A family of linear optimal methods for reconstructing the solution of the Dirichlet problem on a hyperplane from information about its approximate measurements on a finite number of other hyperplanes is constructed. In this case, optimal methods do not use all the available information, but only information about the measurements of the solution on at most two planes.
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This work was supported by the Russian Foundation for Basic Research, grant no. 17-01-00649-a.
Translated by E. Chernokozhin
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Abramova, E.V., Magaril-Il’yaev, G.G. & Sivkova, E.O. Best Recovery of the Solution of the Dirichlet Problem in a Half-Space from Inaccurate Data. Comput. Math. and Math. Phys. 60, 1656–1665 (2020). https://doi.org/10.1134/S0965542520100036
- Dirichlet problem
- optimal recovery
- extremal problem