Over-relaxation methods for Monte Carlo simulations of quadratic and multiquadratic actions

A generalization of the heat-bath algorithm for quadratic and multiquadratic actions allows a Monte Carlo system to over-relax. We present numerical studies of this generalized algorithm on small lattices, which indicate that an over-relaxed Monte Carlo algorithm has advantages over a heat-bath algorithm. The large reduction in computation time for certain operators is similar to that obtained by using over-relaxation in the numerical solution of partial differential equations. Possible applications of this over-relaxed Monte Carlo algorithm to noncompact QCD, lattice fermion calculations, and Higgs theories are discussed.