  We present selected results for the Holstein molecular crystal model in one
space dimension as determined by the Global-Local variational method, including
complete polaron energy bands, ground state energies, and effective masses. We
juxtapose our results with specific comparable results of numerous other
methodologies of current interest, including quantum Monte Carlo, cluster
diagonalization, dynamical mean field theory, density matrix renormalization
group, semiclassical analysis, weak-coupling perturbation theory, and
strong-coupling perturbation theory. This comparison confirms the Global-Local
variational method as being highly accurate over a wide range of the polaron
parameter space, from the non-adiabatic limit to the extremes of high
adiabaticity, from weak coupling through intermediate coupling to strong
coupling.
