  An efficient method, preconditioned conjugate gradient method with a
filtering function (PCG-F), is proposed for solving iteratively the Dirac
equation in 3D lattice space for nuclear systems. The filtering function is
adopted to avoid the variational collapsed problem and a momentum-dependent
preconditioner is introduced to promote the efficiency of the iteration. The
PCG-F method is demonstrated in solving the Dirac equation with given spherical
and deformed Woods-Saxon potentials. The solutions given by the inverse
Hamiltonian method in 3D lattice space and the shooting method in radial
coordinate space are reproduced with a high accuracy. In comparison with the
existing inverse Hamiltonian method, the present PCG-F method is much faster in
the convergence of the iteration, in particular for deformed potentials. It may
also provide a promising way to solve the relativistic Hartree-Bogoliubov
equation iteratively in the future.
