## 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.

Original language | English |
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Pages (from-to) | 213-219 |

Number of pages | 7 |

Journal | Russian Journal of Numerical Analysis and Mathematical Modelling |

Volume | 37 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Aug 2022 |

## Keywords

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

## OECD FOS+WOS

- 1.01 MATHEMATICS