On the error of random quadrature formulae for certain function families
Dalʹnevostočnyj matematičeskij žurnal, Tome 7 (2007) no. 1, pp. 91-100.

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

In this paper, we obtain error of quadrature formulae with random elements for families of periodic functions having $\ell_p$-bounded Fourier coefficients.
@article{DVMG_2007_7_1_a8,
     author = {M. A. Romanov},
     title = {On the error of random quadrature formulae for certain function families},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {91--100},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2007_7_1_a8/}
}
TY  - JOUR
AU  - M. A. Romanov
TI  - On the error of random quadrature formulae for certain function families
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2007
SP  - 91
EP  - 100
VL  - 7
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2007_7_1_a8/
LA  - ru
ID  - DVMG_2007_7_1_a8
ER  - 
%0 Journal Article
%A M. A. Romanov
%T On the error of random quadrature formulae for certain function families
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2007
%P 91-100
%V 7
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2007_7_1_a8/
%G ru
%F DVMG_2007_7_1_a8
M. A. Romanov. On the error of random quadrature formulae for certain function families. Dalʹnevostočnyj matematičeskij žurnal, Tome 7 (2007) no. 1, pp. 91-100. http://geodesic.mathdoc.fr/item/DVMG_2007_7_1_a8/

[1] N. S. Bakhvalov, “Otsenka v srednem ostatochnogo chlena kvadraturnykh formul”, Zhurnal vychislit. matematiki i matem. fiziki, 1:1 (1961), 64–77 | Zbl

[2] N. S. Bakhvalov, “O priblizhennom vychislenii kratnykh integralov”, Vestnik MGU, Seriya “Matem., mekhan., astronom., fiz.”, 1959, no. 4, 3–18 | MR

[3] N. S. Bakhvalov, “Ob optimalnykh otsenkakh skorosti skhodimosti kvadraturnykh protsessov i metodov integrirovaniya tipa Monte-Karlo na klassakh funktsii”, Sb. “Chisl. metody resheniya differ. i integr. uravnenii i kvadraturnye formuly”, Nauka, M., 1964, 5–63

[4] N. S. Bakhvalov, “O skorosti skhodimosti nedeterminirovannykh kvadraturnykh protsessov na klassakh funktsii $W_p^{(l)}$”, Teoriya veroyatnostei, VII:1-2(2), 238

[5] V. A. Bykovskii, Teoretiko-chislovye reshetki v evklidovykh prostranstvakh i ikh prilozheniya, Diss. ... d.f.-m.n., Khabarovskoe otdelenie Instituta prikladnoi matematiki DVO RAN, Khabarovsk, 1989

[6] V. A. Bykovskii, M. A. Romanov, “Kvadraturnyi fazovyi perekhod”, DAN, 416:6 (2007), 727–731 | MR | Zbl

[7] M. A. Romanov, “O pogreshnosti mnogomernykh kvadraturnykh formul na nekotorykh klassakh funktsii”, Matematicheskie zametki, 85:3 (2009), 433 –439 | MR | Zbl

[8] S. A. Smolyak, “Kvadraturnye i interpolyatsionnye formuly na tenzornykh proizvedeniyakh nekotorykh klassov funktsii”, DAN SSSR, 148:5 (1963), 1042–1045 | Zbl

[9] V. F. Lev, O kvadraturnykh formulakh dlya klassov s ogranicheniyami na koeffitsienty Fure, dep. v VINITI 27.8.1987, No6294-V87, M., 1987