  We present a new numerical technique to solve large-scale eigenvalue
problems. It is based on the projection technique, used in strongly correlated
quantum many-body systems, where first an effective approximate model of
smaller complexity is constructed by projecting out high energy degrees of
freedom and in turn solving the resulting model by some standard eigenvalue
solver.
  Here we introduce a generalization of this idea, where both steps are
performed numerically and which in contrast to the standard projection
technique converges in principle to the exact eigenvalues. This approach is not
just applicable to eigenvalue problems encountered in many-body systems but
also in other areas of research that result in large scale eigenvalue problems
for matrices which have, roughly speaking, mostly a pronounced dominant
diagonal part. We will present detailed studies of the approach guided by two
many-body models.
