  We present a preconditioner based on spectral projection that is combined
with a deflated Krylov subspace method for solving ill conditioned linear
systems of equations. Our results show that the proposed algorithm requires
many fewer iterations to achieve the convergence criterion for solving an ill
conditioned problem than a Krylov subspace solver. In our numerical
experiments, the solution obtained by the proposed algorithm is more accurate
in terms of the norm of the distance to the exact solution of the linear system
of equations.
