  We give details on how to calculate spectral functions and Green's functions
for finite systems using the Chebyshev polynomial expansion method. We apply
the method to a finite Anderson impurity system, and furthermore give details
on how to exploit its symmetry to transform the system into smaller orthogonal
subsystems. We also consider systems connected to infinite leads, which we
study by approximating the unknown self-energy with an exact self-energy for a
finite system. As our test case, we consider the single-impurity Anderson
model, where we find that we can capture some aspects of Kondo physics.
