There are tons of different games to play. Designing a preconditioner that's specific to the problem being solved can help you beat incomplete LU, often by a su

There are tons of different games to play. Designing a preconditioner that's specific to the problem being solved can help you beat incomplete LU, often by a substantial (even asymptotic) margin. If you have a problem that's small enough to factorize and solve, that's great. That probably is the best approach. This doesn't scale in parallel. For really big problems, iterative methods are the only game in town. It's all about knowing the range of methods that are applicable to your problem and the regimes in which they operate best. There's no one-size-fits-all solution.