Convergence of Monte Carlo algorithms for reconstructing the scattering phase function with polarization
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 1, pp. 103-116.

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of reconstructing the atmospheric scattering phase function from groundbased solar almucantar sky brightness observations is considered. A newiterative algorithm for solving this problem was developed as a combination of existing additive and multiplicative methods of refining the single-scattering contribution to the observed brightness with polarization of scattered radiation in the atmosphere. Also, some modifications of these methods were proposed. The objective of this paper is to numerically substantiate the convergence of these methods. For this purpose, an algorithm of Jacobi matrix calculation for the iteration operators of the methods was developed, and calculations were carried out for various parameters of the atmosphere.
@article{SJVM_2011_14_1_a8,
     author = {S. A. Ukhinov and A. S. Chimaeva},
     title = {Convergence of {Monte} {Carlo} algorithms for reconstructing the scattering phase function with polarization},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {103--116},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2011_14_1_a8/}
}
TY  - JOUR
AU  - S. A. Ukhinov
AU  - A. S. Chimaeva
TI  - Convergence of Monte Carlo algorithms for reconstructing the scattering phase function with polarization
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2011
SP  - 103
EP  - 116
VL  - 14
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJVM_2011_14_1_a8/
LA  - ru
ID  - SJVM_2011_14_1_a8
ER  - 
%0 Journal Article
%A S. A. Ukhinov
%A A. S. Chimaeva
%T Convergence of Monte Carlo algorithms for reconstructing the scattering phase function with polarization
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2011
%P 103-116
%V 14
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJVM_2011_14_1_a8/
%G ru
%F SJVM_2011_14_1_a8
S. A. Ukhinov; A. S. Chimaeva. Convergence of Monte Carlo algorithms for reconstructing the scattering phase function with polarization. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 1, pp. 103-116. http://geodesic.mathdoc.fr/item/SJVM_2011_14_1_a8/

[1] Antyufeev V. S., Mikhailov G. A., Lifshits G. Sh., Ivanov A. I., “Opredelenie aerozolnykh indikatris rasseyaniya bezoblachnoi atmosfery v spektralnykh oblastyakh $0.55\div2.4$ mkm”, Izv. AN SSSR. Ser. FAO, 16:2 (1980), 146–155

[2] Antyufeev V. S., Nazaraliev M. A., Obratnye zadachi atmosfernoi optiki, Izd-vo VTs SO AN SSSR, Novosibirsk, 1988

[3] Krasnoselskii M. A., Vainikko G. M., Zabreiko P. P., Rutitskii Ya. B., Stetsenko V. Ya., Priblizhennoe reshenie operatornykh uravnenii, Nauka, M., 1969 | MR

[4] Marchuk G. I., Mikhailov G. A., Nazaraliev M. A. i dr., Metod Monte-Karlo v atmosfernoi optike, Nauka, Novosibirsk, 1976

[5] Mikhailov G. A., Nekotorye zadachi teorii i prilozhenii metodov Monte-Karlo, Preprint AN SSSR, Sib. otd-nie VTs, Novosibirsk, 1978

[6] Mikhailov G. A., Ukhinov S. A., Chimaeva A. S., “Dispersiya standartnoi vektornoi otsenki metoda Monte-Karlo v teorii perenosa polyarizovannogo izlucheniya”, Zhurn. vychisl. matematiki i mat. fiziki, 46:11 (2006), 2099–2113 | MR

[7] Mikhailov G. A., Ukhinov S. A., Chimaeva A. S., “Algoritmy metoda Monte-Karlo dlya vosstanovleniya indikatrisy rasseyaniya s uchetom polyarizatsii”, Dokl. RAN, 423:2 (2008), 161–164 | MR

[8] Ukhinov S. A., Yurkov D. I., “Otsenki metodov Monte-Karlo dlya parametricheskikh proizvodnykh polyarizovannogo izlucheniya”, Sib. zhurn. vychisl. matem., 5:1 (2002), 39–56 | Zbl

[9] Chandrasekar S., Perenos luchistoi energii, Nauka, M., 1953

[10] Chimaeva A. S., “Issledovanie dispersii otsenok polyarizatsii metodom Monte-Karlo”, Tr. konferentsii molodykh uchenykh IVMiMG SO RAN, Novosibirsk, 2004, 242–248

[11] Chimaeva A. S., Mikhailov G. A., “Study of polarization estimates variance by the Monte Carlo method”, Russ. J. Numer. Anal. Math. Modelling, 20:3 (2006), 305–317 | MR

[12] Chimaeva A. S., Mikhailov G. A., Ukhiniov S. A., “Monte Carlo algorithms for reconstructing a scattering phase function with polarization taken into account”, Russ. J. Numer. Anal. Math. Modelling, 24:5 (2009), 455–465 | DOI | MR | Zbl

[13] Ukhiniov S. A., Yurkov D. I., “Monte Carlo method of calculating the derivatives of polarized radiation”, Russ. J. Numer. Anal. Math. Modelling, 13:5 (1998), 425–444 | DOI | MR

[14] Ukhinov S. A., Yurkov D. I., “Computation of the parametric derivatives of polarized radiation and the solution of inverse atmosphere optic problems”, Russ. J. Numer. Anal. Math. Modelling, 17:3 (2002), 283–303 | MR | Zbl