The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
Exploiting structural symmetry in unsymmetric sparse symbolic factorization
SIAM Journal on Matrix Analysis and Applications
Elimination structures for unsymmetric sparse LU factors
SIAM Journal on Matrix Analysis and Applications
A mapping algorithm for parallel sparse Cholesky factorization
SIAM Journal on Scientific Computing
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
A Framework for Efficient Sparse LU Factorization in a Cluster Based Platform
IWCC '01 Proceedings of the NATO Advanced Research Workshop on Advanced Environments, Tools, and Applications for Cluster Computing-Revised Papers
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Finding the nonzero structures of the lower and upper triangular factors of an unsymmetric sparse matrix A is an important problem in the field of sparse matrix computations. Complementing previous research on sequential algorithms, we develop a parallel algorithm by appropriately intertwining a fully concurrent algorithm with an experimentally proved efficient algorithm (both algorithms are previous art). The resulting algorithm, intended to use with out-of-core matrices, leads to sensitive improvements in memory usage.The algorithm is described in terms of its theoretical complexity, its experimental implementation with the MPI communication library the Origin 2000 multiprocessor, as well as its performance on large size real world matrices.