Algebraic preconditioning approaches and their applications

Abstract

We will review approaches to numerically treat large-scale systems of equations including preconditioning, in particular those methods which are suitable for solving linear systems in parallel. We will also demonstrate how completion techniques can serve as a useful tool to prevent ill-conditioned systems. Beside parallel aspects for preconditioning, multilevel factorization methods will be investigated and finally we will demonstrate how these methods can be combined for approximate matrix inversion methods.