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Izv. Akad. Nauk SSSR Ser. Mat., 1974, Volume 38, Issue 3, Pages 583–614 (Mi izv1941)  

This article is cited in 17 scientific papers (total in 17 papers)

On the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for some classes of differentiable periodic functions

V. P. Motornyi


Abstract: We solve the problem of the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for the following classes of differentiable periodic functions: $W^r$ ($r>3$), $W^rH_\omega$ (where $\omega$ is a convex modulus of continuity and $r$ is odd), and $W^rL$ ($r=4,6,…$).

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English version:
Mathematics of the USSR-Izvestiya, 1974, 8:3, 591–620

Bibliographic databases:

UDC: 517.5
MSC: 41A55, 41A15
Received: 23.01.1973

Citation: 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”, Izv. Akad. Nauk SSSR Ser. Mat., 38:3 (1974), 583–614; Math. USSR-Izv., 8:3 (1974), 591–620

Citation in format AMSBIB
\Bibitem{Mot74}
\by V.~P.~Motornyi
\paper On the best quadrature formula of the form $\sum_{k=1}^np_kf(x_k)$ for some classes of differentiable periodic functions
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1974
\vol 38
\issue 3
\pages 583--614
\mathnet{http://mi.mathnet.ru/izv1941}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=390610}
\zmath{https://zbmath.org/?q=an:0306.41013}
\transl
\jour Math. USSR-Izv.
\yr 1974
\vol 8
\issue 3
\pages 591--620
\crossref{https://doi.org/10.1070/IM1974v008n03ABEH002122}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. Wilhelm Forst, “Zur Interpolation und Integration differenzierbarer periodischer Funktionen”, Numer Math, 30:2 (1978), 137  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, “Linear differential operators with real spectrum, and optimal quadrature formulas”, Math. USSR-Izv., 25:2 (1985), 391–417  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. Nguyên Th{\d i} Thiêu Hoa, “Some extremal problems on classes of functions determined by linear differential operators”, Math. USSR-Sb., 68:1 (1991), 213–255  mathnet  crossref  mathscinet  zmath  isi
    9. Kai Diethelm, “New error bounds for modified quadrature formulas for Cauchy principal value integrals”, Journal of Computational and Applied Mathematics, 82:1-2 (1997), 93  crossref
    10. S. K. Bagdasarov, “Maximization of functionals in $H^\omega [a,b]$”, Sb. Math., 189:2 (1998), 159–226  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. K. Yu. Osipenko, “Best quadrature formulae on Hardy–Sobolev classes”, Izv. Math., 65:5 (2001), 923–939  mathnet  crossref  crossref  mathscinet  zmath  elib
    12. B. D. Boyanov, “Optimal quadrature formulae”, Russian Math. Surveys, 60:6 (2005), 1035–1055  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. Fang G.S., Li X.H., “Optimal quadrature problem on Hardy-Sobolev classes”, Journal of Complexity, 21:5 (2005), 722–739  crossref  isi  elib
    14. 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
    15. K. I. Oskolkov, “Linear and Nonlinear Methods of Relief Approximation”, Journal of Mathematical Sciences, 155:1 (2008), 129–152  mathnet  crossref  mathscinet  zmath
    16. 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
    17. 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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