An Object-Oriented Collection of Minimum Degree Algorithms
ISCOPE '98 Proceedings of the Second International Symposium on Computing in Object-Oriented Parallel Environments
Impact of reordering on the memory of a multifrontal solver
Parallel Computing - Parallel matrix algorithms and applications (PMAA '02)
Adapting a parallel sparse direct solver to architectures with clusters of SMPs
Parallel Computing - Special issue: Parallel and distributed scientific and engineering computing
A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
A column approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Time-memory trade-offs using sparse matrix methods for large-scale eigenvalue problems
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
A robust ILU preconditioner using constraints diagonal Markowitz
Proceedings of the 48th Annual Southeast Regional Conference
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Greedy algorithms for ordering sparse matrices for Cholesky factorization can be based on different metrics. Minimum degree, a popular and effective greedy ordering scheme, minimizes the number of nonzero entries in the rank-1 update (degree) at each step of the factorization. Alternatively, minimum deficiency minimizes the number of nonzero entries introduced (deficiency) at each step of the factorization. In this paper we develop two new heuristics: modified minimum deficiency (MMDF) and modified multiple minimum degree (MMMD). The former uses a metric similar to deficiency while the latter uses a degree-like metric. Our experiments reveal that on the average, MMDF orderings result in 21% fewer operations to factor than minimum degree; MMMD orderings result in 15% fewer operations to factor than minimum degree. MMMD requires on the average 7--13% more time than minimum degree, while MMDF requires on the average 33--34% more time than minimum degree.