Geodesic
A network version of the non-standard trigonometric basis and its advantages with respect to a similar polynomial basis
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 4, pp. 399-409 
V. V. Smelov. A network version of the non-standard trigonometric basis and its advantages with respect to a similar polynomial basis. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 17 (2014) no. 4, pp. 399-409. http://geodesic.mathdoc.fr/item/SJVM_2014_17_4_a7/
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     title = {A network version of the non-standard trigonometric basis and its advantages with respect to a~similar polynomial basis},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A trigonometry-based functional basis as a network version is proposed. It is aimed at the approximation with high orders of accuracy of smooth and piecewise-smooth functions. A comparative analysis of the features of the basis proposed and a polynomial one is made. The trigonometric version offers considerable advantages over the polynomial bases.

[1] Marchuk G. I., Metody vychislitelnoi matematiki, Nauka, M., 1981 | MR

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

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

[4] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1983 | MR

[5] Lyusternik L. A., Sobolev V. I., Elementy funktsionalnogo analiza, Nauka, M., 1965 | MR | Zbl

[6] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1966 | MR

[7] Mikhlin S. G., Variatsionnye metody v matematicheskoi fizike, Nauka, M., 1970 | MR | Zbl

[8] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, v. 1, GITTL, M.–L., 1947

[9] Samarskii A. A., Vvedenie v teoriyu raznostnykh skhem, Nauka, M., 1971 | MR | Zbl

[10] Glesston S., Edlund M., Osnovy teorii yadernykh reaktorov, Izd-vo inostrannoi literatury, M., 1954

[11] Marchuk G. I., Lebedev V. I., Chislennye metody v teorii perenosa neitronov, Atomizdat, M., 1981 | MR

[12] Smelov V. V., Lektsii po teorii perenosa neitronov, Atomizdat, M., 1978 | MR

[13] 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