Elimination structures for unsymmetric sparse LU factors
SIAM Journal on Matrix Analysis and Applications
Fast and effective algorithms for graph partitioning and sparse-matrix ordering
IBM Journal of Research and Development - Special issue: optical lithography I
An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization
SIAM Journal on Matrix Analysis and Applications
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
Making sparse Gaussian elimination scalable by static pivoting
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
S+: Efficient 2D Sparse LU Factorization on Parallel Machines
SIAM Journal on Matrix Analysis and Applications
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
Using Postordering and Static Symbolic Factorization for Parallel Sparse LU
IPDPS '00 Proceedings of the 14th International Symposium on Parallel and Distributed Processing
Partitioning and blocking issues for a parallel incomplete factorization
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
Applying parallel direct solver techniques to build robust high performance preconditioners
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
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During the past few years, algorithmic improvements alone have shaved almost an order of magnitude off the time required for the direct solution of general sparse systems of linear equations. Combined with a similar increase in the performance to cost ratio due to hardware advances during this period, current sparse solver technology makes it possible to solve those problems quickly and easily that might have been considered impractically large until recently. In this paper, we compare the performance of some commonly used software packages for solving general sparse systems. In particular, we demonstrate the consistently high level of performance achieved by WSMP--the most recent of such solvers. We compare the various algorithmic components of these solvers and show that the choices made in WSMP enable it to run two to three times faster than the best amongst other similar solvers. As a result, WSMP can factor some of the largest sparse matrices available from real applications in a few seconds on 4-CPU workstation.