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

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.

UDC: 519.245

Received: 11.03.2010

 English version: Numerical Analysis and Applications, 2010, 3:4, 344–356

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