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Izv. Akad. Nauk SSSR Ser. Mat., 1977, Volume 41, Issue 5, Pages 1110–1124 (Mi izv1882)  

This article is cited in 11 scientific papers (total in 11 papers)

Best quadrature formula for some classes of periodic differentiable functions

A. A. Zhensykbaev


Abstract: In this work there is solved the problem of the best quadrature formula of the form
$$ \int_0^1f(x) dx=\sum_{i=1}^na_if(x_i)+R(f) $$
on the classes of periodic functions $W^r_p$ ($r=1,2,…$; $1\leqslant p\leqslant\infty$).
Bibliography: 13 titles.

Full text: PDF file (1168 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1977, 11:5, 1055–1071

Bibliographic databases:

UDC: 517.5
MSC: 41A15, 41A55
Received: 19.01.1976

Citation: A. A. Zhensykbaev, “Best quadrature formula for some classes of periodic differentiable functions”, Izv. Akad. Nauk SSSR Ser. Mat., 41:5 (1977), 1110–1124; Math. USSR-Izv., 11:5 (1977), 1055–1071

Citation in format AMSBIB
\Bibitem{Zhe77}
\by A.~A.~Zhensykbaev
\paper Best quadrature formula for some classes of periodic differentiable functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1977
\vol 41
\issue 5
\pages 1110--1124
\mathnet{http://mi.mathnet.ru/izv1882}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=471271}
\zmath{https://zbmath.org/?q=an:0363.41030|0393.41014}
\transl
\jour Math. USSR-Izv.
\yr 1977
\vol 11
\issue 5
\pages 1055--1071
\crossref{https://doi.org/10.1070/IM1977v011n05ABEH001758}


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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. 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
    2. A. A. Zhensykbaev, “Extremality of monosplines of minimal deficiency”, Math. USSR-Izv., 21:3 (1983), 461–482  mathnet  crossref  mathscinet  zmath
    3. S. M. Nikol'skii, “Aleksandrov and Kolmogorov in Dnepropetrovsk”, Russian Math. Surveys, 38:4 (1983), 41–55  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. M. A. Chahkiev, “Linear differential operators with real spectrum, and optimal quadrature formulas”, Math. USSR-Izv., 25:2 (1985), 391–417  mathnet  crossref  mathscinet  zmath
    5. Nguyên Th{\d i} Thiêu Hoa, “On best methods of integration and of recovery of functions on classes given by convolutions that do not increase the oscillation”, Russian Math. Surveys, 39:2 (1984), 183–184  mathnet  crossref  mathscinet  zmath  isi
    6. Nguyên Th{\d i} Thiêu Hoa, “Best quadrature formulas and methods of reconstructing functions defined by variation diminishing kernels”, Math. USSR-Sb., 58:1 (1987), 101–117  mathnet  crossref  mathscinet  zmath
    7. B. D. Bojanov, Daren Huang, “Periodic monosplines and perfect splines of least norm”, Constr Approx, 3:1 (1987), 363  crossref  mathscinet  zmath  isi
    8. B. D. Boyanov, “Optimal quadrature formulae”, Russian Math. Surveys, 60:6 (2005), 1035–1055  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    9. Fang G.S., Li X.H., “Optimal quadrature problem on Hardy-Sobolev classes”, Journal of Complexity, 21:5 (2005), 722–739  crossref  isi  elib
    10. Fang G., Li X., “Optimal quadrature problem on classes defined by kernels satisfying certain oscillation properties”, Numerische Mathematik, 105:1 (2006), 133–158  crossref  isi  elib
    11. V.F. Babenko, S.V. Borodachov, D.S. Skorokhodov, “Optimal cubature formulas for tensor products of certain classes of functions”, Journal of Complexity, 27:6 (2011), 519  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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