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Zh. Vychisl. Mat. Mat. Fiz., 2005, Volume 45, Number 1, Pages 17–26 (Mi zvmmf716)  

This article is cited in 1 scientific paper (total in 1 paper)

On extensions of Chebyshev's inequality

Z. S. Gaeva

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

Abstract: An algorithm for solving the Chebyshev–Markov moment problem is given that permits one to refine the Chebyshev-like inequalities. It is important in practical applications to be able to analyze the sensitivity of the exact upper and lower estimates to errors in the given moments. An algorithm for obtaining exact estimates is modified to allow one to calculate the derivatives of the estimates with respect to each moment.

Key words: extended Chebyshev's inequality, algorithm for solving the Chebyshev–Markov moment problem.

Full text: PDF file (745 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2005, 45:1, 13–22

Bibliographic databases:
UDC: 519.651
Received: 26.11.2003
Revised: 31.05.2004

Citation: Z. S. Gaeva, “On extensions of Chebyshev's inequality”, Zh. Vychisl. Mat. Mat. Fiz., 45:1 (2005), 17–26; Comput. Math. Math. Phys., 45:1 (2005), 13–22

Citation in format AMSBIB
\Bibitem{Gae05}
\by Z.~S.~Gaeva
\paper On extensions of Chebyshev's inequality
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 1
\pages 17--26
\mathnet{http://mi.mathnet.ru/zvmmf716}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2151042}
\zmath{https://zbmath.org/?q=an:1073.41009}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 1
\pages 13--22


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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. Z. S. Gaeva, A. A. Shananin, “The Chebyshev–Markov–Krein algorithm for analyzing microphysical processes in hail clouds”, Comput. Math. Math. Phys., 47:9 (2007), 1551–1569  mathnet  crossref  mathscinet
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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