  We carry Chebyshev-polynomial expansion of the inverse localization length of
Hermitian and non-Hermitian random chains as function of energy. For Hermitian
models, the expansion produces numerically this energy-dependent function in
one run of the algorithm. This is in strong contrast to the standard
transfer-matrix method, which produces the inverse localization length for a
fixed energy in each run. For non-Hermitian models, as in the transfer-matrix
method, our algorithm computes the inverse localization length for a fixed
(complex) energy. We also find a formula of the Chebyshev-polynomial expansion
of the density of states of non-Hermitian models. As explained in more detail
in the Introduction, our algorithm for non-Hermitian models may be the only
available efficient algorithm for finding the density of states of models with
interactions.
