  This talk presents results of a comparitive study of iterative algorithms
like minimal residue ($MR$) and conjugate gradient ($CG$, $BiCG\gamma_5$, and
\bicgstab) used for inverting the Dirac matrix $M$. The tests were done on the
Connection Machine CM-5 using $32^3 \times 64$ lattices. The fermion action
used is of Wilson type, both with and without the clover term. The overall
conclusion is that preconditioned over-relaxed $MR$ is the simplest, uses the
least memory, and is comparable in performance to \bicgstab. We find these two
algorithms to be equally robust, $i.e.$ insensitive to the starting solution
and to round-off errors.
