  The Lanczos algorithm is evaluated for solving the time-independent as well
as the time-dependent Dirac equation with arbitrary electromagnetic fields. We
demonstrate that the Lanczos algorithm can yield very precise eigenenergies and
allows very precise time propagation of relativistic wave packets. The
unboundedness of the Dirac Hamiltonian does not hinder the applicability of the
Lanczos algorithm. As the Lanczos algorithm requires only matrix-vector
products and inner products, which both can be efficiently parallelized, it is
an ideal method for large-scale calculations. The excellent parallelization
capabilities are demonstrated by a parallel implementation of the Dirac Lanczos
propagator utilizing the Message Passing Interface standard.
