  An approach is given for solving large linear systems that combines Krylov
methods with use of two different grid levels. Eigenvectors are computed on the
coarse grid and used to deflate eigenvalues on the fine grid. GMRES-type
methods are first used on both the coarse and fine grids. Then another approach
is given that has a restarted BiCGStab (or IDR) method on the fine grid. While
BiCGStab is generally considered to be a non-restarted method, it works well in
this context with deflating and restarting. Tests show this new approach can be
very efficient for difficult linear equations problems.
