On Generalizing the Algebraic Multigrid Framework
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SIAM Journal on Numerical Analysis 42 (4): 1669--1693 (January 2004)

We present a theory for algebraic multigrid (AMG) methods that allows for general smoothing processes and general coarsening approaches. The goal of the theory is to provide guidance in the development of new, more robust, AMG algorithms. In particular, we introduce several compatible relaxation methods and give theoretical justification for their use as tools for measuring the quality of coarse grids.
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