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@article{FPM_2016_21_4_a7, author = {I. V. Tikhonov and D. G. Tsvetkovich and V. B. Sherstyukov}, title = {Computer analysis of the attractors of zeros for classical {Bernstein} polynomials}, journal = {Fundamentalʹna\^a i prikladna\^a matematika}, pages = {151--174}, publisher = {mathdoc}, volume = {21}, number = {4}, year = {2016}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/FPM_2016_21_4_a7/} }
TY - JOUR AU - I. V. Tikhonov AU - D. G. Tsvetkovich AU - V. B. Sherstyukov TI - Computer analysis of the attractors of zeros for classical Bernstein polynomials JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 2016 SP - 151 EP - 174 VL - 21 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_2016_21_4_a7/ LA - ru ID - FPM_2016_21_4_a7 ER -
%0 Journal Article %A I. V. Tikhonov %A D. G. Tsvetkovich %A V. B. Sherstyukov %T Computer analysis of the attractors of zeros for classical Bernstein polynomials %J Fundamentalʹnaâ i prikladnaâ matematika %D 2016 %P 151-174 %V 21 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_2016_21_4_a7/ %G ru %F FPM_2016_21_4_a7
I. V. Tikhonov; D. G. Tsvetkovich; V. B. Sherstyukov. Computer analysis of the attractors of zeros for classical Bernstein polynomials. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 4, pp. 151-174. http://geodesic.mathdoc.fr/item/FPM_2016_21_4_a7/
[1] Bernshtein S. N., “Démonstration du théorème de Weierstrass fondée sur la calcul des probabilités”, Soobsch. Kharkov. matem. obsch., 13:1 (1912), 1–2
[2] Bernshtein S. N., “O skhodimosti mnogochlenov $\sum\limits_{0}^{n}C_n^mf(\frac{m}{n})x^m(1-x)^{n-m}$ v kompleksnoi oblasti”, Izv. Akad. nauk SSSR. Ser. matem., 7:2 (1943), 49–88
[3] Videnskii V. S., Mnogochleny Bernshteina, Uch. posob. k spetskursu, LGPI im. A. I. Gertsena, L., 1990
[4] Kantorovich L. V., “O skhodimosti posledovatelnosti polinomov S. N. Bernshteina za predelami osnovnogo intervala”, Izv. Akad. nauk SSSR. VII ser. Otd. matem. i estestv. nauk, 1931, no. 8, 1103–1115
[5] Montel P., Normalnye semeistva analiticheskikh funktsii, ONTI NKTP SSSR, M.–L., 1936
[6] Natanson I. P., Konstruktivnaya teoriya funktsii, GITTL, M.–L., 1949 | MR
[7] Novikov I. Ya., “Asimptotika kornei polinomov Bernshteina, ispolzuemykh v postroenii modifitsirovannykh vspleskov Dobeshi”, Matem. zametki, 71:2 (2002), 239–253 | DOI | MR
[8] Titchmarsh E., Teoriya funktsii, Nauka, M., 1980 | MR
[9] Tikhonov I. V., Sherstyukov V. B., “Priblizhenie modulya polinomami Bernshteina”, Vestn. Chelyabinsk. gos. un-ta. Matematika. Mekhanika. Informatika, 15:26 (2012), 6–40
[10] Tikhonov I. V., Sherstyukov V. B., Petrosova M. A., “Polinomy Bernshteina: staroe i novoe”, Matem. forum, 8:1 (2014), 126–175
[11] Tikhonov I. V., Sherstyukov V. B., Tsvetkovich D. G., “Zadacha o nulyakh polinomov Bernshteina na modelnom primere simmetrichnogo modulya”, Sovremennye problemy teorii funktsii i ikh prilozheniya, Materialy 18-i mezhdunar. Saratov. zimnei shkoly, Nauchnaya kniga, Saratov, 2016, 271–275
[12] Tikhonov I. V., Sherstyukov V. B., Tsvetkovich D. G., “Kompyuternaya klassifikatsiya attraktorov dlya nulei polinomov Bernshteina”, Materialy XVII mezhdunar. nauch. konf., Sistemy kompyuternoi matematiki i ikh prilozheniya, 17, SmolGU, Smolensk, 2016, 224–227
[13] Tikhonov I. V., Sherstyukov V. B., Tsvetkovich D. G., “Spetsialnye zadachi dlya polinomov Bernshteina v kompleksnoi oblasti”, Nekotorye aktualnye problemy sovremennoi matematiki i matematicheskogo obrazovaniya, Gertsenovskie chteniya 2016, Materialy nauch. konf. (11–15 aprelya 2016 g.), Izd. RGPU im. A. I. Gertsena, SPb., 2016, 139–145
[14] DeVore R. A., Lorentz G. G., Constructive Approximation, Springer, Berlin, 1993 | MR
[15] Jentzsch R., “Untersuchungen zur Theorie der Folgen analytischer Funktionen”, Acta Math., 41 (1918), 219–251 | DOI | MR
[16] Lorentz G. G., Bernstein Polynomials, Univ. of Toronto Press, Toronto, 1953 | MR
[17] Phillips G. M., Interpolation and Approximation by Polynomials, Springer, Berlin, 2003 | MR
[18] Popoviciu T., “Sur l'approximation des fonctions convexes d'ordre supérieur”, Mathematica, 10 (1935), 49–54
[19] Rahman Q. I., Schmeisser G., Analytic Theory of Polynomials, Clarendon Press, Oxford, 2002 | MR