Research output: Contribution to journal › Article › peer-review
Construction of Effective Randomized Projective Estimates for Solutions of Integral Equations Based on Legendre Polynomials. / Mikhailov, G. A.; Korda, A. S.; Rogasinsky, S. V.
In: Doklady Mathematics, Vol. 106, No. 3, 2022, p. 475-478.Research output: Contribution to journal › Article › peer-review
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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 -
ID: 55695292