  The best quadratic approximation to the retarded polaron action due to
Adamowski {\it et al.} and Saitoh is investigated numerically for a wide range
of coupling constants. The non-linear variational equations are solved
iteratively with an efficient method in order to obtain the ground state energy
and the effective mass of the polaron. The virial theorem and expansions for
small and large couplings are used to check the high accuracy of the numerical
results. Only small improvements over Feynman's (non-optimal) results are
observed. For a moving polaron it is shown that the most general quadratic
trial action may contain anisotropic terms which, however, do not lead to
improvements for the ground state energy and effective mass.
