Direct methods for sparse matrices
Direct methods for sparse matrices
A nondeterministic parallel algorithm for general unsymmetric sparse lu factorization
SIAM Journal on Matrix Analysis and Applications
Parallel sparse LU decomposition on a mesh network of transputers
SIAM Journal on Matrix Analysis and Applications
Parallel sparse matrix solution and performance
Parallel Computing
The design of MA48: a code for the direct solution of sparse unsymmetric linear systems of equations
ACM Transactions on Mathematical Software (TOMS)
Solving large nonsymmetric sparse linear systems using MCSPARSE
Parallel Computing
Highly Scalable Parallel Algorithms for Sparse Matrix Factorization
IEEE Transactions on Parallel and Distributed Systems
Efficient Sparse LU Factorization with Partial Pivoting on Distributed Memory Architectures
IEEE Transactions on Parallel and Distributed Systems
Solving Linear Systems on Vector and Shared Memory Computers
Solving Linear Systems on Vector and Shared Memory Computers
A parallel algorithm for sparse unsymmetric lu factorization
A parallel algorithm for sparse unsymmetric lu factorization
Sparse gaussian elimination on high-performance computers
Sparse gaussian elimination on high-performance computers
Data Locality Exploitation in Algorithms including Sparse Communications
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
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Solving large nonsymmetric sparse linear systems on distributed memory multiprocessors is an active research area. We present a loop-level parallelized generic LU algorithm which comprises analyse-factorize and solve stages. To further exploit matrix sparsity and parallelism, the analyse step looks for a set of compatible pivots. Sparse techniques are applied until the reduced submatrix reaches a threshold density. At this point, a switch to dense routines takes place in both analyse-factorize and solve stages. The SPMD code follows a sparse cyclic distribution to map the system matrix onto a P × Q processor mesh. Experimental results show a good behavior of our sequential algorithm compared with a standard generic solver: the MA48 routine. Additionally, a parallel version on the Cray T3E exhibits high performance in terms of speed-up and efficiency.