Improvements for iterative methods?

Krylov subspace methods offer good possibilities for the solution of

large sparse linear systems of equations.For general systems, some of

the popular methods often show an irregular type of convergence

behavior and one may wonder whether that could be improved or not. Many

suggestions have been made for improvement and the question arises

whether these corrections are cosmetic or not. There is also the

question whether the irregularity shows inherent numerical instability.

In such cases one should take extra care in the application of

smoothing techniques. We will discuss strategies that work well and

strategies that might have been expected to work well.