Efficiency of numerical integration algorithms related to divisor theory in cyclotomic fields
Matematičeskie zametki, Tome 61 (1997) no. 2, pp. 297-301.

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

For function classes with dominant mixed derivative and bounded mixed difference in the metric of $L^q$ ($1$), quadrature formulas are constructed so that the following properties are achieved simultaneously: the grid is simple, the algorithm is efficient and close to the optimal algorithm for constructing the grid, and the order of the error on the power scale cannot be further improved. The case $q=2$ was studied earlier.
@article{MZM_1997_61_2_a10,
     author = {N. Temirgaliev},
     title = {Efficiency of numerical integration algorithms related to divisor theory in cyclotomic fields},
     journal = {Matemati\v{c}eskie zametki},
     pages = {297--301},
     publisher = {mathdoc},
     volume = {61},
     number = {2},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_2_a10/}
}
TY  - JOUR
AU  - N. Temirgaliev
TI  - Efficiency of numerical integration algorithms related to divisor theory in cyclotomic fields
JO  - Matematičeskie zametki
PY  - 1997
SP  - 297
EP  - 301
VL  - 61
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_61_2_a10/
LA  - ru
ID  - MZM_1997_61_2_a10
ER  - 
%0 Journal Article
%A N. Temirgaliev
%T Efficiency of numerical integration algorithms related to divisor theory in cyclotomic fields
%J Matematičeskie zametki
%D 1997
%P 297-301
%V 61
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1997_61_2_a10/
%G ru
%F MZM_1997_61_2_a10
N. Temirgaliev. Efficiency of numerical integration algorithms related to divisor theory in cyclotomic fields. Matematičeskie zametki, Tome 61 (1997) no. 2, pp. 297-301. http://geodesic.mathdoc.fr/item/MZM_1997_61_2_a10/

[1] Frolov K. K., “Otsenki sverkhu pogreshnosti kvadraturnykh formul na klassakh funktsii 33”, Dokl. AN SSSR, 231:4 (1976), 818–821 | MR | Zbl

[2] Bykovskii V. A., O pravilnom poryadke pogreshnosti optimalnykh kubaturnykh formul v prostranstvakh s dominiruyuschei proizvodnoi i kvadraticheskikh otkloneniyakh setok, Preprint No. 23, VTs DVNTs AN SSSR, Vladivostok, 1985

[3] Temlyakov V. N., “Ob odnom prieme polucheniya otsenok snizu pogreshnostei kvadraturnykh formul”, Matem. sb., 181:10 (1990), 1403–1413 | Zbl

[4] Bakhvalov N. S., “Otsenki snizu asimptoticheskikh kharakteristik funktsii s dominiruyuschei smeshannoi proizvodnoi”, Matem. zametki, 12:6 (1972), 655–664 | MR | Zbl

[5] Dubinin V. V., “Ob optimalnykh formulakh dlya klassov funktsii s ogranichennoi smeshannoi proizvodnoi”, Matem. sb., 183:7 (1992), 23–34 | MR | Zbl

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

[7] Korobov N. M., Teoretiko-chislovye metody v priblizhennom analize, Fizmatgiz, M., 1963

[8] Hua Loo Keng, Wang Yuang, Applications of Number Theory of Numerical Analysis, Springer-Verlag, Berlin–Heidelberg–N. Y., 1981

[9] Hlawka E., Firneis F., Zinterhof P., Zahlen-theoretische Methoden in der numerishen Mathematik, Wein–München–Oldenbourg, 1981

[10] Keipers L., Niderreiter G., Ravnomernoe raspredelenie, Nauka, M., 1985

[11] Skriganov M. M., “O reshetkakh v polyakh algebraicheskikh chisel”, Dokl. AN SSSR, 306:3 (1989), 353–355 | MR

[12] Wang Yuang, “Number theoretic method in numerical analysis”, Contemp. Math., 1988, no. 77, 63–82 | Zbl

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

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

[15] Edvards R., Ryady Fure v sovremennom izlozhenii, Mir, M., 1985

[16] Temlyakov V. N., Priblizhenie funktsii s ogranichennoi smeshannoi proizvodnoi, Tr. MIAN, 178, Nauka, M., 1986 | MR | Zbl