  We consider procedures through which an ultraviolet cut-off regularization
scheme can be modified to reproduce the same results for nonperturbative
renormalized Green's functions as obtained from a dimensional regularization
scheme. These issues are considered within the Dyson-Schwinger equation
framework, where ultraviolet cut-off regularization can lead to explicit
violations of gauge invariance. As a specific illustration, we consider the
electron self-energy in quenched QED_4 in both schemes and establish those
procedures for which the UV cut-off scheme can be expected to lead to the
dimensional regularization results. We also compare results from precise
numerical studies using the two types of regularization.
