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.

UDC: 513.88

Received: 22.12.1966

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

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