Geodesic
Error estimates of cubature formulas exact for Haar polynomials in classes of two-variable functions satisfying a general Lipschitz condition
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 1985-1996 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Upper error estimates are obtained for cubature formulas with the Haar $d$-property in the classes $\mathrm{Lip}(L_1,L_2)$ of two-variable functions satisfying a general Lipschitz condition. It is shown that the error of minimal cubature formulas possessing the Haar $d$-property have the best order of convergence to zero in the indicated classes. 
@article{ZVMMF_2013_53_12_a3,
     author = {K. A. Kirillov},
     title = {Error estimates of cubature formulas exact for {Haar} polynomials in classes of two-variable functions satisfying a general {Lipschitz} condition},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1985--1996},
     year = {2013},
     volume = {53},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a3/}
}
TY  - JOUR
AU  - K. A. Kirillov
TI  - Error estimates of cubature formulas exact for Haar polynomials in classes of two-variable functions satisfying a general Lipschitz condition
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2013
SP  - 1985
EP  - 1996
VL  - 53
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a3/
LA  - ru
ID  - ZVMMF_2013_53_12_a3
ER  - 
%0 Journal Article
%A K. A. Kirillov
%T Error estimates of cubature formulas exact for Haar polynomials in classes of two-variable functions satisfying a general Lipschitz condition
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2013
%P 1985-1996
%V 53
%N 12
%U http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a3/
%G ru
%F ZVMMF_2013_53_12_a3
K. A. Kirillov. Error estimates of cubature formulas exact for Haar polynomials in classes of two-variable functions satisfying a general Lipschitz condition. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 12, pp. 1985-1996. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_12_a3/

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

[2] Kirillov K. A., Noskov M. V., “Minimalnye kvadraturnye formuly, tochnye dlya polinomov Khaara”, Zh. vychisl. matem. i matem. fiz., 42:6 (2002), 791–799 | MR | Zbl

[3] Kirillov K. A., “Ob otsenke pogreshnosti minimalnykh vesovykh kvadraturnykh formul, tochnykh dlya funktsii Khaara”, Vychisl. tekhnologii, 11, Spets. vypusk (2006), 44–50 | Zbl

[4] Kirillov K. A., “Otsenki normy funktsionala pogreshnosti na prostranstvakh $S_p$ vesovykh kvadraturnykh formul, tochnykh dlya polinomov Khaara”, Vychisl. metody i programmirovanie, Razdel 1, 2012, 324–331 http://num-meth.srcc.msu.ru/ | Zbl

[5] Kirillov K. A., “Otsenki normy funktsionala pogreshnosti kvadraturnykh formul, tochnykh dlya polinomov Khaara”, Zh. Sib. feder. un-ta. Seriya “Matematika i fizika”, 4:4 (2011), 479–488

[6] Kirillov K. A., “Otsenki na prostranstvakh $S_p$ normy funktsionala pogreshnosti kvadraturnykh formul, tochnykh dlya polinomov Khaara”, Zh. vychisl. matem. i matem. fiz., 52:10 (2012), 1747–1755 | Zbl

[7] Kirillov K. A., “Minimalnye kubaturnye formuly, tochnye dlya polinomov Khaara v $\mathbb{R}^2$”, Voprosy matematicheskogo analiza, 6, Izd-vo Krasnoyarskogo gos. tekhn. un-ta, Krasnoyarsk, 2003, 108–117

[8] Kirillov K. A., “Nizhnie otsenki chisla uzlov kubaturnykh formul, tochnykh dlya polinomov Khaara v dvumernom sluchae”, Vychisl. tekhnologii, 9, Spets. vypusk (2004), 62–71 | Zbl

[9] Kirillov K. A., “Postroenie minimalnykh kubaturnykh formul, tochnykh dlya polinomov Khaara vysshikh stepenei v dvumernom sluchae”, Vychisl. tekhnologii, 10, Spets. vypusk (2005), 29–47 | Zbl

[10] Noskov M. V., Kirillov K. A., “Minimal cubature formulas exact for Haar polynomials”, J. Approximation Theory, 162:3 (2010), 615–627 | DOI | MR | Zbl

[11] Kirillov K. A., “Algoritm postroeniya minimalnykh kubaturnykh formul, obladayuschikh $d$-svoistvom Khaara v dvumernom sluchae”, Zh. Sib. feder. un-ta. Seriya “Matematika i fizika”, 3:2 (2010), 205–215

[12] Kirillov K. A., “Minimalnye kubaturnye formuly, tochnye dlya polinomov Khaara malykh stepenei v dvumernom sluchae”, Vestn. Krasnoyarskogo gos. agrarnogo un-ta, 2012, no. 10, 7–12

[13] Kirillov K. A., Noskov M. V., “Otsenki pogreshnosti na prostranstvakh $S_p$ kubaturnykh formul, tochnykh dlya polinomov Khaara v dvumernom sluchae”, Zh. vychisl. matem. i matem. fiz., 49:1 (2009), 3–13 | MR

[14] Kirillov K. A., “Otsenki normy funktsionala pogreshnosti na prostranstvakh $H_\alpha$ kubaturnykh formul, tochnykh dlya polinomov Khaara v dvumernom sluchae”, Zh. Sib. feder. un-ta. Seriya “Matematika i fizika”, 5:3 (2012), 382–387

[15] Kirillov K. A., “Ob otsenkakh pogreshnosti kubaturnykh formul, tochnykh dlya polinomov Khaara”, Vestn. Sib. gos. aerokosmicheskogo un-ta im. akademika M. F. Reshetneva, 2012, no. 2(42), 33–36

[16] Sobol I. M., “O kvadraturnykh formulakh ot funktsii neskolkikh peremennykh, udovletvoryayuschikh obschemu usloviyu Lipshitsa”, Zh. vychisl. matem. i matem. fiz., 29:6 (1989), 935–941 | MR | Zbl

[17] Haar A., “Zur Theorie der orthogonalen Funktionensysteme”, Math. Ann., 69 (1910), 331–371 | DOI | MR | Zbl