On two‐grid convergence estimates

Abstract We derive a new representation for the exact convergence factor of classical two‐level and two‐grid preconditioners. Based on this result, we establish necessary and sufficient conditions for constructing the components of efficient algebraic multigrid (AMG) methods. The relation of the sharp estimate to the classical two‐level hierarchical basis methods is discussed as well. Lastly, as an application, we give an optimal two‐grid convergence proof of a purely algebraic ‘window’‐AMG method. Published in 2005 by John Wiley & Sons, Ltd.