Cutting down on Fill Using Nested Dissection: Provably Good Elimination Orderings

In the last two decades, many heuristics have been developed for finding good elimination orderings for sparse Cholesky factorization. These heuristics aim to find elimination orderings with either low fill, low operation count, or low elimination height. Though many heuristics seem to perform well in practice, there has been a marked absence of much theoretical analysis to back these heuristics. Indeed, few heuristics are known to provide any guarantee on the quality of the elimination ordering produced for arbitrary matrices.

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