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Mat. Zametki, 1969, Volume 6, Issue 4, Pages 475–481 (Mi mz6954)  

This article is cited in 7 scientific papers (total in 7 papers)

Best quadrature formulas on classes of differentiable periodic functions

N. E. Lushpai

Dnepropetrovsk State University

Abstract: A solution is given to the problem of finding the best quadrature formula among formulas of the form
$$ \int_0^{2\pi}f(x) dx\approx\sum_{k=0}^{m-1}\sum_{l=0}^\rho p_{k,l}f^{(l)}(x_k) $$
which are exact in the case of a constant, for $\rho=r-1$, $r=1,2,3,…$ and $\rho=r-2$, $r$ even, for the classes $W^{(r)}L_qM$ of $2\pi$-periodic functions.

Full text: PDF file (356 kB)

English version:
Mathematical Notes, 1969, 6:4, 740–744

Bibliographic databases:

UDC: 51
Received: 09.12.1968

Citation: N. E. Lushpai, “Best quadrature formulas on classes of differentiable periodic functions”, Mat. Zametki, 6:4 (1969), 475–481; Math. Notes, 6:4 (1969), 740–744

Citation in format AMSBIB
\Bibitem{Lus69}
\by N.~E.~Lushpai
\paper Best quadrature formulas on classes of differentiable periodic functions
\jour Mat. Zametki
\yr 1969
\vol 6
\issue 4
\pages 475--481
\mathnet{http://mi.mathnet.ru/mz6954}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=251901}
\zmath{https://zbmath.org/?q=an:0187.02101}
\transl
\jour Math. Notes
\yr 1969
\vol 6
\issue 4
\pages 740--744
\crossref{https://doi.org/10.1007/BF01093812}


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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
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