  In this paper, we develop rapidly convergent forward-backward algorithms for
computing zeroes of the sum of finitely many maximally monotone operators. A
modification of the classical forward-backward method for two general operators
is first considered, by incorporating an inertial term (closed to the
acceleration techniques introduced by Nesterov), a constant relaxation factor
and a correction term. In a Hilbert space setting, we prove the weak
convergence to equilibria of the iterates $(x_n)$, with worst-case rates of $
o(n^{-2})$ in terms of both the discrete velocity and the fixed point residual,
instead of the classical rates of ${\cal O}(n^{-1})$ established so far for
related algorithms. Our procedure is then adapted to more general monotone
inclusions and a fast primal-dual algorithm is proposed for solving
convex-concave saddle point problems.
