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Izv. RAN. Ser. Mat., 2009, Volume 73, Issue 2, Pages 183–224 (Mi izv956)  

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

An application of tensor products of functionals in problems of numerical integration

N. Temirgalieva, S. S. Kudaibergenovb, A. A. Shomanovaa

a L. N. Gumilev Eurasian National University
b M. O. Auezov South Kazakhstan State University

Abstract: We introduce a new notion of tensor product of functionals and apply it to problems of numerical integration. We find the exact orders of the errors arising on various classes of functions, some of which are known and some are new.

Keywords: tensor products of functionals, numerical integration, Smolyak quadrature formulae, discrepancy, Korobov grid, number-theoretic methods, theory of divisors, Chebyshev system, recovery from inexact information.


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English version:
Izvestiya: Mathematics, 2009, 73:2, 393–434

Bibliographic databases:

UDC: 517.5
MSC: Primary 65D30; Secondary 41A55
Received: 11.03.2005
Revised: 05.04.2008

Citation: N. Temirgaliev, S. S. Kudaibergenov, A. A. Shomanova, “An application of tensor products of functionals in problems of numerical integration”, Izv. RAN. Ser. Mat., 73:2 (2009), 183–224; Izv. Math., 73:2 (2009), 393–434

Citation in format AMSBIB
\by N.~Temirgaliev, S.~S.~Kudaibergenov, A.~A.~Shomanova
\paper An application of tensor products of functionals in problems of numerical integration
\jour Izv. RAN. Ser. Mat.
\yr 2009
\vol 73
\issue 2
\pages 183--224
\jour Izv. Math.
\yr 2009
\vol 73
\issue 2
\pages 393--434

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    This publication is cited in the following articles:
    1. N. Temirgaliev, S. S. Kudaibergenov, A. A. Shomanova, “Applications of Smolyak quadrature formulas to the numerical integration of Fourier coefficients and in function recovery problems”, Russian Math. (Iz. VUZ), 54:3 (2010), 45–62  mathnet  crossref  mathscinet  elib
    2. Temirgaliev N., “Tensor products of functionals and their application”, Dokl. Math., 81:1 (2010), 78–82  crossref  mathscinet  zmath  isi  elib
    3. Nauryzbayev N., Temirgaliyev N., “An exact order of discrepancy of the Smolyak grid and some general conclusions in the theory of numerical integration”, Found. Comput. Math., 12:2 (2012), 139–172  crossref  mathscinet  zmath  isi  elib
    4. S. S. Kudaibergenov, S. G. Sabitova, “Discretization of solutions to Poisson’s equation in the Korobov class”, Comput. Math. Math. Phys., 53:7 (2013), 896–907  mathnet  crossref  crossref  mathscinet  isi  elib
    5. E. A. Bailov, M. B. Sikhov, N. Temirgaliev, “General algorithm for the numerical integration of functions of several variables”, Comput. Math. Math. Phys., 54:7 (2014), 1061–1078  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. N. Temirgaliyev, N. Zh. Nauryzbayev, A. A. Shomanova, “Approximative possibilities of computational aggregates of the “Smolyak type” with Dirichlet, Fejer and Vallée-Poussin kernels in the scale of Ul'yanov classes”, Russian Math. (Iz. VUZ), 59:7 (2015), 67–72  mathnet  crossref
    7. A. Zh. Zhubanysheva, N. Temirgaliev, “Informative cardinality of trigonometric Fourier coefficients and their limiting error in the discretization of a differentiation operator in multidimensional Sobolev classes”, Comput. Math. Math. Phys., 55:9 (2015), 1432–1443  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    8. N. Temirgaliev, A. Zhubanysheva, “Order estimates of the norms of derivatives of functions with zero values on linear functionals and their applications”, Russian Math. (Iz. VUZ), 61:3 (2017), 77–82  mathnet  crossref  isi
    9. N. Temirgaliev, S. S. Kudaibergenov, N. Zh. Nauryzbaev, “Poryadkovo tochnoe vychislenie integralov ot proizvedenii funktsii metodom tenzornykh proizvedenii funktsionalov”, Izv. vuzov. Matem., 2019, no. 11, 94–99  mathnet  crossref
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