  We have developed a new type of self-consistent scheme within the $GW$
approximation, which we call quasiparticle self-consistent $GW$ (QS$GW$). We
have shown that QS$GW$ rather well describes energy bands for a wide-range of
materials, including many where the local-density approximation fails. QS$GW$
contains physical effects found in other theories such as LDA$+U$, SIC and $GW$
in a satisfactory manner without many of their drawbacks (partitioning of
itinerant and localized electrons, adjustable parameters, ambiguities in
double-counting, etc.). We present some theoretical discussion concerning the
formulation of QS$GW$, including a prescriptino for calculating the total
energy. We also address several key methodological points needed for
implementation. We then show convergence checks and some representative results
in a variety of materials.
