[en] I formulate a successive over-relaxation (SOR) procedure for the Monte Carlo evaluation of the Euclidean partition function for multiquadratic actions (such as the Yang-Mills action with canonical gauge fixing). A convergence analysis for the quadratic-action (Abelian) case shows that as thermalization proceeds the mean nodal fields relax according to the difference equation arising from the standard SOR analysis of the associated classical Euclidean field equation. Hence, SOR should accelerate the thermalization process, just as it accelerates convergence in the numerical solution of second-order elliptic differential equations