Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2022, Volume 506, Pages 41–44
DOI: https://doi.org/10.31857/S2686954322050095 (Mi danma295) 		 
MATHEMATICS

On the equivalence of singular and ill-posed problems: The $p$-factor regularization method

Yu. G. Evtushenkoab, E. Bednarczukc, A. Prusińskad, A. A. Tret'yakovadc

a Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow, Russia
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region, Russia
c System Res. Inst., Polish Acad. Sciences, Warsaw, Poland
d Siedlce University, Faculty of Sciences, Siedlce, Poland
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DOI: https://doi.org/10.31857/S2686954322050095
Abstract: The local equivalence of singular and ill-posed problems in a class of sufficiently smooth mappings is shown, which justifies the use of the $p$-factor regularization method to solve them. The main constructions in $p$-regularity theory that are necessary for stable solution of approximate problems are described, and estimation theorems for regularizing algorithms are proved.
Keywords: singular, ill-posed, $p$-regular, factor method.
Funding agency Grant number
Russian Science Foundation 21-71-30005
Ministry of Science and Higher Education, Poland 165/0015
This work was supported by the Russian Science Foundation (project no. 21-71-30005) and by the scientific theme no. 165/0015 of the Ministry of Education and Science of Poland.
Received: 25.05.2022
Revised: 18.08.2022
Accepted: 20.08.2022
English version:
Doklady Mathematics, 2022, Volume 106, Issue 2, Pages 336–339
DOI: https://doi.org/10.1134/S1064562422050118
Bibliographic databases:
Document Type: Article
UDC: 519.615
Language: Russian
Citation: Yu. G. Evtushenko, E. Bednarczuk, A. Prusińska, A. A. Tret'yakov, “On the equivalence of singular and ill-posed problems: The $p$-factor regularization method”, Dokl. RAN. Math. Inf. Proc. Upr., 506 (2022), 41–44; Dokl. Math., 106:2 (2022), 336–339
Citation in format AMSBIB
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\by Yu.~G.~Evtushenko, E.~Bednarczuk, A.~Prusi{\'n}ska, A.~A.~Tret'yakov
\paper On the equivalence of singular and ill-posed problems: The $p$-factor regularization method
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2022
\vol 506
\pages 41--44
\mathnet{http://mi.mathnet.ru/danma295}
\crossref{https://doi.org/10.31857/S2686954322050095}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4531981}
\elib{https://elibrary.ru/item.asp?id=49787599}
\transl
\jour Dokl. Math.
\yr 2022
\vol 106
\issue 2
\pages 336--339
\crossref{https://doi.org/10.1134/S1064562422050118}
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