  In this paper, we study the proximal gradient algorithm with extrapolation
for minimizing the sum of a Lipschitz differentiable function and a proper
closed convex function. Under the error bound condition used in [19] for
analyzing the convergence of the proximal gradient algorithm, we show that
there exists a threshold such that if the extrapolation coefficients are chosen
below this threshold, then the sequence generated converges $R$-linearly to a
stationary point of the problem. Moreover, the corresponding sequence of
objective values is also $R$-linearly convergent. In addition, the threshold
reduces to $1$ for convex problems and, as a consequence, we obtain the
$R$-linear convergence of the sequence generated by FISTA with fixed restart.
Finally, we present some numerical experiments to illustrate our results.
