Analysis and comparison of two general sparse solvers for distributed memory computers
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)
Parallel Computing - Parallel matrix algorithms and applications
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Solving Unsymmetric Sparse Systems of Linear Equations with PARDISO
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
MUMPS: A General Purpose Distributed Memory Sparse Solver
PARA '00 Proceedings of the 5th International Workshop on Applied Parallel Computing, New Paradigms for HPC in Industry and Academia
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
ACM Transactions on Mathematical Software (TOMS)
Fast computational methods for locating fold points for the power flow equations
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Solving unsymmetric sparse systems of linear equations with PARDISO
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Parallel sparse LU factorization on second-class message passing platforms
Proceedings of the 19th annual international conference on Supercomputing
Stabilized bordered block diagonal forms for parallel sparse solvers
Parallel Computing
An overview of SuperLU: Algorithms, implementation, and user interface
ACM Transactions on Mathematical Software (TOMS) - Special issue on the Advanced CompuTational Software (ACTS) Collection
Editorial: Identity fusion in unsupervised environments
Information Fusion
Parallel sparse LU factorization on different message passing platforms
Journal of Parallel and Distributed Computing
ACM Transactions on Mathematical Software (TOMS)
Computational Optimization and Applications
Recursive approach in sparse matrix LU factorization
Scientific Programming
Neural Networks for Predicting the Behavior of Preconditioned Iterative Solvers
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
On Using Reinforcement Learning to Solve Sparse Linear Systems
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
A scaling algorithm for polynomial constraint satisfaction problems
Journal of Global Optimization
ACM Transactions on Mathematical Software (TOMS)
A two-phase preconditioning strategy of sparse approximate inverse for indefinite matrices
Computers & Mathematics with Applications
PSPIKE: A Parallel Hybrid Sparse Linear System Solver
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
On projected Newton-Krylov solvers for instationary laminar reacting gas flows
Journal of Computational Physics
Stabilized bordered block diagonal forms for parallel sparse solvers
Parallel Computing
VECPAR'06 Proceedings of the 7th international conference on High performance computing for computational science
Hardware-oriented implementation of cache oblivious matrix operations based on space-filling curves
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
A parallel approximation algorithm for the weighted maximum matching problem
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
A robust ILU preconditioner using constraints diagonal Markowitz
Proceedings of the 48th Annual Southeast Regional Conference
A Supernodal Approach to Incomplete LU Factorization with Partial Pivoting
ACM Transactions on Mathematical Software (TOMS)
Weighted Matrix Ordering and Parallel Banded Preconditioners for Iterative Linear System Solvers
SIAM Journal on Scientific Computing
On techniques to improve robustness and scalability of a parallel hybrid linear solver
VECPAR'10 Proceedings of the 9th international conference on High performance computing for computational science
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Improved Balanced Incomplete Factorization
SIAM Journal on Matrix Analysis and Applications
Improved Scaling for Quantum Monte Carlo on Insulators
SIAM Journal on Scientific Computing
Using performance profiles to evaluate preconditioners for iterative methods
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part III
Sparse LU factorization for parallel circuit simulation on GPU
Proceedings of the 49th Annual Design Automation Conference
A parallel 3d unstructured implicit RANS solver for compressible and incompressible CFD simulations
PPAM'11 Proceedings of the 9th international conference on Parallel Processing and Applied Mathematics - Volume Part II
Approximate weighted matching on emerging manycore and multithreaded architectures
International Journal of High Performance Computing Applications
VBARMS: A variable block algebraic recursive multilevel solver for sparse linear systems
Journal of Computational and Applied Mathematics
| Hi-index | 0.02 |
We consider techniques for permuting a sparse matrix so that the diagonal of the permuted matrix has entries of large absolute value. We discuss various criteria for this and consider their implementation as computer codes. We then indicate several cases where such a permutation can be useful. These include the solution of sparse equations by a direct method and by an iterative technique. We also consider its use in generating a preconditioner for an iterative method. We see that the effect of these reorderings can be dramatic although the best a priori strategy is by no means clear.