Variance of a standard vector Monte Carlo estimate in the theory of polarized radiative transfer
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 11, pp. 2099-2113
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The spectral radius $\rho$ of the matrix integral operator defining the covariance matrix of a standard vector Monte Carlo estimate in the polarized radiative transfer problem is examined. The theory of positive operators is used to analytically calculate $\rho=\rho_0$ for transfer through an infinite homogeneous medium. For a bounded medium, it is shown that $\rho$ is approximately equal to $\rho_0$ times the spectral radius of the operator corresponding to radiative transfer without polarization. This is shown numerically by estimating the iterations of the corresponding resolvent and approximately analytically by using a perturbation of a special functional.
@article{ZVMMF_2006_46_11_a13,
author = {G. A. Mikhailov and S. A. Uhinov and A. S. Chimaeva},
title = {Variance of a~standard vector {Monte} {Carlo} estimate in the theory of polarized radiative transfer},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {2099--2113},
publisher = {mathdoc},
volume = {46},
number = {11},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_11_a13/}
}
TY - JOUR AU - G. A. Mikhailov AU - S. A. Uhinov AU - A. S. Chimaeva TI - Variance of a standard vector Monte Carlo estimate in the theory of polarized radiative transfer JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2006 SP - 2099 EP - 2113 VL - 46 IS - 11 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_11_a13/ LA - ru ID - ZVMMF_2006_46_11_a13 ER -
%0 Journal Article %A G. A. Mikhailov %A S. A. Uhinov %A A. S. Chimaeva %T Variance of a standard vector Monte Carlo estimate in the theory of polarized radiative transfer %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2006 %P 2099-2113 %V 46 %N 11 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_11_a13/ %G ru %F ZVMMF_2006_46_11_a13
G. A. Mikhailov; S. A. Uhinov; A. S. Chimaeva. Variance of a standard vector Monte Carlo estimate in the theory of polarized radiative transfer. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 11, pp. 2099-2113. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_11_a13/