  Several research groups have recently reported {\em ab initio} calculations
of the melting properties of metals based on density functional theory, but
there have been unexpectedly large disagreements between results obtained by
different approaches. We analyze the relations between the two main approaches,
based on calculation of the free energies of solid and liquid and on direct
simulation of the two coexisting phases. Although both approaches rely on the
use of classical reference systems consisting of parameterized empirical
interaction models, we point out that in the free energy approach the final
results are independent of the reference system, whereas in the current form of
the coexistence approach they depend on it. We present a scheme for correcting
the predictions of the coexistence approach for differences between the
reference and {\em ab initio} systems. To illustrate the practical operation of
the scheme, we present calculations of the high-pressure melting properties of
iron using the corrected coexistence approach, which agree closely with earlier
results from the free energy approach. A quantitative assessment is also given
of finite-size errors, which we show can be reduced to a negligible size.
