Elimination structures for unsymmetric sparse LU factors
SIAM Journal on Matrix Analysis and Applications
An efficient block-oriented approach to parallel sparse Cholesky factorization
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
Scalable iterative solution of sparse linear systems
Parallel Computing
Modification of the minimum-degree algorithm by multiple elimination
ACM Transactions on Mathematical Software (TOMS)
Solving large nonsymmetric sparse linear systems using MCSPARSE
Parallel Computing
Applied numerical linear algebra
Applied numerical linear algebra
ScaLAPACK user's guide
Efficient Sparse LU Factorization with Partial Pivoting on Distributed Memory Architectures
IEEE Transactions on Parallel and Distributed Systems
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
On Algorithms for Obtaining a Maximum Transversal
ACM Transactions on Mathematical Software (TOMS)
Algorithm 575: Permutations for a Zero-Free Diagonal [F1]
ACM Transactions on Mathematical Software (TOMS)
Sparse Gaussian Elimination on High Performance Computers
Sparse Gaussian Elimination on High Performance Computers
An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian
An Asynchronous Parallel Supernodal Algorithm for Sparse Gaussian
A Supernodal Approach to Sparse Partial Pivoting
A Supernodal Approach to Sparse Partial Pivoting
Test Planning for Core-based 3D Stacked ICs with Through-Silicon Vias
VLSID '12 Proceedings of the 2012 25th International Conference on VLSI Design
Analysis and comparison of two general sparse solvers for distributed memory computers
ACM Transactions on Mathematical Software (TOMS)
Design, implementation and testing of extended and mixed precision BLAS
ACM Transactions on Mathematical Software (TOMS)
Recent advances in direct methods for solving unsymmetric sparse systems of linear equations
ACM Transactions on Mathematical Software (TOMS)
Proceedings of the 2001 ACM/IEEE conference on Supercomputing
Parallel Computing - Parallel matrix algorithms and applications
Recent Progress in General Sparse Direct Solvers
ICCS '01 Proceedings of the International Conference on Computational Sciences-Part I
An Experimental Comparison of some Direct Sparse Solver Packages
IPDPS '01 Proceedings of the 15th International Parallel & Distributed Processing Symposium
A new scheduling algorithm for parallel sparse LU factorization with static pivoting
Proceedings of the 2002 ACM/IEEE conference on Supercomputing
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
An overview of SuperLU: Algorithms, implementation, and user interface
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Is 1.7 x 10^10 Unknowns the Largest Finite Element System that Can Be Solved Today?
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
On the design of interfaces to sparse direct solvers
ACM Transactions on Mathematical Software (TOMS)
Scaling and pivoting in an out-of-core sparse direct solver
ACM Transactions on Mathematical Software (TOMS)
FPGA accelerated parallel sparse matrix factorization for circuit simulations
ARC'11 Proceedings of the 7th international conference on Reconfigurable computing: architectures, tools and applications
Partial factorization of a dense symmetric indefinite matrix
ACM Transactions on Mathematical Software (TOMS)
Pivoting strategies for tough sparse indefinite systems
ACM Transactions on Mathematical Software (TOMS)
| Hi-index | 0.00 |
We propose several techniques as alternatives to partial pivoting to stabilize sparse Gaussian elimination. From numerical experiments we demonstrate that for a wide range of problems the new method is as stable as partial pivoting. The main advantage of the new method over partial pivoting is that it permits a priori determination of data structures and communication pattern for Gaussian elimination, which makes it more scalable on distributed memory machines. Based on this a priori knowledge, we design highly parallel algorithms for both sparse Gaussian elimination and triangular solve and we show that they are suitable for large-scale distributed memory machines.