Geodesic
On a~continuous analog of the gradient method
Matematičeskie zametki, Tome 3 (1968) no. 4, pp. 421-426

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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. 
@article{MZM_1968_3_4_a6,
     author = {E. I. Lin'kov},
     title = {On a~continuous analog of the gradient method},
     journal = {Matemati\v{c}eskie zametki},
     pages = {421--426},
     publisher = {mathdoc},
     volume = {3},
     number = {4},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_4_a6/}
}
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E. I. Lin'kov. On a~continuous analog of the gradient method. Matematičeskie zametki, Tome 3 (1968) no. 4, pp. 421-426. http://geodesic.mathdoc.fr/item/MZM_1968_3_4_a6/