Run-time compilation for parallel sparse matrix computations
ICS '96 Proceedings of the 10th international conference on Supercomputing
Efficient Sparse LU Factorization with Partial Pivoting on Distributed Memory Architectures
IEEE Transactions on Parallel and Distributed Systems
Elimination forest guided 2D sparse LU factorization
Proceedings of the tenth annual ACM symposium on Parallel algorithms and architectures
A combined unifrontal/multifrontal method for unsymmetric sparse matrices
ACM Transactions on Mathematical Software (TOMS)
Next-generation generic programming and its application to sparse matrix computations
Proceedings of the 14th international conference on Supercomputing
Sparse LU factorization with partial pivoting on distributed memory machines
Supercomputing '96 Proceedings of the 1996 ACM/IEEE conference on Supercomputing
A framework for sparse matrix code synthesis from high-level specifications
Proceedings of the 2000 ACM/IEEE conference on Supercomputing
Making sparse Gaussian elimination scalable by static pivoting
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
SIPR: A New Framework for Generating Efficient Code for Sparse Matrix Computations
LCPC '98 Proceedings of the 11th International Workshop on Languages and Compilers for Parallel Computing
HPF-2 Support for Dynamic Sparse Computations
LCPC '98 Proceedings of the 11th International Workshop on Languages and Compilers for Parallel Computing
Recursive approach in sparse matrix LU factorization
Scientific Programming
The Journal of Supercomputing
A high-performance UL factorization for the frontal method
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Multi-pass mapping schemes for parallel sparse matrix computations
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
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We investigate several ways to improve the performance of sparse LU factorization with partial pivoting, as used to solve unsymmetric linear systems. To perform most of the numerical computation in dense matrix kernels, we introduce the notion of unsymmetric supernodes. To better exploit the memory hierarchy, we introduce unsymmetric supernode-panel updates and two-dimensional data partitioning. To speed up symbolic factorization, we use Gilbert and Peierls''s depth-first search with Eisenstat and Liu''s symmetric structural reductions. We have implemented a sparse LU code using all these ideas. We present experiments demonstrating that it is significantly faster than earlier partial pivoting codes. We also compare performance with UMFPACK, which uses a multifrontal approach; our code is usually faster.