  A novel method for nonperturbative renormalization of lattice operators is
introduced, which lends itself to the calculation of renormalization factors
for nonsinglet as well as singlet operators. The method is based on the
Feynman-Hellmann relation, and involves computing two-point correlators in the
presence of generalized background fields arising from introducing additional
operators into the action. As a first application, and test of the method, we
compute the renormalization factors of the axial vector current $A_\mu$ and the
scalar density $S$ for both nonsinglet and singlet operators for $N_f=3$
flavors of SLiNC fermions. For nonsinglet operators, where a meaningful
comparison is possible, perfect agreement with recent calculations using
standard three-point function techniques is found.
