  We present an iterative method to reconstruct the linear-theory initial
conditions from the late-time cosmological matter density field, with the
intent of improving the recovery of the cosmic distance scale from the baryon
acoustic oscillations (BAOs). We present tests using the dark matter density
field in both real and redshift space generated from an $N$-body simulation. In
redshift space at $z = 0.5$, we find that the reconstructed displacement field
using our iterative method are more than 80\% correlated with the true
displacement field of the dark matter particles on scales $k < 0.10h\ {\rm
Mpc}^{-1}$. Furthermore, we show that the two-point correlation function of our
reconstructed density field matches that of the initial density field
substantially better, especially on small scales ($< 40h^{-1}\ {\rm Mpc}$). Our
redshift-space results are improved if we use an anisotropic smoothing so as to
account for the reduced small-scale information along the line of sight in
redshift space.
