Abstract:Algebraic multigrid (AMG) methods are often robust and effective solvers for solving the large and sparse linear systems that arise from discretized PDEs and other problems, relying on heuristic graph algorithms to achieve their performance. Reduction‐based AMG (AMGr) algorithms attempt to formalize these heuristics by providing two‐level convergence bounds that depend concretely on properties of the partitioning of the given matrix into its fine‐ and coarse‐grid degrees of freedom. MacLachlan and Saad (SISC 2… Show more
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