On Generalizing the AMG Framework

Abstract: We present a theory for algebraic multigrid (AMG) methods that allows for generalsmoothing processes and general coarsening approaches. The goal of the theory is to provide guidancein the development of new, more robust, AMG algorithms. In particular, we introduce severalcompatible relaxation methods and give theoretical justification for their use as tools for measuringthe quality of coarse grids.