TY - JOUR

T1 - Construction of Effective Randomized Projective Estimates for Solutions of Integral Equations Based on Legendre Polynomials

AU - Mikhailov, G. A.

AU - Korda, A. S.

AU - Rogasinsky, S. V.

N1 - Публикация для корректировки.

PY - 2022

Y1 - 2022

N2 - Numerical-statistical projective estimates for solutions of integral equations are constructed and optimized using Legendre polynomials as motivated by the computational complexity of orthogonal expansions with an adapted weight. By applying analytical and corresponding numerical computations, the mean-square error is minimized as a function of the length of the projection expansion segment, while the sample size for the expansion coefficients is fixed. The proposed technique is successfully verified in a test problem close to the Milne one and is found to be more effective than the regularized expansion in terms of Laguerre polynomials.

AB - Numerical-statistical projective estimates for solutions of integral equations are constructed and optimized using Legendre polynomials as motivated by the computational complexity of orthogonal expansions with an adapted weight. By applying analytical and corresponding numerical computations, the mean-square error is minimized as a function of the length of the projection expansion segment, while the sample size for the expansion coefficients is fixed. The proposed technique is successfully verified in a test problem close to the Milne one and is found to be more effective than the regularized expansion in terms of Laguerre polynomials.

KW - Henyey–Greenstein phase function

KW - Legendre polynomials

KW - Monte Carlo method

KW - collision estimator

KW - direct simulation

KW - mean-square error

KW - projective estimate

UR - https://www.mendeley.com/catalogue/ccafd883-dc03-3020-bcf8-d308bf4f25f5/

U2 - 10.1134/S1064562422700156

DO - 10.1134/S1064562422700156

M3 - Article

VL - 106

SP - 475

EP - 478

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 3

ER -