  We consider Adaptively Restrained Langevin dynamics, in which the kinetic
energy function vanishes for small velocities. Properly parameterized, this
dynamics makes it possible to reduce the computational complexity of updating
inter-particle forces, and to accelerate the computation of ergodic averages of
molecular simulations. In this paper, we analyze the influence of the method
parameters on the total achievable speed-up. In particular, we estimate both
the algorithmic speed-up, resulting from incremental force updates, and the
influence of the change of the dynamics on the asymptotic variance. This allows
us to propose a practical strategy for the parametrization of the method. We
validate these theoretical results by representative numerical experiments.
