  We introduce a new Monte Carlo method for pure gauge theories. It is not
intended for use with dynamical fermions. It belongs to the class of Local
Hybrid Monte Carlo (LHMC) algorithms, which make use of the locality of the
action by updating individual sites or links by following a classical mechanics
trajectory in fictitious time. We choose to update a one-parameter subgroup of
the gauge field on each link of the lattice, and the classical trajectory can
be found in closed form in terms of elliptic functions for this case. We show
that this gives an overrelaxation algorithm with a tunable parameter which,
unlike some previous methods, does not require the numerical integration of the
equations of motion.
