“…Also, incomplete factorization preconditioners have been shown to provide good smoothers for multigrid (see, e.g., [290]). Recent studies [69,70,270] have shown that sparse approximate inverses can also provide effective and robust smoothers for both geometric and algebraic multigrid, especially for tough problems (see also [19,29,30,234] for early work in this direction). Conversely, the ever-increasing size of the linear systems arising in countless applications has exposed the limitations of nonscalable methods (such as incomplete factorization and sparse approximate inverse preconditioners), and it is now generally agreed that the multilevel paradigm must somehow be incorporated into these techniques in order for these to remain competitive.…”