Due to the retarded nature of the phonon-mediated electron-electron interac
tion, neither fast Fourier transform (FFT) nor previously developed NRG met
hods for Hubbard-type purely electronic models are applicable, while brute-
force solutions are limited by the demands on computational time and storag
e which increase rapidly at low temperature T. A new numerical renormalizat
ion group (NRG) approach to the solution of self-consistent-field equations
for correlated lattice electrons is illustrated for the two-dimensional Hu
bbard-type model. This approach allows us to handle the fermion frequency m
atrix inversions in the FLEX equations efficiently. Several orders of magni
tude of CPU time and storage can be saved at the temperature scales relevan
t to electronic phase transitions.