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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 1, Pages 14–25 (Mi zvmmf50)  

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

Application of divisor theory to the construction of tables of optimal coefficients for quadrature formulas

A. Zh. Zhubanysheva, N. Temirgaliev, Zh. N. Temirgalieva

Eurasian National University, ul. Munaitpasova 5, Astana, 473021, Kazakhstan

Abstract: Based on the theory of divisors, an effective theoretical algorithm designed previously by the authors for constructing good quadrature formulas with a Korobov grid (i.e., an algorithm for finding optimal coefficients) is used to develop a computer search method that produces tables of optimal coefficients giving more accurate integration error estimates with a smaller number of nodes than in all previously known cases.

Key words: discrepancy, uniformly distributed grids, Korobov grids, optimal coefficients, quadrature formulas, divisor theory, lattice, ideal, extreme function of a class, numerical experiments.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:1, 12–22

Bibliographic databases:

UDC: 519.644
Received: 03.06.2007
Revised: 29.04.2008

Citation: A. Zh. Zhubanysheva, N. Temirgaliev, Zh. N. Temirgalieva, “Application of divisor theory to the construction of tables of optimal coefficients for quadrature formulas”, Zh. Vychisl. Mat. Mat. Fiz., 49:1 (2009), 14–25; Comput. Math. Math. Phys., 49:1 (2009), 12–22

Citation in format AMSBIB
\by A.~Zh.~Zhubanysheva, N.~Temirgaliev, Zh.~N.~Temirgalieva
\paper Application of divisor theory to the construction of tables of optimal coefficients for quadrature formulas
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
\vol 49
\issue 1
\pages 14--25
\jour Comput. Math. Math. Phys.
\yr 2009
\vol 49
\issue 1
\pages 12--22

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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. Temirgaliev N., “Tensor products of functionals and their application”, Dokl. Math., 81:1 (2010), 78–82  crossref  mathscinet  zmath  isi  elib  elib  scopus
    2. M. B. Sikhov, N. Temirgaliev, “On an Algorithm for Constructing Uniformly Distributed Korobov Grids”, Math. Notes, 87:6 (2010), 916–917  mathnet  crossref  crossref  mathscinet  isi
    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  scopus
    4. 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
    5. Zh. N. Temirgaliyeva, N. Temirgaliyev, “Rapid “algebraic” Fourier transforms on uniformly distributed meshes”, Russian Math. (Iz. VUZ), 60:5 (2016), 81–85  mathnet  crossref  isi
    6. Zh. N. Temirgaliyeva, N. Temirgaliyev, ““Geometry of numbers” in a context of algebraic theory of numbers”, Russian Math. (Iz. VUZ), 60:10 (2016), 77–81  mathnet  crossref  isi
    7. N. Zh. Nauryzbaev, A. A. Shomanova, N. Temirgaliyev, “On some special effects in theory on numerical integration and functions recovery”, Russian Math. (Iz. VUZ), 62:3 (2018), 84–88  mathnet  crossref  isi
    8. N. Temirgaliyev, Sh. K. Abikenova, Sh. U. Azhgaliev, G. E. Taugynbaeyva, “The Radon transform in the scheme C(N)D-inverstigations and the quasi-Monte Carlo theory”, Russian Math. (Iz. VUZ), 64:3 (2020), 87–92  mathnet  crossref  crossref  isi
    9. S. S. Kudaibergenov, Ye. Ye. Nurmoldin, N. Zh. Nauryzbayev, N. Temirgaliyev, “Formulas for approximate calculation of the Chebyshev coefficients”, Russian Math. (Iz. VUZ), 65:2 (2021), 69–74  mathnet  crossref  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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