  We develop numerical algorithms for solving the Einstein equation on
Calabi-Yau manifolds at arbitrary values of their complex structure and Kahler
parameters. We show that Kahler geometry can be exploited for significant gains
in computational efficiency. As a proof of principle, we apply our methods to a
one-parameter family of K3 surfaces constructed as blow-ups of the T^4/Z_2
orbifold with many discrete symmetries. High-resolution metrics may be obtained
on a time scale of days using a desktop computer. We compute various geometric
and spectral quantities from our numerical metrics. Using similar resources we
expect our methods to practically extend to Calabi-Yau three-folds with a high
degree of discrete symmetry, although we expect the general three-fold to
remain a challenge due to memory requirements.
