  We present a new all-electron, augmented-wave implementation of the GW
approximation using eigenfunctions generated by a recent variant of the
full-potential LMTO method. The dynamically screened Coulomb interaction W is
expanded in a mixed basis set which consists of two contributions, local
atom-centered functions confined to muffin-tin spheres, and plane waves with
the overlap to the local functions projected out. The former can include any of
the core states; thus the core and valence states can be treated on an equal
footing. Systematic studies of semiconductors and insulators show that the GW
fundamental bandgaps consistently fall low in comparison to experiment, and
also the quasiparticle levels differ significantly from other, approximate
methods, in particular those that approximate the core with a pseudopotential.
