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Izv. Akad. Nauk SSSR Ser. Mat., 1969, Volume 33, Issue 6, Pages 1416–1437 (Mi izv2244)  

This article is cited in 9 scientific papers (total in 9 papers)

Best quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation

N. P. Korneichuk, N. E. Lushpai


Abstract: 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.

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English version:
Mathematics of the USSR-Izvestiya, 1969, 3:6, 1335–1355

Bibliographic databases:

UDC: 517.5
MSC: 65D32, 41A10, 41A15, 65D07
Received: 31.03.1969

Citation: N. P. Korneichuk, N. E. Lushpai, “Best quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation”, Izv. Akad. Nauk SSSR Ser. Mat., 33:6 (1969), 1416–1437; Math. USSR-Izv., 3:6 (1969), 1335–1355

Citation in format AMSBIB
\Bibitem{KorLus69}
\by N.~P.~Korneichuk, N.~E.~Lushpai
\paper Best quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1969
\vol 33
\issue 6
\pages 1416--1437
\mathnet{http://mi.mathnet.ru/izv2244}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=278519}
\zmath{https://zbmath.org/?q=an:0198.08902|0209.09802}
\transl
\jour Math. USSR-Izv.
\yr 1969
\vol 3
\issue 6
\pages 1335--1355
\crossref{https://doi.org/10.1070/IM1969v003n06ABEH000875}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. P. Motornyi, “On the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for some classes of differentiable periodic functions”, Math. USSR-Izv., 8:3 (1974), 591–620  mathnet  crossref  mathscinet  zmath
    2. A. A. Zhensykbaev, “Best quadrature formula for some classes of periodic differentiable functions”, Math. USSR-Izv., 11:5 (1977), 1055–1071  mathnet  crossref  mathscinet  zmath
    3. A. A. Zhensykbaev, “Monosplines of minimal norm and the best quadrature formulae”, Russian Math. Surveys, 36:4 (1981), 121–180  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. A. A. Zhensykbaev, “Extremality of monosplines of minimal deficiency”, Math. USSR-Izv., 21:3 (1983), 461–482  mathnet  crossref  mathscinet  zmath
    5. S. M. Nikol'skii, “Aleksandrov and Kolmogorov in Dnepropetrovsk”, Russian Math. Surveys, 38:4 (1983), 41–55  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. M. A. Chahkiev, “Exponential polynomials of least deviation from zero and optimal quadrature formulas”, Math. USSR-Sb., 48:1 (1984), 273–285  mathnet  crossref  mathscinet  zmath
    7. N. P. Korneichuk, “S. M. Nikol'skii and the development of research on approximation theory in the USSR”, Russian Math. Surveys, 40:5 (1985), 83–156  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. V.F. Babenko, S.V. Borodachov, “On the construction of optimal cubature formulae which use integrals over hyperspheres”, Journal of Complexity, 23:3 (2007), 346  crossref
    9. S. V. Arkhipov, “The programmed MOCODISS package and its application to design of rod systems on the elastic base”, Autom. Remote Control, 72:7 (2011), 1380–1388  mathnet  crossref  mathscinet  zmath  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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