Formulas for the approximate calculation of integrals over the whole plane
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 3, pp. 466-470
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Cubature formulas with $4s+1$ and $4s-1$ nodes, which have the $(4s-1)$ property and $(4s-3)$ property, respectively, are constructed for the approximate evaluation of an integral over a plane. The nodes of the formulas are common zeros of certain orthogonal polynomials.
@article{ZVMMF_1990_30_3_a11,
author = {A. K. Ponomarenko},
title = {Formulas for the approximate calculation of integrals over the whole plane},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {466--470},
year = {1990},
volume = {30},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_3_a11/}
}
TY - JOUR AU - A. K. Ponomarenko TI - Formulas for the approximate calculation of integrals over the whole plane JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 1990 SP - 466 EP - 470 VL - 30 IS - 3 UR - http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_3_a11/ LA - ru ID - ZVMMF_1990_30_3_a11 ER -
A. K. Ponomarenko. Formulas for the approximate calculation of integrals over the whole plane. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 3, pp. 466-470. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_3_a11/
[1] Mysovskikh I. P., Interpolyatsionnye kubaturnye formuly, Nauka, M., 1981 | MR
[2] Sege G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962
[3] Krylov V. I., Priblizhennoe vychislenie integralov, Nauka, M., 1967 | MR
[4] Mysovskikh I. P., “Primenenie ortogonalnykh mnogochlenov k postroeniyu kubaturnykh formul”, Zh. vychisl. matem. i matem. fiz., 12:2 (1972), 467–475 | Zbl
[5] Radon J., “Zur mechanischen Kubatur”, Monatsh. Math., 52:4 (1948), 286–300 | DOI | MR
[6] Ponomarenko A. K., “Nekotorye kubaturnye formuly dlya ploskosti, soderzhaschie proizvodnye”, Metody vychislenii, 14, Izd-vo LGU, L., 1985, 24–35 | MR