Stochastic Overrelaxation Algorithms and Critical Slowing Down

Abstract

Recently overtaxation methods, used to speed up convergence of matrix inversion algorithms, have been generalized to stochastic processes and resulted in faster decorrelations. We discuss this stochastic overtaxation in a field theoretical formulation based on a Langevin equation. Reversible mode coupling is shown to cause reduction of the dynamical critical exponent from z = 2 to z = 1 for a free field theory. Numerical results indicate that this conclusion also holds for certain interacting models. This suggests that stochastic overtaxation algorithms might have their own dynamical universality class.