Geodesic
An analog to Gaussian quadrature implemented on a~specific trigonometric basis
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 4, pp. 439-450.

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A new quadrature formula based on a nonstandard basis of trigonometric functions is constructed. The quadrature is comparable in accuracy to the Gauss quadrature formula and is used with the same class of functions. However, this quadrature has nothing to do with the quadrature for periodic functions, which is also based on trigonometric functions. 
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V. V. Smelov; A. S. Popov. An analog to Gaussian quadrature implemented on a~specific trigonometric basis. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 4, pp. 439-450. http://geodesic.mathdoc.fr/item/SJVM_2010_13_4_a6/

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

[2] Krylov V. I., Shulgina L. T., Spravochnaya kniga po chislennomu integrirovaniyu, Nauka, M., 1966 | MR

[3] Smelov V. V., “Gauss type quadratures based on trigonometric bases”, Russ. J. Numer. Anal. Math. Modelling, 23:3 (2008), 265–281 | DOI | MR | Zbl

[4] Smelov V. V., Zadachi Shturma–Liuvillya i razlozheniya funktsii v bystroskhodyaschiesya ryady, Izd-vo SO RAN, Novosibirsk, 2000

[5] Smelov V. V., “O predstavlenii kusochno-gladkikh funktsii bystroskhodyaschimisya trigonometricheskimi ryadami”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 2:4 (1999), 385–394 | Zbl

[6] Smelov V. V., “Effective approximation of piecewise smooth functions by their expansion into fast convergent series in terms of functions formed by eigenfunctions of Sturm–Liouville problems”, Russ. J. Numer. Anal. Math. Modelling, 19:5 (2004), 449–465 | DOI | MR | Zbl

[7] Smelov V. V., “O priblizhennom reshenii smeshannoi zadachi dlya parabolicheskogo uravneniya s ispolzovaniem spetsificheskogo bazisa funktsii”, Sib. zhurn. industrialnoi matematiki (Novosibirsk), 8:1(21) (2005), 117–128 | MR

[8] Smelov V. V., “Ob obobschennom reshenii dvumernoi ellipticheskoi zadachi s kusochno-postoyannymi koeffitsientami na osnove rasschepleniya differentsialnogo operatora i ispolzovaniya spetsificheskikh bazisnykh funktsii”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 6:1 (2003), 59–72 | Zbl

[9] Vladimirov V. S., “Matematicheskie zadachi odnoskorostnoi teorii perenosa chastits”, Tr. Matematicheskogo instituta im. V. A. Steklova AN SSSR, 61, Izd-vo AN SSSR, M., 1961, 3–158 | MR

[10] Suetin P. K., Klassicheskie ortogonalnye mnogochleny, Nauka, M., 1976 | MR