  A GW approximation (GWA) method named U+GWA is proposed, where we can start
GWA with more localized wave functions obtained by the local spin-density
approximation (LSDA)+U method. Then GWA and U+GWA are applied to MnO, NiO, and
V$_2$O$_3$ in antiferromagnetic phase. The band gaps and energy spectra show an
excellent agreement with the experimentally observed results and are discussed
in details. The calculated width of d-bands of V$_2$O$_3$ is much narrower than
that of the observed one which may be a mixture of t$_{2g}^2$ multiplet and
single electron t$_{2g}$ level. GWA or U+GWA does not work also in the
paramagnetic phase of V$_2$O$_3$ and the reason for thois is clarified. The
method of the unique choice of on-site Coulomb interaction is discussed in
details. The criterion for whether we should adopt GWA or U+GWA is discussed
and is assessed with the help of the off-diagonal elements of the self-energy.
