  This note considers the momentum method by Polyak and the accelerated
gradient method by Nesterov, both without line search but with fixed step
length applied to strictly convex quadratic functions assuming that exact
gradients are used and appropriate upper and lower bounds for the extreme
eigenvalues of the Hessian matrix are known. Simple 2-d-examples show that the
Euclidean distance of the iterates to the optimal solution is non-monotone. In
this context an explicit bound is derived on the number of iterations needed to
guarantee a reduction of the Euclidean distance to the optimal solution by a
factor $\varepsilon$. For both methods the bound is optimal up to a constant
factor, it complements earlier asymptotically optimal results for the momentum
method, and it establishes another link of the momentum method and Nesterov's
accelerated gradient method.
