Bundle Adjustment - A Modern Synthesis
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Algorithm 837: AMD, an approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Multi-level direct K-way hypergraph partitioning with multiple constraints and fixed vertices
Journal of Parallel and Distributed Computing
PT-Scotch: A tool for efficient parallel graph ordering
Parallel Computing
Optimal block-tridiagonalization of matrices for coherent charge transport
Journal of Computational Physics
Hypergraph-Based Unsymmetric Nested Dissection Ordering for Sparse LU Factorization
SIAM Journal on Scientific Computing
Hypergraph Partitioning-Based Fill-Reducing Ordering for Symmetric Matrices
SIAM Journal on Scientific Computing
A fast direct solver for elliptic problems on general meshes in 2D
Journal of Computational Physics
A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices
Journal of Computational Physics
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When performing sparse matrix factorization, the ordering of matrix rows and columns has a dramatic impact on the factorization time. This paper describes an approach to the reordering problem that produces significantly better orderings than prior methods. The algorithm is a hybrid of nested dissection and minimum degree ordering, and combines an assortment of different algorithmic advances. New or improved algorithms are described for graph compression, multilevel partitioning, and separator improvement. When these techniques are combined, the resulting orderings average 39% better than minimum degree over a suite of test matrices, while requiring roughly 2.7 times the run time of Liu's multiple minimum degree.