Construction and optimization of numerically-statistical projection algorithms for solving integral equations-Reference-Cited by-同舟云学术

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

Published:2022-08-01 Issue:4 Volume:37 Page:213-219
ISSN:0927-6467
Container-title:Russian Journal of Numerical Analysis and Mathematical Modelling
language:en
Short-container-title:

Author:

Korda Anna S.¹,Mikhailov Gennady A.¹²,Rogasinsky Sergey V.¹²

Affiliation:

1. Institute of Computational Mathematics and Mathematical Geophysics, SB RAS , Novosibirsk 630090 , Russia

2. Novosibirsk State University , Novosibirsk 630090 , Russia

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Modeling and Simulation,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/rnam-2022-0018/pdf

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