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

Результат исследования: Научные публикации в периодических изданияхстатьярецензирование

Аннотация

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.

Язык оригиналаанглийский
Страницы (с-по)213-219
Число страниц7
ЖурналRussian Journal of Numerical Analysis and Mathematical Modelling
Том37
Номер выпуска4
DOI
СостояниеОпубликовано - 1 авг. 2022

Предметные области OECD FOS+WOS

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