On a continuous analog of the gradient method

In a real Hilbert space H we consider the nonlinear operator equation P(x)=0 and the continuous gradient methodx (t)= –P (x)^* P (x), x (0) = x₀. Two theorems on the convergence of the process (*) to the solution of the equation P(x)=0 are proved.Translated from Matematicheskie Zametki, Vol. 3, No. 4, pp. 421–426, April, 1968.