Asymptotic behaviour of the $s$-dimensional optimal gradient method in Hilbert space

The asymptotic behaviour of the well-known method of minimizing the functional $H(x)$, namely the $s$-dimensional, $s > 1$, optimal gradient method in Hilbert space $H$, is investigated. It is found that the results of the usual, $s = 1$, optimal gradient method, given in [1], transfer to the $s$-dimensional process.