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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, Number 3, Pages 52–71 (Mi ivm6712)  
This article is cited in 12 scientific papers (total in 12 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
Full-text PDF (318 kB) Citations (12)
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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.
Received: 16.11.2007
Revised: 04.05.2009
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, Volume 54, Issue 3, Pages 45–62
DOI: https://doi.org/10.3103/S1066369X10030084
Bibliographic databases:
UDC: 517.5
Language: Russian
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://mathscinet.ams.org/mathscinet-getitem?mr=2778325}
\elib{https://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{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649605387}
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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