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This article is cited in 10 scientific papers (total in 10 papers)
Optimal recovery of semi-group operators from inaccurate data
G. G. Magaril-Il'yaevab, E. O. Sivkovacd a Institute for Information Transmission Problems,
Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, str. 1,
Moscow, 127051 Russia
b Southern Mathematical Institute — the Affiliate of the Vladikavkaz
Scientific Centre of the Russian Academy of Sciences, ul. Vatutina 53,
Vladikavkaz, 362025 Russia
c Faculty of Mechanics and Mathematics, Moscow State University,
Moscow, 119991 Russia
d Moscow Pedagogical State University (MPGU),
1/1 M. Pirogovskaya St, Moscow, 119991 Russia
Abstract:
The problem of optimal recovery of the operator at a given value of the parameter from inaccurate information about the other parameters is solved for a special one-parameter semi-group of operators. A family of optimal recovery methods is constructed. As a corollary, we obtain families of optimal recovery methods in the problem of recovery of a solution of the heat equation on the line and in the problem of recovery of a solution to the Dirichlet problem for the half-plane.
Keywords and phrases:
semi-group of operators, optimal recovery, extremal problem, Fourier transform.
Received: 01.03.2019
Citation:
G. G. Magaril-Il'yaev, E. O. Sivkova, “Optimal recovery of semi-group operators from inaccurate data”, Eurasian Math. J., 10:4 (2019), 75–84
Linking options:
https://www.mathnet.ru/eng/emj349 https://www.mathnet.ru/eng/emj/v10/i4/p75
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Abstract page: | 231 | Full-text PDF : | 86 | References: | 20 |
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