AMG Preconditioners for Sparse Approximate Inverse Matrices

Matthias Bollhöfer
Dep. of Mathematics
Chemnitz University of Technology
D-09107 Chemnitz
Germany

Abstract:

In this talk we discuss the construction of an algebraic multilevel method which is adapted to a given sparse approximate inverse of a symmetric positive definite matrix. The idea behind this construction is a heuristic observation, that sparse approximate inverse preconditioners often approximate the large eigenvalues of the given matrix quite well, while the smaller ones are only fairly poor approximated. The AMG consists of a strategy that uses suitably selected columns of the scaled residual matrix to construct the restriction/prolongation operator.