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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.

Full text: PDF file (428 kB)

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

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}