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{\large Bram Metsch \\
{\bf Algebraic Multigrid (AMG) - Beyond the M-Matrix case}}

Universitaet Bonn \\ Institut fuer Numerische Simulation \\ Wegelerstrasse 6 \\ 53115 Bonn \\ GERMANY
\\
{\tt metsch@ins.uni-bonn.de}\\
Michael Griebel\\
{\em Universitaet Bonn
Institut fuer Numerische Simulation}\\
Marc Alexander Schweitzer\\
{\em Universitaet Bonn
Institut fuer Numerische Simulation}\end{center}

Algebraic Multigrid methods (AMG) are known to be robust linear
solvers for a wide class of linear systems arising from the
discretization of partial differential equations.
However, the construction as well as the convergence analysis of
classical AMG methods is based on the assumption that the linear system
matrix is a symmetric positive definite $M$-matrix.

In this talk we present an approach to extend the applicability of AMG to
a wider class of problems. In particular, we focus on higher-order
prolongation schemes to obtain a more accurate representation of the
smooth error components.


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