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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2010, Volume 13, Number 4, Pages 423–438 (Mi sjvm417)  
Vector estimators of the Monte Carlo method: dual representation and optimization

G. A. Mikhailov, I. N. Medvedev

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk
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Abstract: In this paper, a detailed analysis of the vector Monte-Carlo estimator theory for solving a system of integral equations is given. A dual representation for the variances of such estimators is introduced. With the dual representation we minimize the majorant mean-square error of a global solution estimator (of the histogram type). Also, for the first time we give a detailed description of the scalar Monte-Carlo algorithms for solving a system of integral equations and a comparison between the scalar and vector algorithms.
Key words: vector estimator of Monte-Carlo method, solving systems of integral equations, dual estimator representation, optimization, scalar Monte-Carlo algorithm.
Received: 11.03.2010
English version:
Numerical Analysis and Applications, 2010, Volume 3, Issue 4, Pages 344–356
DOI: https://doi.org/10.1134/S1995423910040063
Bibliographic databases:
Document Type: Article
UDC: 519.245
Language: Russian
Citation: G. A. Mikhailov, I. N. Medvedev, “Vector estimators of the Monte Carlo method: dual representation and optimization”, Sib. Zh. Vychisl. Mat., 13:4 (2010), 423–438; Num. Anal. Appl., 3:4 (2010), 344–356
Citation in format AMSBIB
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\by G.~A.~Mikhailov, I.~N.~Medvedev
\paper Vector estimators of the Monte Carlo method: dual representation and optimization
\jour Sib. Zh. Vychisl. Mat.
\yr 2010
\vol 13
\issue 4
\pages 423--438
\mathnet{http://mi.mathnet.ru/sjvm417}
\transl
\jour Num. Anal. Appl.
\yr 2010
\vol 3
\issue 4
\pages 344--356
\crossref{https://doi.org/10.1134/S1995423910040063}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78650378401}
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