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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 507, Pages 81–85
DOI: https://doi.org/10.31857/S2686954322700059 (Mi danma323) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Construction of effective randomized projective estimates for solutions of integral equations based on Legendre polynomials

G. A. Mikhailovab, A. S. Kordaa, S. V. Rogazinskiiab

a Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University
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DOI: https://doi.org/10.31857/S2686954322700059
Abstract: Numerical-statistical projective estimates for solutions of integral equations are constructed and optimized using Legendre polynomials as motivated by the computational complexity of orthogonal expansions with an adapted weight. By applying analytical and corresponding numerical computations, the mean-square error is minimized as a function of the length of the projection expansion segment, while the sample size for the expansion coefficients is fixed. The proposed technique is successfully verified in a test problem close to the Milne one and is found to be more effective than the regularized expansion in terms of Laguerre polynomials.
Keywords: Monte Carlo method, projective estimate, mean-square error, collision estimator, direct simulation, Legendre polynomials, Henyey–Greenstein, phase function.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 0251-2021-0002
This work was performed at the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences within state assignment no. 0251-2021-0002.
Received: 02.06.2022
Revised: 08.09.2022
Accepted: 21.11.2022
English version:
Doklady Mathematics, 2022, Volume 106, Issue 3, Pages 475–478
DOI: https://doi.org/10.1134/S1064562422700156
Bibliographic databases:
Document Type: Article
UDC: 519.642
Language: Russian
Citation: G. A. Mikhailov, A. S. Korda, S. V. Rogazinskii, “Construction of effective randomized projective estimates for solutions of integral equations based on Legendre polynomials”, Dokl. RAN. Math. Inf. Proc. Upr., 507 (2022), 81–85; Dokl. Math., 106:3 (2022), 475–478
Citation in format AMSBIB
\Bibitem{MikChiRog22}
\by G.~A.~Mikhailov, A.~S.~Korda, S.~V.~Rogazinskii
\paper Construction of effective randomized projective estimates for solutions of integral equations based on Legendre polynomials
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 507
\pages 81--85
\mathnet{http://mi.mathnet.ru/danma323}
\crossref{https://doi.org/10.31857/S2686954322700059}
\elib{https://elibrary.ru/item.asp?id=49991289}
\transl
\jour Dokl. Math.
\yr 2022
\vol 106
\issue 3
\pages 475--478
\crossref{https://doi.org/10.1134/S1064562422700156}
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