Algebraic Multilevel Methods and Sparse Approximate Inverses
Matthias Bollhöfer, Volker Mehrmann · SIAM Journal on Matrix Analysis and Applications · 2002
In this paper we introduce a new approach to algebraic multilevel methods and their use as preconditioners in iterative methods for the solution of symmetric positive definite linear systems. The multilevel process and, in particular, the coarsening process are based on the construction of sparse approximate inverses and their augmentation with corrections of smaller size. We present comparisons of the effectiveness of the resulting multilevel technique and numerical results.