  Covergent eigensolutions of the Dirac Equation for a relativistic electron in
an external Coulomb potential are obtained using the Lanczos Algorithm. A
tri-diagonal matrix representation of the Dirac Hamiltonian operator is
constructed iteratively and diagonalized after each iteration step to form a
sequence of convergent eigenvalue solutions. Any spurious solutions which arise
from the presence of continuum states can easily be identified.
