Formulas for approximate calculation of the Chebyshev coefficients
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2021), pp. 79-85.

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

The approximate calculation of integrals is a common part of research in various fields of mathematics, primarily in the theory of approximations and computational mathematics. In turn, within the theory of numerical integration, distinctions take place depending on the features of the integrand, the scale of which is "Quadrature (cubature) formulas" and "Theory of oscillations". This article belongs to the second type of problems and consists in the approximate calculation of the Chebyshev coefficients.
Mots-clés : quadrature formulas
Keywords: oscillatory integral, Chebyshev system, tensor product of functionals.
@article{IVM_2021_2_a6,
     author = {S. S. Kudaibergenov and Ye. Ye. Nurmoldin and N. Zh. Nauryzbayev and N. Temirgaliyev},
     title = {Formulas for approximate calculation of the {Chebyshev} coefficients},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {79--85},
     publisher = {mathdoc},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_2_a6/}
}
TY  - JOUR
AU  - S. S. Kudaibergenov
AU  - Ye. Ye. Nurmoldin
AU  - N. Zh. Nauryzbayev
AU  - N. Temirgaliyev
TI  - Formulas for approximate calculation of the Chebyshev coefficients
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2021
SP  - 79
EP  - 85
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2021_2_a6/
LA  - ru
ID  - IVM_2021_2_a6
ER  - 
%0 Journal Article
%A S. S. Kudaibergenov
%A Ye. Ye. Nurmoldin
%A N. Zh. Nauryzbayev
%A N. Temirgaliyev
%T Formulas for approximate calculation of the Chebyshev coefficients
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2021
%P 79-85
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2021_2_a6/
%G ru
%F IVM_2021_2_a6
S. S. Kudaibergenov; Ye. Ye. Nurmoldin; N. Zh. Nauryzbayev; N. Temirgaliyev. Formulas for approximate calculation of the Chebyshev coefficients. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2021), pp. 79-85. http://geodesic.mathdoc.fr/item/IVM_2021_2_a6/

[1] Manin Yu. I., Matematika kak metafora, Izd-vo MTsNMO, M., 2008

[2] Khavin V. P., Osnovy matematicheskogo analiza, Izd-vo Leningradsk. un-ta, L., 1989

[3] Nikolskii S. M., Kvadraturnye formuly, Nauka, M., 1988 | MR

[4] Bakhvalov N. S., Zhidkov N. P., Kobelkov G. M., Chislennye metody, Nauka, M., 1987 | MR

[5] Babenko K. I., Osnovy chislennogo analiza, Nauka, M., 1986 | MR

[6] Korobov N. M., Teoretiko–chislovye metody v priblizhennom analize, Fizmatgiz, M., 1963

[7] Hua Loo Keng, Wang Yuan, Application of Number Theory of Numerical Analysis, Springer Verlag, Berlin–Heidelberg–New York, 1981 | MR

[8] Nurmoldin E., “Vosstanovlenie funktsii, integralov i reshenii uravneniya teploprovodnosti iz $U_2$-klassov Ulyanova”, Sib. zhurn. vychisl. matem., 8:4 (2005), 337–351 | Zbl

[9] Temirgaliev N., Kudaibergenov S. S., Shomanova A. A., “Primenenie tenzornykh proizvedenii funktsionalov v zadachakh chislennogo integrirovaniya”, Izv. RAN, Ser. matem., 73:2 (2009), 183–224 | MR | Zbl

[10] Temirgaliev N., “Primenenie teorii divizorov k chislennomu integrirovaniyu periodicheskikh funktsii mnogikh peremennykh”, Matem. sb., 181:4 (1990), 490–505

[11] Zhubanysheva A. Zh., Temirgalieva Zh. N., Temirgaliev N., “Primenenie teorii divizorov k postroeniyu tablits optimalnykh koeffitsientov kvadraturnykh formul”, Zhurn. vychisl. matem. i matem. fiz., 49:1 (2009), 14–25 | MR | Zbl

[12] Filon L. N. G., “On a quadrature formula for trigonometric integrals”, Proc. Roy. Soc. Edinburgh, 49 (1928), 38–47 | DOI

[13] Ilin A. M. Danilin A. R., Asimptoticheskie metody v analize, Fizmatlit, M., 2009

[14] Zhileikin Ya. M., Kukarkin A. B., “Ob optimalnom vychislenii integralov ot bystroostsilliruyuschikh funktsii”, Zhurn. vychisl. matem. i matem. fiz., 18:2 (1978), 294–301 | MR

[15] Iserles A., “On the numerical quadrature of highly-oscillatory integrals, II: Irregular oscillators”, IMA J. Num. Anal., 25 (2005), 25–44 | DOI | MR | Zbl

[16] Levin D., “Procedures for computing one-and-two dimensional integrals of functions with rapid irregular oscillations”, Math. Comp., 38 (1982), 531–538 | DOI | MR | Zbl

[17] Temirgaliev N., Kudaibergenov S. S., Nauryzbaev N. Zh., “Poryadkovo tochnoe vychislenie integralov ot proizvedenii funktsii metodom tenzornykh proizvedenii funktsionalov”, Izv. vuzov. Matem., 2019, no. 11, 94–99

[18] Suetin P. K., Klassicheskie ortogonalnye mnogochleny, Fizmatlit, M., 2005

[19] Uitteker E. T., Vatson Dzh.N., Kurs sovremennogo analiza, Per. s angl., v. 2, Transtsendentnye funktsii, 2-e izd., ed. F.V. Shirokov, Gl. red. fiz.-mat. lit., M., 1963