  Current widely-used approaches to calculate spectral functions using the
density-matrix renormalization group in frequency space either necessarily
include an artificial broadening (correction-vector method) or have limited
resolution (time-domain density-matrix renormalization group with Fourier
transform method). Here we propose an adaptive Lanczos-vector method to
calculate the coefficients of a continued fraction expansion of the spectral
function iteratively. We show that one can obtain a very accurate
representation of the spectral function very efficiently, and that one can also
directly extract the spectral weights and poles for the discrete system. As a
test case, we study spinless fermions in one dimension and compare our approach
to the correction vector method.
