We link linear prediction of Chebyshev and Fourier expansions to analytic
continuation. We push the resolution in the Chebyshev-based computation of
T=0 many-body spectral functions to a much higher precision by deriving a
modified Chebyshev series expansion that allows to reduce the expansion order
by a factor ∼61. We show that in a certain limit the Chebyshev
technique becomes equivalent to computing spectral functions via time evolution
and subsequent Fourier transform. This introduces a novel recursive time
evolution algorithm that instead of the group operator e−iHt only involves
the action of the generator H. For quantum impurity problems, we introduce an
adapted discretization scheme for the bath spectral function. We discuss the
relevance of these results for matrix product state (MPS) based DMRG-type
algorithms, and their use within dynamical mean-field theory (DMFT). We present
strong evidence that the Chebyshev recursion extracts less spectral information
from H than time evolution algorithms when fixing a given amount of created
entanglement.Comment: 12 pages + 6 pages appendix, 11 figure