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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 7, Pages 1281–1288
DOI: https://doi.org/10.31857/S0044466920050105 (Mi zvmmf11110) 		 
Uniformly a posteriori error estimates for regularizing algorithms

M. M. Kokurin

Mari State University, Yoshkar-Ola, 424000 Russia
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DOI: https://doi.org/10.31857/S0044466920050105
Abstract: A modification for the definition of an a posteriori error estimate for a regularizing algorithm for solving an ill-posed problem is proposed. We introduce, analyze and illustrate by examples the concept of a uniformly a posteriori error estimate for a regularizing algorithm. A necessary and sufficient condition for the existence of a regularizing algorithm satisfying such an estimate is established. The class of conditionally well-posed problems is characterized in terms of regularizability with uniformly a posteriori error estimates.
Key words: ill-posed problem, regularizing algorithm, error estimate, a posteriori estimate, uniformly a posteriori estimate.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation 1.5420.2017/8.9
СП-5252.2018.5
This work was supported by the Ministry of Education and Science of the Russian Federation within state assignment (project no. 1.5420.2017/8.9) and by a grant from the Russian Federation President for young scientists and graduate students (project no. SP-5252.2018.5).
Received: 18.09.2019
Revised: 18.09.2019
Accepted: 10.03.2020
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 7, Pages 1240–1247
DOI: https://doi.org/10.1134/S0965542520050103
Bibliographic databases:
Document Type: Article
UDC: 517.988.8
Language: Russian
Citation: M. M. Kokurin, “Uniformly a posteriori error estimates for regularizing algorithms”, Zh. Vychisl. Mat. Mat. Fiz., 60:7 (2020), 1281–1288; Comput. Math. Math. Phys., 60:7 (2020), 1240–1247
Citation in format AMSBIB
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\vol 60
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