Construction of weight lattice optimal quadrature formulas in the space $L_2^m(0,N)$
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 5 (2002) no. 3, pp. 275-293.

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

In this paper, the optimal coefficients of weight quadrature formulas are explicitly found in the space $L_2^m(0,N)$ for any $m\geq 1$ using the algorithm proposed by S. L. Sobolev.
@article{SJVM_2002_5_3_a6,
     author = {Kh. M. Shadimetov},
     title = {Construction of weight lattice optimal quadrature formulas in the space $L_2^m(0,N)$},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {275--293},
     publisher = {mathdoc},
     volume = {5},
     number = {3},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2002_5_3_a6/}
}
TY  - JOUR
AU  - Kh. M. Shadimetov
TI  - Construction of weight lattice optimal quadrature formulas in the space $L_2^m(0,N)$
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2002
SP  - 275
EP  - 293
VL  - 5
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2002_5_3_a6/
LA  - ru
ID  - SJVM_2002_5_3_a6
ER  - 
%0 Journal Article
%A Kh. M. Shadimetov
%T Construction of weight lattice optimal quadrature formulas in the space $L_2^m(0,N)$
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2002
%P 275-293
%V 5
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2002_5_3_a6/
%G ru
%F SJVM_2002_5_3_a6
Kh. M. Shadimetov. Construction of weight lattice optimal quadrature formulas in the space $L_2^m(0,N)$. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 5 (2002) no. 3, pp. 275-293. http://geodesic.mathdoc.fr/item/SJVM_2002_5_3_a6/

[1] Sobolev S. L., Vvedenie v teoriyu kubaturnykh formul, Nauka, M., 1974 | MR

[2] Sobolev S. L., “Koeffitsienty optimalnykh kvadraturnykh formul”, DAN SSSR, 235:1 (1977), 34–37 | MR | Zbl

[3] Sobolev S. L., Vaskevich V. L., Kubaturnye formuly, Izd-vo IM RAN, Novosibirsk, 1996 | Zbl

[4] Sard A., “Best approximate integration Formulas, best approximate formulas”, American J. of Math., 71 (1949), 80–91 | DOI | MR | Zbl

[5] Meyers, Sard A., “Best approximate integration formulas”, J. Math. and Phys., 29 (1950), 118–123 | MR | Zbl

[6] Coman Ch., “Formule de cuadrature de tip Sard”, Univ. Bales – Bp Iyoi. Ser. Math.-Mech., 17:2 (1972), 77 | MR | Zbl

[7] Coman Ch., “Monosplines and optimal quadrature formulae in $L_p$”, Rend. Math., 5:3 (1972), 567–577 | MR | Zbl

[8] Schoenberg I. J., Silliman S. D., “On semicardinal quadrature formulae”, Math. Comp., 28 (1974), 483–497 | DOI | MR | Zbl

[9] Zagirova F. Ya., O postroenii optimalnykh formul s ravnootstoyaschimi uzlami, Preprint / AN SSSR. Sib otd-nie. IM; 25, Novosibirsk, 1982

[10] Malyukov A. A., Orlov N. N., “Postroenie koeffitsientov nailuchshei kvadraturnoi formuly dlya klassa s ravnootstoyaschimi uzlami”, Metody optimizatsii i issledovanii operatsii. Prikladnaya matematika, Irkutsk, 1976, 174–177

[11] Zhamalov Z.Zh., Shadimetov Kh. M., “Optimalnaya kvadraturnaya formula s ravnootstoyaschimi uzlami v $L_2^{(2)}(E_1)$”, Pyatoe sovetsko-chekhoslovatskoe soveschanie po primeneniyu metodov teorii funktsii i funktsionalnogo analiza k zadacham matematicheskoi fiziki, materialy soveschaniya, Novosibirsk, 1978, 87–89

[12] Zhamalov Z. Zh., Shadimetov Kh. M., “O vychislenii koeffitsientov optimalnykh kvadraturnykh formul”, DAN UzSSR, 1980, no. 4, 4–7 | MR | Zbl

[13] Zhamalov Z. Zh., Shadimetov Kh. M., “Ob optimalnykh kvadraturnykh formulakh”, DAN UzSSR, 1980, no. 7, 3–5 | MR | Zbl

[14] Shadimetov Kh. M., “Optimalnye kvadraturnye formuly v $L_2^{(m)}(\Omega)$ i $L_2^{(m)}(R^1)$”, DAN UzSSR, 1983, no. 3, 5–8 | MR | Zbl

[15] Shadimetov Kh. M., “Vesovye optimalnye kvadraturnye formuly”, Materialy vsesoyuznogo kollokviuma po kubaturnym formulam, (otvetstvennyi S. L. Sobolev), Voprosy vychislitelnoi i prikladnoi matematiki, 51, Tashkent, 1978, 169–177 | MR | Zbl

[16] Israilov M. I., Shadimetov Kh. M., “Vesovye optimalnye kvadraturnye formuly dlya singulyarnykh integralov tipa Koshi”, DAN RUz., 1991, no. 8, 10–11 | MR

[17] Vasilenko V. A., Splain funktsii: teoriya, algoritmy, programmy, Nauka, Novosibirsk, 1983 | MR

[18] Shadimetov Kh. M., “Ob odnom yavnom predstavlenii diskretnogo analoga differentsialnogo operatora $2m$-go poryadka”, DAN RUz., 1996, no. 9, 5–7 | Zbl

[19] Gelfond A. O., Ischislenie konechnykh raznostei, Nauka, M., 1967 | MR