Invariant cubature formulas of Gregory type for a~multidimensional cube

V. L. Vaskevich

Sibirskij žurnal industrialʹnoj matematiki, Tome 6 (2003) no. 3, pp. 34-66.

Bibliographie

[1] Mysovskikh I. P., Interpolyatsionnye kubaturnye formuly, Nauka, M., 1981 | MR | Zbl

[2] Sobolev S. L., “O kubaturnykh formulakh na sfere, invariantnykh pri preobrazovaniyakh konechnykh grupp vraschenii”, Dokl. AN SSSR, 146:2 (1962), 310–313 | MR | Zbl

[3] Sobolev S. L., “O chisle uzlov kubaturnykh formul na sfere”, Dokl. AN SSSR, 146:4 (1962), 770–773 | MR

[4] Sobolev S. L., “O formulakh mekhanicheskikh kubatur na poverkhnosti sfery”, Sib. mat. zhurn., 3:5 (1962), 769–796 | MR | Zbl

[5] Rozenfeld B. A., Mnogomernye prostranstva, Nauka, M., 1966 | MR

[6] Khemming R. V., Chislennye metody, Nauka, M., 1968

[7] Bakhvalov N. S., “Ob optimalnykh svoistvakh formul Adamsa i Gregori”, Voprosy vychislitelnoi matematiki i vychislitelnoi tekhniki, Mashgiz, M., 1963, 9–26

[8] Polovinkin V. I., “Posledovatelnosti kvadraturnykh formul s pogranichnym sloem i posledovatelnosti tipa Gregori”, Kvadraturnye i kubaturnye formuly. Reshenie funktsionalnykh uravnenii, Izd-vo Leningrad. un-ta, L., 1981, 7–25 | MR

[9] Khoroshikh A. N., “Tochnye asimptoticheskie vyrazheniya norm funktsionalov oshibok formul Gregori v $L_2^{(m)}[a,b]^*$”, Voprosy vychisl. i prikl. matematiki, no. 40, In-t kibernetiki AN UzSSR, Tashkent, 1976, 3–8

[10] Girschovich J., “Extremal properties of Euler–Maclorin and Gregory quadrature formulas”, Izv. AN EstSSR. Ser. fiz.-mat., 27:3 (1978), 259–265 | MR

[11] De Villiers J. M., “Ano dal spline interpolant for the Gregory rule of even order”, Numer. Math., 66:1 (1993), 123–137 | DOI | MR | Zbl

[12] Förster K. J., “Uber Monotonie und Fehlerkontrolle bei den Gregoryschen Quadraturverfahren”, Z. Angew. Math. Mech., 67, 257–266 | MR | Zbl

[13] Martensen E., “Optimale Fehlerschranken für die Quadraturformel von Gregory”, Z. Angew. Math. Mech., 44, 159–168 | DOI | MR | Zbl

[14] Martensen E., “Darstellung und Entwicklung des Restgliedes der Gregoryschen Quadraturformel mit Hilfe von Spline-Funktionen”, Numer. Math., 21, 70–80 | DOI | MR | Zbl

[15] Solak W., Szydelko Z., “Quadrature rules with Gregory–Laplace end corrections”, J. Comput. Appl. Math., 36, 251–253 | DOI | MR | Zbl

[16] Vaskevich V. L., “O skhodimosti kvadraturnykh formul Gregori”, Dokl. AN SSSR, 261:5 (1981), 1041–1043 | MR | Zbl

[17] Vaskevich V. L., Ob odnoi zadache teorii kvadraturnykh formul, Preprint AN SSSR. Sib. otd-nie. Institut matematiki; No 3, Novosibirsk, 1982, 50 pp. | MR

[18] Sobolev S. L., “Kubaturnye formuly s regulyarnym pogranichnym sloem”, Dokl. AN SSSR, 163:3 (1965), 587–590 | MR | Zbl

[19] Sobolev S. L., “Teoriya kubaturnykh formul”, Wiss. Z. Hochsch. Archit. und Brauwesen Weimar, 12:5/6 (1965), 537–546 | MR | Zbl

[20] Sobolev S. L., Vaskevich V. L., Kubaturnye formuly, Izd-vo Instituta matematiki, Novosibirsk, 1996 | Zbl

[21] Blinov N. I., Voitishek L. V., “O postroenii kubaturnykh formul s regulyarnym pogranichnym sloem dlya ratsionalnykh mnogogrannikov”, Tr. seminara akad. S. L. Soboleva, no. 1, IM SO AN SSSR, Novosibirsk, 1979, 5–15

[22] Blinov N. I., Voitishek L. V., “Kubaturnye formuly s regulyarnym pogranichnym sloem dlya kuba”, Voprosy vychislitelnoi i prikladnoi matematiki, no. 38, In-t kibernetiki AN UzSSR, Tashkent, 1970, 8–15

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

[24] Polovinkin V. I., “Posledovatelnosti funktsionalov s pogranichnym sloem”, Sib. mat. zhurn., 15:2 (1974), 413–429 | MR | Zbl

[25] Butler R., “On the evaluation of $\int_0^\infty(\sin t)^m/t^m dt$ by the trapezoidal rule”, Amer. Math. Monthly, 67:6 (1960), 566–569 | DOI | MR | Zbl

[26] Ditkin V. A., Prudnikov A. P., Integralnye preobrazovaniya i operatsionnoe ischislenie, Nauka, M., 1974 | MR | Zbl