Construction and optimization of numerically-statistical projection algorithms for solving integral equations
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Anna S. Korda
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Sergey V. Rogasinsky
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.
Funding statement: The work was supported by the State Task of ICM&MG SB RAS No. 0251–2021–0002.
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Glacier parameterization in SLAV numerical weather prediction model
- Optimal disturbances for periodic solutions of time-delay differential equations
- Construction and optimization of numerically-statistical projection algorithms for solving integral equations
- Linear regularized finite difference scheme for the quasilinear subdiffusion equation
- On the efficiency of using correlative randomized algorithms for solving problems of gamma radiation transfer in stochastic medium
- Error identities for the reaction–convection–diffusion problem and applications to a posteriori error control
Artikel in diesem Heft
- Frontmatter
- Glacier parameterization in SLAV numerical weather prediction model
- Optimal disturbances for periodic solutions of time-delay differential equations
- Construction and optimization of numerically-statistical projection algorithms for solving integral equations
- Linear regularized finite difference scheme for the quasilinear subdiffusion equation
- On the efficiency of using correlative randomized algorithms for solving problems of gamma radiation transfer in stochastic medium
- Error identities for the reaction–convection–diffusion problem and applications to a posteriori error control
