. RAN. Ser. matem., 63:3 (1999), 77–118 | MR | Zbl

[20] Krein M. G., Nudelman A. A., Problema momentov Markova i ekstremalnye zadachi, Nauka, M., 1973 | MR

[21] Loran P.-Zh., Approksimatsiya i optimizatsiya, Mir, M., 1975

[22] Chumak A. A., “Ob algoritme postroeniya polinoma naimenshego ukloneniya dlya approksimatsii so znakochuvstvitelnym vesom”, Abstracts of Internat. Conf. dedicated to M. A. Lavrentyev on the occasion of his birthday centenary, Inst. Math. Nat. Acad. Sci. Ukraine, Kiev, 2000, 85–87