Application of divisor theory to the construction of tables of optimal coefficients for quadrature formulas
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 1, pp. 14-25 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Based on the theory of divisors, an effective theoretical algorithm designed previously by the authors for constructing good quadrature formulas with a Korobov grid (i.e., an algorithm for finding optimal coefficients) is used to develop a computer search method that produces tables of optimal coefficients giving more accurate integration error estimates with a smaller number of nodes than in all previously known cases.
@article{ZVMMF_2009_49_1_a1,
     author = {A. Zh. Zhubanysheva and N. Temirgaliev and Zh. N. Temirgalieva},
     title = {Application of divisor theory to the construction of tables of optimal coefficients for quadrature formulas},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {14--25},
     year = {2009},
     volume = {49},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a1/}
}
TY  - JOUR
AU  - A. Zh. Zhubanysheva
AU  - N. Temirgaliev
AU  - Zh. N. Temirgalieva
TI  - Application of divisor theory to the construction of tables of optimal coefficients for quadrature formulas
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 14
EP  - 25
VL  - 49
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a1/
LA  - ru
ID  - ZVMMF_2009_49_1_a1
ER  - 
%0 Journal Article
%A A. Zh. Zhubanysheva
%A N. Temirgaliev
%A Zh. N. Temirgalieva
%T Application of divisor theory to the construction of tables of optimal coefficients for quadrature formulas
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 14-25
%V 49
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a1/
%G ru
%F ZVMMF_2009_49_1_a1
A. Zh. Zhubanysheva; N. Temirgaliev; Zh. N. Temirgalieva. Application of divisor theory to the construction of tables of optimal coefficients for quadrature formulas. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 1, pp. 14-25. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_1_a1/

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

[2] Roth K. F., “On irregularities of distribution”, Mathematica, 1:2 (1954), 73–79 | MR | Zbl

[3] Korobov N. M., “O priblizhennom vychislenii kratnykh integralov”, Dokl. AN SSSR, 124:6 (1959), 1207–1210 | MR | Zbl

[4] Korobov N. M., Teoretiko-chislovye metody v priblizhennom analize, Fizmatgiz, M., 1963 | MR | Zbl

[5] Korobov N. M., Teoretiko-chislovye metody v priblizhennom analize, Izd. 2-e, pererab. i dop., MTsNMO, M., 2004 | MR

[6] Hua Loo Keng, Wang Yuan, Application of number theory of numerical analysis, Springer, Berlin etc., 1981 | MR

[7] Hlawka E., Firneis F., Zinterhof P., Zahlentheoretische Methoden in der numerischen Mathematik, Wien etc., 1981 | MR

[8] Keipers L., Niderreiter F., Ravnomernoe raspredelenie posledovatelnostei, Nauka, M., 1985 | MR

[9] Bakhvalov H. S., “O priblizhennom vychislenii kratnykh integralov”, Vestn. MGU. Ser. matem., mekhan., 1959, no. 4, 3–18 | MR

[10] Wang Yuan, “Number theoretic method in numerical analysis”, Contemporary Math., 77, Amer. Math. Soc., Providence, RI, 1988, 63–82 | MR

[11] Temlyakov V. H., “Kvadraturnye formuly i vosstanovlenie po znacheniyam v uzlakh teoretiko-chislovykh setok dlya klassov funktsii maloi gladkosti”, Uspekhi matem. nauk, 40:4(244) (1985), 203–204

[12] Temlyakov V. N., “Cubature formulas, discrepancy, and nonlinear approximation”, J. Complexity, 19 (2003), 352–391 | DOI | MR | Zbl

[13] Temlyakov V. N., “O vosstanovlenii periodicheskikh funktsii neskolkikh peremennykh po znacheniyam v uzlakh teoretiko-chislovykh setok”, Analys. Math., 12 (1986), 287–305 | DOI | MR | Zbl

[14] Dobrovolskii H. M., Klepikova H. L., Tablitsa optimalnykh koeffitsientov dlya priblizhennogo vychisleniya kratnykh integralov, Preprint No 63, In-t obschei fiz. AN SSSR. Prikl. matem., M., 1990

[15] Sharygin I. F., “Otsenki snizu pogreshnosti kvadraturnykh formul na klassakh funktsii”, Zh. vychisl. matem. i matem. fiz., 3:2 (1963), 370–376 | Zbl

[16] Roth K. F., “Ogranicheniya dlya regulyarnosti”, Matematika: granitsy i perspektivy, M., 2005, 375–394

[17] Voronin S. M., Temirgaliev N., “O kvadraturnykh formulakh, svyazannykh s divizorami polya gaussovykh chisel”, Matem. zametki, 46:2 (1989), 34–41 | MR | Zbl

[18] Voronin S. M., Izbrannye trudy: Matematika, Izd-vo MGTU im. N. E. Baumana, M., 2006

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

[20] Temirgaliev N., Bailov E. A., Zhubanysheva A. Zh., “Ob obschem algoritme chislennogo integrirovaniya periodicheskikh funktsii mnogikh peremennykh”, Dokl. RAN, 416:2 (2007), 169–173 | MR | Zbl

[21] Temirgaliev N., “Ob effektivnosti algoritmov chislennogo integrirovaniya, svyazannykh s teoriei divizorov v krugovykh polyakh”, Matem. zametki, 61:2 (1997), 297–301 | MR | Zbl

[22] Temirgaliev N., “Teoretiko-chislovye metody i teoretiko-veroyatnostnyi podkhod k zadacham analiza. Teoriya vlozhenii i priblizhenii, absolyutnaya skhodimost i preobrazovaniya ryadov Fure”, Vestn. Evraziiskogo un-ta, 1997, no. 3, 90–144 ; 2002, no. 3–4, 222–272 | MR

[23] Sobol I. M., Mnogomernye kvadraturnye formuly i funktsii Khaara, Nauka, M., 1969 | MR

[24] Tekke E., Lektsii po teorii algebraicheskikh chisel, M., 1940