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 Mat. Zametki, 1997, Volume 61, Issue 2, Pages 297–301 (Mi mz1502)

Efficiency of numerical integration algorithms related to divisor theory in cyclotomic fields

N. Temirgaliev

Al-Farabi Kazakh National University

Abstract: For function classes with dominant mixed derivative and bounded mixed difference in the metric of $L^q$ ($1<q\le2$), quadrature formulas are constructed so that the following properties are achieved simultaneously: the grid is simple, the algorithm is efficient and close to the optimal algorithm for constructing the grid, and the order of the error on the power scale cannot be further improved. The case $q=2$ was studied earlier.

DOI: https://doi.org/10.4213/mzm1502

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English version:
Mathematical Notes, 1997, 61:2, 242–245

Bibliographic databases:

UDC: 519.644

Citation: N. Temirgaliev, “Efficiency of numerical integration algorithms related to divisor theory in cyclotomic fields”, Mat. Zametki, 61:2 (1997), 297–301; Math. Notes, 61:2 (1997), 242–245

Citation in format AMSBIB
\Bibitem{Tem97} \by N.~Temirgaliev \paper Efficiency of numerical integration algorithms related to divisor theory in cyclotomic fields \jour Mat. Zametki \yr 1997 \vol 61 \issue 2 \pages 297--301 \mathnet{http://mi.mathnet.ru/mz1502} \crossref{https://doi.org/10.4213/mzm1502} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1619951} \zmath{https://zbmath.org/?q=an:0912.65010} \transl \jour Math. Notes \yr 1997 \vol 61 \issue 2 \pages 242--245 \crossref{https://doi.org/10.1007/BF02355734} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1997XM39800027} 

• http://mi.mathnet.ru/eng/mz1502
• https://doi.org/10.4213/mzm1502
• http://mi.mathnet.ru/eng/mz/v61/i2/p297

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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. E. D. Nursultanov, N. T. Tleukhanova, “Approximate computation of integrals for functions in $W_p^\alpha[0,1]^n$”, Russian Math. Surveys, 55:6 (2000), 1165–1167
2. I. M. Kovaleva, “Vosstanovlenie i integrirovanie funktsii iz anizotropnogo klassa Korobova”, Sib. zhurn. vychisl. matem., 5:3 (2002), 255–266
3. E. D. Nursultanov, N. T. Tleukhanova, “Quadrature formulae for classes of functions of low smoothness”, Sb. Math., 194:10 (2003), 1559–1584
4. Temirgaliev, N, “General algorithm for the numerical integration of periodic functions of several variables”, Doklady Mathematics, 76:2 (2007), 681
5. A. Zh. Zhubanysheva, N. Temirgaliev, Zh. N. Temirgalieva, “Application of divisor theory to the construction of tables of optimal coefficients for quadrature formulas”, Comput. Math. Math. Phys., 49:1 (2009), 12–22
6. 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
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