Preconditioned Krylov subspace methods

Preconditioned Krylov subspace techniques have had a substantial impact on the numerical solution of engineering and scientific problems. These methods can be mandatory for large problems arising from 3-dimensional models, However, although iterative methods are rapidly gaining ground, there are still a number of open questions and unresolved issues related to their use in representative applications. In this paper we give an overview of the most commonly used techniques, and discuss open questions and current trends.