Direct methods for sparse matrices
Direct methods for sparse matrices
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
Elimination structures for unsymmetric sparse LU factors
SIAM Journal on Matrix Analysis and Applications
Exploiting structural symmetry in a sparse partial pivoting code
SIAM Journal on Scientific Computing
Modification of the minimum-degree algorithm by multiple elimination
ACM Transactions on Mathematical Software (TOMS)
An Approximate Minimum Degree Ordering Algorithm
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 combined unifrontal/multifrontal method for unsymmetric sparse matrices
ACM Transactions on Mathematical Software (TOMS)
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian Elimination
SIAM Journal on Matrix Analysis and Applications
Analysis and comparison of two general sparse solvers for distributed memory computers
ACM Transactions on Mathematical Software (TOMS)
Making sparse Gaussian elimination scalable by static pivoting
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
Future Generation Computer Systems - I. High Performance Numerical Methods and Applications. II. Performance Data Mining: Automated Diagnosis, Adaption, and Optimization
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
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
SIAM Journal on Matrix Analysis and Applications
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
An Experimental Comparison of some Direct Sparse Solver Packages
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
Using Postordering and Static Symbolic Factorization for Parallel Sparse LU
IPDPS '00 Proceedings of the 14th International Symposium on Parallel and Distributed Processing
On the lu factorization of sequences of identically structured sparse matrices within a distributed memory environment
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
ACM Transactions on Mathematical Software (TOMS)
Parallelization of Direct Algorithms using Multisplitting Methods in Grid Environments
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 13 - Volume 14
Large-scale nonlinear optimization in circuit tuning
Future Generation Computer Systems
Using dense storage to solve small sparse linear systems
ACM Transactions on Mathematical Software (TOMS)
Parallel unsymmetric-pattern multifrontal sparse LU with column preordering
ACM Transactions on Mathematical Software (TOMS)
GREMLINS: a large sparse linear solver for grid environment
Parallel Computing
Large-scale nonlinear optimization in circuit tuning
Future Generation Computer Systems
A shared- and distributed-memory parallel sparse direct solver
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Computers & Mathematics with Applications
Journal of Real-Time Image Processing
Taking advantage of low radiative coupling in 3D urban models
UDMV '13 Proceedings of the Eurographics Workshop on Urban Data Modelling and Visualisation
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During the past few years, algorithmic improvements alone have reduced the time required for the direct solution of unsymmetric sparse systems of linear equations by almost an order of magnitude. This paper compares the performance of some well-known software packages for solving general sparse systems. In particular, it demonstrates the consistently high level of performance achieved by WSMP---the most recent of such solvers. It compares the various algorithmic components of these solvers and discusses their impact on solver performance. Our experiments show that the algorithmic choices made in WSMP enable it to run more than twice as fast as the best among similar solvers and that WSMP can factor some of the largest sparse matrices available from real applications in only a few seconds on a 4-CPU workstation. Thus, the combination of advances in hardware and algorithms makes it possible to solve those general sparse linear systems quickly and easily that might have been considered too large until recently.