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Teor. Veroyatnost. i Primenen., 1960, Volume 5, Issue 4, Pages 473–476 (Mi tvp4858)  

Short Communications

Polynomial Approximations and the Monte-Carlo Method

S. M. Ermakov, V. G. Zolotukhin

Moscow

Abstract: A new method of computing multiple integrals is proposed, which is a generalization of the ordinary Monte-Caro method.
This new method in evaluating the integral makes use of its approximate value as obtained by formulas for mechanical quadratures in accordance with a special distribution law for the integrational points.
This new method in evaluating the integral makes use of its approximate value as obtained by formulas for mechanical quadratures in accordance with a special distribution law for the integrational points.
It is shown that the standard deviation of the estimation may be considerably decreased, especially when the integrand possesses good differential properties.

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English version:
Theory of Probability and its Applications, 1960, 5:4, 428–431

Received: 14.07.1959

Citation: S. M. Ermakov, V. G. Zolotukhin, “Polynomial Approximations and the Monte-Carlo Method”, Teor. Veroyatnost. i Primenen., 5:4 (1960), 473–476; Theory Probab. Appl., 5:4 (1960), 428–431

Citation in format AMSBIB
\Bibitem{ErmZol60}
\by S.~M.~Ermakov, V.~G.~Zolotukhin
\paper Polynomial Approximations and the Monte-Carlo Method
\jour Teor. Veroyatnost. i Primenen.
\yr 1960
\vol 5
\issue 4
\pages 473--476
\mathnet{http://mi.mathnet.ru/tvp4858}
\transl
\jour Theory Probab. Appl.
\yr 1960
\vol 5
\issue 4
\pages 428--431
\crossref{https://doi.org/10.1137/1105046}


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