  We present a new method, ePT, for extrapolating few known coefficients of a
perturbative expansion. Controlled by comparisons with numerically exact
quantum Monte Carlo (QMC) results, 10th order strong-coupling perturbation
theory (PT) for the Hubbard model on the Bethe lattice is reliably extrapolated
to infinite order. Within dynamical mean-field theory (DMFT), we obtain
continuous estimates of energy E and double occupancy D with unprecedented
precision O(10^{-5}) for the Mott insulator above its stability edge
U_{c1}=4.78 as well as critical exponents. In addition, we derive corresponding
precise estimates for E and D in the metallic ground state from extensive
low-temperature QMC simulations using a fit to weak-coupling PT while enforcing
thermodynamic consistency.
