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Mat. Zametki, 1968, Volume 3, Issue 5, Pages 565–576 (Mi mz6715)  

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

Best cubature formulas for some classes of functions of many variables

N. P. Korneichuk

Dnepropetrovsk State University

Abstract: The problem of minimizing the error in the cubature formula for a given class of functions is considered. For cubature formulas with a lattice arrangement of points this problems is solved exactly for a wide class of functions of $m$ variables.

Full text: PDF file (675 kB)

English version:
Mathematical Notes, 1968, 3:5, 360–367

Bibliographic databases:

UDC: 517.5
Received: 08.12.1967

Citation: N. P. Korneichuk, “Best cubature formulas for some classes of functions of many variables”, Mat. Zametki, 3:5 (1968), 565–576; Math. Notes, 3:5 (1968), 360–367

Citation in format AMSBIB
\Bibitem{Kor68}
\by N.~P.~Korneichuk
\paper Best cubature formulas for some classes of functions of many variables
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 5
\pages 565--576
\mathnet{http://mi.mathnet.ru/mz6715}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=227679}
\zmath{https://zbmath.org/?q=an:0169.07802|0164.36402}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 5
\pages 360--367
\crossref{https://doi.org/10.1007/BF01150990}


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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. N. P. Korneichuk, N. E. Lushpai, “Best quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation”, Math. USSR-Izv., 3:6 (1969), 1335–1355  mathnet  crossref  mathscinet  zmath
    2. G. K. Lebed', “On quadrature formulas with smallest bound for the remainder on certain classes of functions. II”, Math. USSR-Izv., 4:3 (1970), 645–669  mathnet  crossref  mathscinet  zmath
    3. 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
    4. N. P. Korneichuk, “Widths in $L_p$ of classes of continuous and of differentiable functions, and optimal methods of coding and recovering functions and their derivatives”, Math. USSR-Izv., 18:2 (1982), 227–247  mathnet  crossref  mathscinet  zmath
    5. 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
    6. A. A. Zhensykbaev, “Extremality of monosplines of minimal deficiency”, Math. USSR-Izv., 21:3 (1983), 461–482  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. I. V. Boykov, “Optimal cubature formulae for computing many-dimensional integrals of functions in the class $Q_{r,\gamma}(\Omega,1)$”, U.S.S.R. Comput. Math. Math. Phys., 30:4 (1990), 110–117  mathnet  crossref  mathscinet  zmath
    9. D. B. Bazarkhanov, “Approximation of certain classes of smooth periodic functions of several variables by means of interpolation splines defined over a uniform net”, Math. Notes, 57:6 (1995), 646–648  mathnet  crossref  mathscinet  zmath  isi
    10. M. Sh. Shabozov, “Ob odnoi optimalnoi kubaturnoi formule dlya klassov funktsii, zadavaemykh modulyami nepreryvnosti”, Model. i analiz inform. sistem, 21:3 (2014), 91–105  mathnet
    11. M. Sh. Shabozov, “On Best Quadrature Formulas for Evaluating Curvilinear Integrals for Some Classes of Functions and Curves”, Math. Notes, 96:4 (2014), 613–617  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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