Vector estimators of the Monte Carlo method: dual representation and optimization
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 4, pp. 423-438
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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.
@article{SJVM_2010_13_4_a5,
author = {G. A. Mikhailov and I. N. Medvedev},
title = {Vector estimators of the {Monte} {Carlo} method: dual representation and optimization},
journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
pages = {423--438},
publisher = {mathdoc},
volume = {13},
number = {4},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/SJVM_2010_13_4_a5/}
}
TY - JOUR AU - G. A. Mikhailov AU - I. N. Medvedev TI - Vector estimators of the Monte Carlo method: dual representation and optimization JO - Sibirskij žurnal vyčislitelʹnoj matematiki PY - 2010 SP - 423 EP - 438 VL - 13 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SJVM_2010_13_4_a5/ LA - ru ID - SJVM_2010_13_4_a5 ER -
%0 Journal Article %A G. A. Mikhailov %A I. N. Medvedev %T Vector estimators of the Monte Carlo method: dual representation and optimization %J Sibirskij žurnal vyčislitelʹnoj matematiki %D 2010 %P 423-438 %V 13 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/SJVM_2010_13_4_a5/ %G ru %F SJVM_2010_13_4_a5
G. A. Mikhailov; I. N. Medvedev. Vector estimators of the Monte Carlo method: dual representation and optimization. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 13 (2010) no. 4, pp. 423-438. http://geodesic.mathdoc.fr/item/SJVM_2010_13_4_a5/