求解积分方程的数值统计投影算法的构建与优化

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Russian Journal of Numerical Analysis and Mathematical Modelling Pub Date : 2022-08-01 DOI:10.1515/rnam-2022-0018

A. S. Korda, G. A. Mikhailov, S. V. Rogasinsky

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引用次数: 0

摘要

摘要:研究了一类积分方程解的数值-统计投影估计的均方根误差最小化问题。结果表明，当所利用的分解余数的范数与其长度成反比减小时，可以通过平衡误差的确定性和随机分量来获得这种意义上的最优估计量。作为检验，用拉盖尔多项式求解了半无限层物质中辐射传递的米尔恩问题。为了在有限层的情况下解决这一问题，使用了一种特殊的正则化投影算法。

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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.

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来源期刊

Russian Journal of Numerical Analysis and Mathematical Modelling 数学-工程：综合

CiteScore

1.40

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： The Russian Journal of Numerical Analysis and Mathematical Modelling, published bimonthly, provides English translations of selected new original Russian papers on the theoretical aspects of numerical analysis and the application of mathematical methods to simulation and modelling. The editorial board, consisting of the most prominent Russian scientists in numerical analysis and mathematical modelling, selects papers on the basis of their high scientific standard, innovative approach and topical interest. Topics: -numerical analysis- numerical linear algebra- finite element methods for PDEs- iterative methods- Monte-Carlo methods- mathematical modelling and numerical simulation in geophysical hydrodynamics, immunology and medicine, fluid mechanics and electrodynamics, geosciences.