  We identify a set of "energy" functionals on the space of metrics in a given
Kaehler class on a Calabi-Yau manifold, which are bounded below and minimized
uniquely on the Ricci-flat metric in that class. Using these functionals, we
recast the problem of numerically solving the Einstein equation as an
optimization problem. We apply this strategy, using the "algebraic" metrics
(metrics for which the Kaehler potential is given in terms of a polynomial in
the projective coordinates), to the Fermat quartic and to a one-parameter
family of quintics that includes the Fermat and conifold quintics. We show that
this method yields approximations to the Ricci-flat metric that are
exponentially accurate in the degree of the polynomial (except at the conifold
point, where the convergence is polynomial), and therefore orders of magnitude
more accurate than the balanced metrics, previously studied as approximations
to the Ricci-flat metric. The method is relatively fast and easy to implement.
On the theoretical side, we also show that the functionals can be used to give
a heuristic proof of Yau's theorem.
