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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2012, Volume 15, Number 1, Pages 83–100 (Mi sjvm460)  
This article is cited in 25 scientific papers (total in 25 papers)

A posteriori accuracy estimations of solutions of ill-posed inverse problems and extra-optimal regularizing algorithms for their solution

A. S. Leonov

Moscow Engineering Physics Institute (State University), Moscow
Full-text PDF (1195 kB) Citations (25)
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Abstract: A new scheme of a posteriori accuracy estimation for approximate solutions of ill-posed inverse problems is presented along with an algorithm of calculating this estimation. A new notion of extra-optimal regularizing algorithm is introduced as a method for solving ill-posed inverse problems having optimal in order a posteriori accuracy estimation. Sufficient conditions of extra-optimality are formulated and an example of extra-optimal regularizing algorithm is given. The developed theory is illustrated by numerical experiments.
Key words: ill-posed problems, regularizing algorithms, a posteriori accuracy estimation, extra-optimal algorithm.
Received: 15.02.2011
English version:
Numerical Analysis and Applications, 2012, Volume 5, Issue 1, Pages 68–83
DOI: https://doi.org/10.1134/S1995423912010077
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: A. S. Leonov, “A posteriori accuracy estimations of solutions of ill-posed inverse problems and extra-optimal regularizing algorithms for their solution”, Sib. Zh. Vychisl. Mat., 15:1 (2012), 83–100; Num. Anal. Appl., 5:1 (2012), 68–83
Citation in format AMSBIB
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\paper A posteriori accuracy estimations of solutions of ill-posed inverse problems and extra-optimal regularizing algorithms for their solution
\jour Sib. Zh. Vychisl. Mat.
\yr 2012
\vol 15
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\pages 83--100
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\elib{https://elibrary.ru/item.asp?id=17979185}
\transl
\jour Num. Anal. Appl.
\yr 2012
\vol 5
\issue 1
\pages 68--83
\crossref{https://doi.org/10.1134/S1995423912010077}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84857860648}
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    • This publication is cited in the following 25 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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