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Mat. Zametki, 1968, Volume 3, Issue 4, Pages 421–426 (Mi mz6697)  

On a continuous analog of the gradient method

E. I. Lin'kov

Moscow Region Pedagogical Institute named after N. K. Krupskaya

Abstract: In a real Hilbert space $H$ we consider the nonlinear operator equation $P(x)=0$ and the continuous gradient method
\begin{equation} x'(t)=-P'(x)*P(x),\qquad x(0)=x_0. \tag{*} \end{equation}
Two theorems on the convergence of the process (*) to the solution of the equation $P(x)=0$ are proved.

Full text: PDF file (389 kB)

English version:
Mathematical Notes, 1968, 3:4, 267–271

Bibliographic databases:

UDC: 513.88
Received: 22.12.1966

Citation: E. I. Lin'kov, “On a continuous analog of the gradient method”, Mat. Zametki, 3:4 (1968), 421–426; Math. Notes, 3:4 (1968), 267–271

Citation in format AMSBIB
\Bibitem{Lin68}
\by E.~I.~Lin'kov
\paper On a~continuous analog of the gradient method
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 4
\pages 421--426
\mathnet{http://mi.mathnet.ru/mz6697}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=232251}
\zmath{https://zbmath.org/?q=an:0169.47601}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 4
\pages 267--271
\crossref{https://doi.org/10.1007/BF01159943}


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