The exponential growth of communication costs relative to computation on
modern computers motivates revisiting a previously dismissed set of
algorithms: 
-step Krylov subspace methods. One iteration of an
-step method has almost the same communication cost as one iteration
of its related standard Krylov method, but accomplishes the same work as
of these iterations. We address concerns which hindered the earlier
acceptance of these algorithms: performance, numerical stability, and
preconditioning.