TY - JOUR
T1 - Construction and optimization of numerically-statistical projection algorithms for solving integral equations
AU - Korda, Anna S.
AU - Mikhailov, Gennady A.
AU - Rogasinsky, Sergey V.
N1 - Publisher Copyright:
© 2022 Walter de Gruyter GmbH, Berlin/Boston.
PY - 2022/8/1
Y1 - 2022/8/1
N2 - The problem of minimizing the root-mean-square error of the numerical-statistical projection estimation of the solution to an integral equation is solved. It is shown that the optimal estimator in this sense can be obtained by equalizing deterministic and stochastic components of the error in the case when the norm of the remainder of the utilized decomposition decreases inversely proportional to its length. As a test, the Milne problem of radiation transfer in a semi-infinite layer of matter is solved using Laguerre polynomials. To solve such a problem in the case of a finite layer, a special regularized projection algorithm is used.
AB - The problem of minimizing the root-mean-square error of the numerical-statistical projection estimation of the solution to an integral equation is solved. It is shown that the optimal estimator in this sense can be obtained by equalizing deterministic and stochastic components of the error in the case when the norm of the remainder of the utilized decomposition decreases inversely proportional to its length. As a test, the Milne problem of radiation transfer in a semi-infinite layer of matter is solved using Laguerre polynomials. To solve such a problem in the case of a finite layer, a special regularized projection algorithm is used.
KW - direct simulation
KW - estimation over collisions
KW - Henyey-Greenstein indicatrix
KW - Laguerre polynomials
KW - Monte Carlo method
KW - projection estimator
KW - root-mean-square error
UR - http://www.scopus.com/inward/record.url?scp=85137715442&partnerID=8YFLogxK
U2 - 10.1515/rnam-2022-0018
DO - 10.1515/rnam-2022-0018
M3 - Article
AN - SCOPUS:85137715442
VL - 37
SP - 213
EP - 219
JO - Russian Journal of Numerical Analysis and Mathematical Modelling
JF - Russian Journal of Numerical Analysis and Mathematical Modelling
SN - 0927-6467
IS - 4
ER -