  We compute the spectral functions for the two-site dynamical cluster theory
and for the two-orbital dynamical mean-field theory in the density-matrix
renormalization group (DMRG) framework using Chebyshev expansions represented
with matrix product states (MPS). We obtain quantitatively precise results at
modest computational effort through technical improvements regarding the
truncation scheme and the Chebyshev rescaling procedure. We furthermore
establish the relation of the Chebyshev iteration to real-time evolution, and
discuss technical aspects as computation time and implementation in detail.
