Construction and optimization of numerically-statistical projection algorithms for solving integral equations

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Construction and optimization of numerically-statistical projection algorithms for solving integral equations. / Korda, Anna S.; Mikhailov, Gennady A.; Rogasinsky, Sergey V.

в: Russian Journal of Numerical Analysis and Mathematical Modelling, Том 37, № 4, 01.08.2022, стр. 213-219.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{ef5eb6d45ca244c3ac0f45fd478c0f1b,

title = "Construction and optimization of numerically-statistical projection algorithms for solving integral equations",

abstract = "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.",

keywords = "direct simulation, estimation over collisions, Henyey-Greenstein indicatrix, Laguerre polynomials, Monte Carlo method, projection estimator, root-mean-square error",

author = "Korda, {Anna S.} and Mikhailov, {Gennady A.} and Rogasinsky, {Sergey V.}",

note = "Publisher Copyright: {\textcopyright} 2022 Walter de Gruyter GmbH, Berlin/Boston.",

year = "2022",

month = aug,

day = "1",

doi = "10.1515/rnam-2022-0018",

language = "English",

volume = "37",

pages = "213--219",

journal = "Russian Journal of Numerical Analysis and Mathematical Modelling",

issn = "0927-6467",

publisher = "Walter de Gruyter GmbH",

number = "4",

}

RIS

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.

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 -

ID: 38058636