  The Dynamical Mean-Field theory (DMFT) approach to the Hubbard model requires
a method to solve the problem of a quantum impurity in a bath of
non-interacting electrons. Iterated Perturbation Theory (IPT) has proven its
effectiveness as a solver in many cases of interest. Based on general
principles and on comparisons with an essentially exact Continuous-Time Quantum
Monte Carlo (CTQMC) solver, here we show that the standard implementation of
IPT fails away from half-filling when the interaction strength is much larger
than the bandwidth. We propose a slight modification to the IPT algorithm that
replaces one of the equations by the requirement that double occupancy
calculated with IPT gives the correct value. We call this method IPT-$D$. We
recover the Fermi liquid ground state away from half-filling. The Fermi liquid
parameters, density of states, chemical potential, energy and specific heat on
the FCC lattice are calculated with both IPT-$D$ and CTQMC as benchmark
examples. We also calculated the resistivity and the optical conductivity
within IPT-$D$. Particle-hole asymmetry persists even at coupling twice the
bandwidth. Several algorithms that speed up the calculations are described in
appendices.
