  In this paper, we study the convergence rate of the gradient (or steepest
descent) method with fixed step lengths for finding a stationary point of an
$L$-smooth function. We establish a new convergence rate, and show that the
bound may be exact in some cases, in particular when all step lengths lie in
the interval $(0,1/L]$. In addition, we derive an optimal step length with
respect to the new bound.
