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Mathematics of the USSR-Sbornik, 1984, Volume 48, Issue 1, Pages 273–285
DOI: https://doi.org/10.1070/SM1984v048n01ABEH002674 (Mi sm2130) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Exponential polynomials of least deviation from zero and optimal quadrature formulas

M. A. Chahkiev
English version PDF (555 kB) Citations (2)
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DOI: https://doi.org/10.1070/SM1984v048n01ABEH002674
Abstract: Certain properties of polynomials of exponential functions of least deviation from zero in mean on a segment are established. The dependence of the norm of the extremal polynomial and its roots on the length of the segment is investigated first. On the basis of these properties optimality of equidistant nodes is established in the problem of the best quadrature formula for periodic classes which are prescribed by a constraint on the action of a linear differential operator with real eigenvalues. Formulas for determining the weights of the optimal quadrature formula and a relation for optimal error are presented.
Bibliography: 12 titles.
Received: 10.07.1981
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1983, Volume 120(162), Number 2, Pages 273–285
Bibliographic databases:
UDC: 517.5
MSC: 41A10, 41A55
Language: English
Original paper language: Russian
Citation: M. A. Chahkiev, “Exponential polynomials of least deviation from zero and optimal quadrature formulas”, Mat. Sb. (N.S.), 120(162):2 (1983), 273–285; Math. USSR-Sb., 48:1 (1984), 273–285
Citation in format AMSBIB
\Bibitem{Cha83}
\by M.~A.~Chahkiev
\paper Exponential polynomials of least deviation from zero and optimal quadrature formulas
\jour Mat. Sb. (N.S.)
\yr 1983
\vol 120(162)
\issue 2
\pages 273--285
\mathnet{http://mi.mathnet.ru/sm2130}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=687617}
\zmath{https://zbmath.org/?q=an:0557.41022|0529.41028}
\transl
\jour Math. USSR-Sb.
\yr 1984
\vol 48
\issue 1
\pages 273--285
\crossref{https://doi.org/10.1070/SM1984v048n01ABEH002674}
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  • https://www.mathnet.ru/eng/sm/v162/i2/p273
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:551
    Russian version PDF:306
    English version PDF:41
    References:66
     
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