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Izv. Vyssh. Uchebn. Zaved. Mat., 2009, Number 2, Pages 3–24 (Mi ivm1257)  

This article is cited in 1 scientific paper (total in 2 paper)

Iterative processes of the Fejér type in ill-posed problems with a prori information

V. V. Vasin

Ural State University

Abstract: In the latter thirty years, the solution of ill-posed problems with a priori information formed a separate field of research in the theory of ill-posed problems. We mean the class of problems, where along with the basic equation one has some additional data on the desired solution. Namely, one states some relations and constraints which contain important information on the object under consideration. As a rule, taking into account these data in a solution algorithm, one can essentially increase its accuracy for solving ill-posed (unstable) problems. It is especially important in the solution of applied problems in the case when a solution is not unique, because this approach allows one to choose a solution that meets the reality. In this paper we survey the methods for solving such problems. We briefly describe all relevant approaches (known to us), but we pay the main attention to the method proposed by us. This technique is based on the application of iterative processes of the Fejér type which admit a flexible and effective realization for a wide class of a priori constraints.

Keywords: ill-posed problem, Fejér mapping, a priori information, iterative process, pseudo-contractive operator, regularizing algorithm.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2009, 53:2, 1–20

Bibliographic databases:

UDC: 517.983.54+517.988.68
Received: 23.06.2008

Citation: V. V. Vasin, “Iterative processes of the Fejér type in ill-posed problems with a prori information”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 2, 3–24; Russian Math. (Iz. VUZ), 53:2 (2009), 1–20

Citation in format AMSBIB
\Bibitem{Vas09}
\by V.~V.~Vasin
\paper Iterative processes of the Fej\'er type in ill-posed problems with a~prori information
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2009
\issue 2
\pages 3--24
\mathnet{http://mi.mathnet.ru/ivm1257}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2530592}
\zmath{https://zbmath.org/?q=an:1186.47051}
\elib{https://elibrary.ru/item.asp?id=11668274}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2009
\vol 53
\issue 2
\pages 1--20
\crossref{https://doi.org/10.3103/S1066369X09020017}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Tang Limin, “A Regularization Homotopy Iterative Method for Ill-Posed Nonlinear Least Squares Problem and its Application”, Advances in Civil Engineering, Pts 1-4, Applied Mechanics and Materials, 90-93, ed. Zhou X., Trans Tech Publications Ltd, 2011, 3268–3273  crossref  adsnasa  isi  scopus
    2. “Vladimir Vasil'evich Vasin. On the occasion of his 70th birsday”, Proc. Steklov Inst. Math. (Suppl.), 280, suppl. 1 (2013), 1–12  mathnet  crossref  isi
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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