Geodesic
Best quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation
Izvestiya. Mathematics , Tome 3 (1969) no. 6, pp. 1335-1355.

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

In this article we obtain characteristic properties of piecewise-polynomial functions (“spline” functions) that have least deviation from zero in the metric of $C$. This has allowed us to obtain quadrature formulas with least estimate of the remainder on a number of classes of differentiable functions. 
@article{IM2_1969_3_6_a10,
     author = {N. P. Korneichuk and N. E. Lushpai},
     title = {Best quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation},
     journal = {Izvestiya. Mathematics },
     pages = {1335--1355},
     publisher = {mathdoc},
     volume = {3},
     number = {6},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1969_3_6_a10/}
}
TY  - JOUR
AU  - N. P. Korneichuk
AU  - N. E. Lushpai
TI  - Best quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation
JO  - Izvestiya. Mathematics 
PY  - 1969
SP  - 1335
EP  - 1355
VL  - 3
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1969_3_6_a10/
LA  - en
ID  - IM2_1969_3_6_a10
ER  - 
%0 Journal Article
%A N. P. Korneichuk
%A N. E. Lushpai
%T Best quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation
%J Izvestiya. Mathematics 
%D 1969
%P 1335-1355
%V 3
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1969_3_6_a10/
%G en
%F IM2_1969_3_6_a10
N. P. Korneichuk; N. E. Lushpai. Best quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation. Izvestiya. Mathematics , Tome 3 (1969) no. 6, pp. 1335-1355. http://geodesic.mathdoc.fr/item/IM2_1969_3_6_a10/

[1] Nikolskii S. M., “K voprosu ob otsenkakh priblizhenii kvadraturnymi formulami”, Uspekhi matem. nauk, 5:2(36) (1950), 165–177 | MR

[2] Nikolskii S. M., Kvadraturnye formuly, Fizmatgiz, M., 1958

[3] Doronin G. Ya., “K voprosu o formulakh mekhanicheskikh kvadratur”, Sbornik nauchnykh trudov Dnepropetrovskogo inzhenerno-stroitelnogo instituta, t. 1–2, 1955, 210–217

[4] Shaidaeva T. A., “Kvadraturnye formuly s naimenshei otsenkoi ostatka dlya nekotorykh klassov funktsii”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 53, 1959, 313–341 | Zbl

[5] Ibragimov I. I., Aliev R. M., “Nailuchshie kvadraturnye formuly dlya nekotorykh klassov funktsii”, Dokl. AN SSSR, 162:1 (1965), 23–25 | MR | Zbl

[6] Aksen M. B., Turetskii A. X., “O nailuchshikh kvadraturnykh formulakh dlya nekotorykh klassov funktsii”, Dokl. AN SSSR, 166:5 (1966), 1019–1021 | MR | Zbl

[7] Lushpai N. E., “Nailuchshie kvadraturnye formuly na nekotorykh klassakh funktsii”, Materialy mezhvuzovskoi konferentsii molodykh uchenykh-matematikov, Kharkov, 1967, 58–62

[8] Korneichuk N. P., “Nailuchshie kubaturnye formuly dlya nekotorykh klassov funktsii mnogikh peremennykh”, Matem. zametki, 3:5 (1968), 565–576

[9] Krylov V. I., Priblizhennoe vychislenie integralov, Nauka, M., 1967 | MR

[10] Aliev R. M., Faradzhev F. A., “Ekstremalnye zadachi dlya nekotorykh klassov funktsii”, Dokl. AN AzerbSSR, 23:3 (1967), 3–6 | MR | Zbl

[11] Ahlberg I. H., Nilson E. N., Walsh I. L., “Best approximation and convergence properties of higherorder spline approximations”, J. Math. Mech., 14:2 (1965), 231–243 | MR | Zbl

[12] Ahlberg I. H., Nilson E. N., Walsh I. L., The theory of splines and their applications, Academic Press, 1967 | MR | Zbl

[13] Goncharov V. L., Teoriya interpolirovaniya i priblizheniya funktsii, GITTL, M., 1954

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