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Izv. Vyssh. Uchebn. Zaved. Mat., 2010, Number 3, Pages 52–71 (Mi ivm6712)  

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

Applications of Smolyak quadrature formulas to the numerical integration of Fourier coefficients and in function recovery problems

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

a Eurasian National University, Astana, Republic of Kazakhstan
b Chair of Mathematical Modeling and Education, Southern-Kazakhstan State University, Shymkent, Republic of Kazakhstan

Abstract: In this paper with the help of Smolyak quadrature formulas we calculate exact orders of errors of the numerical integration of trigonometric Fourier coefficients of functions from generalized classes of the Korobov and Sobolev type. We apply the obtained results to the recovery of functions from their values at a finite number of points in terms of K. Sherniyazov approach.

Keywords: Ul'yanov classes, numerical integration, Smolyak quadrature formula, trigonometric Fourier coefficients, restoration operators.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:3, 45–62

Bibliographic databases:

UDC: 517.5
Received: 16.11.2007
Revised: 04.05.2009

Citation: 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”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 3, 52–71; Russian Math. (Iz. VUZ), 54:3 (2010), 45–62

Citation in format AMSBIB
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\by N.~Temirgaliev, S.~S.~Kudaibergenov, A.~A.~Shomanova
\paper Applications of Smolyak quadrature formulas to the numerical integration of Fourier coefficients and in function recovery problems
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 3
\pages 52--71
\mathnet{http://mi.mathnet.ru/ivm6712}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2778325}
\elib{http://elibrary.ru/item.asp?id=12993377}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 3
\pages 45--62
\crossref{https://doi.org/10.3103/S1066369X10030084}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649605387}


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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. Goryainov V.V., “Analiz pogreshnosti bystrykh ryadov fure pri ikh mnogokratnom differentsirovanii dlya sluchaya vychisleniya koeffitsientov ryada potochechnym metodom”, Vestnik Voronezhskogo gosudarstvennogo tekhnicheskogo universiteta, 7:2 (2011), 36–40  elib
    2. Chernyshov A.D., Goryainov V.V., “O vybore optimalnogo poryadka granichnoi funktsii v bystrom razlozhenii”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Sistemnyi analiz i informatsionnye tekhnologii, 2011, no. 1, 60–65  elib
    3. Chernyshov A.D., Khozyainova N.A., Goryainov V.V., “Issledovanie pogreshnosti potochechnogo metoda vychisleniya koeffitsientov bystrykh ryadov fure”, Vestnik Voronezhskogo gosudarstvennogo universiteta inzhenernykh tekhnologii, 2011, no. 2, 64–67  elib
    4. Chernyshov A.D., Goryainov V.V., “O sposobe naneseniya raschetnykh tochek na otrezok pri realizatsii potochechnogo metoda vychisleniya koeffitsientov bystrykh razlozhenii dlya resheniya kraevoi zadachi s usloviyami dirikhle”, Vestnik voronezhskogo gosudarstvennogo universiteta. seriya: sistemnyi analiz i informatsionnye tekhnologii, 2012, no. 2, 30–35  elib
    5. 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
    6. 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
    7. 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
    8. 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
    9. Oba R.M., “Minimal Sparse Sampling For Fourier-Polynomial Chaos in Acoustic Scattering”, Int. J. Uncertain. Quantif., 5:1 (2015), 1–20  crossref  mathscinet  isi  elib
    10. N. Temirgaliev, A. Zh. Zhubanysheva, “Kompyuternyi (vychislitelnyi) poperechnik v kontekste obschei teorii vosstanovleniya”, Izv. vuzov. Matem., 2019, no. 1, 89–97  mathnet  crossref
    11. 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
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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