Geodesic
A method of computing nodes and weights of the Gauss--Christoffel quadratures
Matematičeskoe modelirovanie, Tome 25 (2013) no. 3, pp. 3-13.

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In this paper we propose a new efficient numerical method for determining the nodes and weights for quadrature formulas of Gauss, which is adapted to calculate the integrals with rapidly oscillating integrand. In particular, the application, the method used for the integrals of the kinetic theory of gases.
Mots-clés : orthogonal polynomials, Gaussian quadrature
Keywords: the nodes and weights, the existence and uniqueness, iterative process, a rapidly oscillating integrand. 
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I. V. Anisimova; R. R. Ginijatullina; V. N. Ignatiev. A method of computing nodes and weights of the Gauss--Christoffel quadratures. Matematičeskoe modelirovanie, Tome 25 (2013) no. 3, pp. 3-13. http://geodesic.mathdoc.fr/item/MM_2013_25_3_a0/

[1] Kalitkin H. H., Chislennye metody, Nauka, M., 1978, 512 pp. | MR

[2] Bakhvalov N. S., Zhidkov N. P., Kobelkov G. M., Chislennye metody, BINOM. Laboratoriya bazovykh znanii, M., 2003, 630 pp.

[3] Chebyshev P. L., Izbrannye matematicheskie trudy, Klassiki estestvoznaniya, ed. A. O. Gelfond, OGIZ Gostekhizdat, M.–L., 1946

[4] Krylov V. I., Priblizhennoe vychislenie integralov, Nauka, M., 1967 | MR

[5] Demidovich B. P., Maron I. A., Osnovy vychislitelnoi matematiki, Nauka, M., 1966 | MR

[6] Fertsiger Dzh., Kaper G., Matematicheskaya teoriya protsessov perenosa v gazakh, Mir, M., 1976

[7] Bakhvalov N. S., Chislennye metody, v. 1, Nauka, M., 1973 | MR | Zbl

[8] Anisimova I. V., Giniyatullina R. R., “O nepreryvnosti nesobstvennogo integrala ot parametra pri vychislenii ugla rasseivaniya v kineticheskoi teorii gazov”, Vestnik KGTU im. A. N. Tupoleva, 2010, no. 4, 93–100

[9] Anisimova I. V., Ignatev V. N., “Potentsial $(2\mathrm{N},6)$ v kineticheskoi teorii gazov i ego vliyanie na znachenie srednego ugla rasseivaniya”, Vestnik KGTU im. A. N. Tupoleva, 2011, no. 1, 89–93 | Zbl

[10] Nikiforov A. F., Uvarov V. B., Spetsialnye funktsii matematicheskoi fiziki, Nauka, M., 1984, 344 pp. | MR

[11] Faddeev D. K., Faddeeva V. N., Vychislitelnye metody lineinoi algebry, Fizmatgiz, M., 1960, 656 pp. | MR

[12] Marchuk G. I., Kuznetsov Yu. A., Iteratsionnye metody i kvadratichnye funktsionaly, Nauka, Novosibirsk, 1972, 205 pp. | Zbl