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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2006, Volume 46, Number 11, Pages 2099–2113
(Mi zvmmf388)
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This article is cited in 25 scientific papers (total in 25 papers)
Variance of a standard vector Monte Carlo estimate in the theory of polarized radiative transfer
G. A. Mikhailov, S. A. Uhinov, A. S. Chimaeva Institute of Computational Mathematics and Mathematical Geophysics, Siberian Division, Russian Academy of Sciences,
pr. Akademika Lavrent'eva 6, Novosibirsk, 630090, Russia
Abstract:
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.
Key words:
transfer of polarized radiation, statistical simulation, variance of a standard vector Monte Carlo estimate.
Received: 10.05.2006
Citation:
G. A. Mikhailov, S. A. Uhinov, A. S. Chimaeva, “Variance of a standard vector Monte Carlo estimate in the theory of polarized radiative transfer”, Zh. Vychisl. Mat. Mat. Fiz., 46:11 (2006), 2099–2113; Comput. Math. Math. Phys., 46:11 (2006), 2006–2019
Linking options:
https://www.mathnet.ru/eng/zvmmf388 https://www.mathnet.ru/eng/zvmmf/v46/i11/p2099
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Abstract page: | 458 | Full-text PDF : | 186 | References: | 45 | First page: | 1 |
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