# Algebraic multilevel preconditioner for the graph Laplacian based on matching of graphs

## Priv.-Doz. Dr. Johannes Kraus

Nov. 23, 2010, 3:30 p.m. P 004

We introduce an algebraic multilevel method for the Graph Laplacian based on matching of graphs. We show that the resulting piecewise constant coarse spaces and an appropriately chosen Algebraic Multilevel Iteration (or AMLI) yield a (nearly) optimal order method.