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Dal'nevostochnyi Matematicheskii Zhurnal, 2019, Volume 19, Number 1, Pages 10–19 (Mi dvmg391)  

This article is cited in 2 scientific papers (total in 2 papers)

Extremal cubature formulas for anisotropic classes

V. A. Bykovskii

Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences
Full-text PDF (530 kB) Citations (2)
References:
Abstract: Let E(α;s) be a class of periodical functions
f(x1,,xs)=(m1,,ms)Zsc(m1,,ms)exp(2πi(m1x1++msxs))
with |c(m1,,ms)|j=1(max(1,|mj|))α, and 1<α<. In this work for all natural numbers 1<N< we prove best possible estimation
RN(E(α;s))α,s(logN)s1Nα
for the error of the best cubature formula on the class E(α;s) with N nodes and weights. Similar results are proved for other classes of functions.
Key words: cubature formulas, anisotropic classes of functions.
Received: 21.05.2019
Document Type: Article
UDC: 519.68
MSC: 65J01
Language: Russian
Citation: V. A. Bykovskii, “Extremal cubature formulas for anisotropic classes”, Dal'nevost. Mat. Zh., 19:1 (2019), 10–19
Citation in format AMSBIB
\Bibitem{Byk19}
\by V.~A.~Bykovskii
\paper Extremal cubature formulas for anisotropic classes
\jour Dal'nevost. Mat. Zh.
\yr 2019
\vol 19
\issue 1
\pages 10--19
\mathnet{http://mi.mathnet.ru/dvmg391}
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  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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