  We compute the gravitational self-force (or ``radiation reaction'' force)
acting on a particle falling radially into a Schwarzschild black hole. Our
calculation is based on the ``mode-sum'' method, in which one first calculates
the individual $\ell$-multipole contributions to the self-force (by numerically
integrating the decoupled perturbation equations) and then regularizes the sum
over modes by applying a certain analytic procedure. We demonstrate the
equivalence of this method with the $\zeta-$function scheme. The convergence
rate of the mode-sum series is considerably improved here (thus notably
reducing computational requirements) by employing an analytic approximation at
large $\ell$.
