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Russian Academy of Sciences. Sbornik. Mathematics, 1995, Volume 80, Issue 2, Pages 467–495
DOI: https://doi.org/10.1070/SM1995v080n02ABEH003534 (Mi sm1033) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Asymptotic behavior of the $s$-step method of steepest descent for eigenvalue problems in Hilbert space

P. Ph. Zhuk
English version PDF (1353 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM1995v080n02ABEH003534
Abstract: On the example of the Rayleigh functional a new approach is developed to the study of the asymptotic behavior of the $s$-step method, based on the proof of the existence of limit iteration parameters of the method in even (odd) iterations. This approach may be used to analyze the asymptotic behavior of the $s$-step method in the optimization of arbitrary sufficiently smooth functionals defined on a Hilbert space.
Received: 10.06.1992
Russian version:
Matematicheskii Sbornik, 1993, Volume 184, Number 12, Pages 87–122
Bibliographic databases:
UDC: 519.61
MSC: Primary 49M10; Secondary 41A60, 49R10
Language: English
Original paper language: Russian
Citation: P. P. Zhuk, “Asymptotic behavior of the $s$-step method of steepest descent for eigenvalue problems in Hilbert space”, Mat. Sb., 184:12 (1993), 87–122; Russian Acad. Sci. Sb. Math., 80:2 (1995), 467–495
Citation in format AMSBIB
\Bibitem{Zhu93}
\by P.~P.~Zhuk
\paper Asymptotic behavior of the~$s$-step method of steepest descent for eigenvalue problems in Hilbert space
\jour Mat. Sb.
\yr 1993
\vol 184
\issue 12
\pages 87--122
\mathnet{http://mi.mathnet.ru/sm1033}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1254806}
\zmath{https://zbmath.org/?q=an:0830.49021}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 80
\issue 2
\pages 467--495
\crossref{https://doi.org/10.1070/SM1995v080n02ABEH003534}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995QR47400011}
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  • https://doi.org/10.1070/SM1995v080n02ABEH003534
  • https://www.mathnet.ru/eng/sm/v184/i12/p87
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник - 1992–2005 Sbornik: Mathematics
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    Abstract page:365
    Russian version PDF:89
    English version PDF:10
    References:68
    First page:1
     
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