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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 5, Pages 59–72 (Mi izv41)  

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

A generalization of the method of least squares for operator equations in some Frechet spaces

D. N. Zarnadze

Muskhelishvili Institute of Computational Mathematics

Abstract: The classical method of least squares is extended to equations with an operator between Frechet spaces. Approximate solutions are obtained by minimizing the discrepancy relative to a metric, which in the Hilbert space case coincides with the metric induced by the scalar product. The convergence of a sequence of approximate solutions to the exact solution is proved. A concrete realization of the results obtained is given in the case of continuously invertible and so-called tamely invertible operators that map Frechet spaces of power series of finite and infinite type, Frechet spaces of rapidly decreasing sequences and the Frechet spaces of analytic functions given in Stein's monograph to themselves.

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English version:
Izvestiya: Mathematics, 1995, 59:5, 935–948

Bibliographic databases:

MSC: 46A06, 41A35
Received: 25.07.1994

Citation: D. N. Zarnadze, “A generalization of the method of least squares for operator equations in some Frechet spaces”, Izv. RAN. Ser. Mat., 59:5 (1995), 59–72; Izv. Math., 59:5 (1995), 935–948

Citation in format AMSBIB
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\paper A~generalization of the method of least squares for operator equations in some Frechet spaces
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 5
\pages 59--72
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1360634}
\zmath{https://zbmath.org/?q=an:0880.46001}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 5
\pages 935--948
\crossref{https://doi.org/10.1070/IM1995v059n05ABEH000041}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995UH54100004}


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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. Aytuna A., “Tameness in Fréchet spaces of analytic functions”, Studia Math., 232:3 (2016), 243–266  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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