  We present a new method for the computation of self-energy corrections in
large supercells. It eliminates the explicit summation over unoccupied states,
and uses an iterative scheme based on an expansion of the Green's function
around a set of reference energies. This improves the scaling of the
computational time from the fourth to the third power of the number of atoms
for both the inverse dielectric matrix and the self-energy, yielding improved
efficiency for 8 or more silicon atoms per unit cell.
