  We have implemented the $GW$+dynamical mean field theory (DMFT) approach in
the Vienna ab initio simulation package. Employing the interaction values
obtained from the locally unscreened random phase approximation (RPA), we
compare $GW$+DMFT and LDA+DMFT against each other and against experiment for
SrVO$_3$. We observed a partial compensation of stronger electronic
correlations due to the reduced $GW$ bandwidth and weaker correlations due to a
larger screening of the RPA interaction, so that the obtained spectra are quite
similar and well agree with experiment. Noteworthily, the $GW$+DMFT better
reproduces the position of the lower Hubbard side band.
