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ACM Transactions on Mathematical Software (TOMS)
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Journal of Computational Physics
SuperLU_DIST: A scalable distributed-memory sparse direct solver for unsymmetric linear systems
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A two-phase preconditioning strategy of sparse approximate inverse for indefinite matrices
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PSPIKE: A Parallel Hybrid Sparse Linear System Solver
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Preconditioning Helmholtz linear systems
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Heuristics for a matrix symmetrization problem
PPAM'07 Proceedings of the 7th international conference on Parallel processing and applied mathematics
A tearing-based hybrid parallel sparse linear system solver
Journal of Computational and Applied Mathematics
Weighted Matrix Ordering and Parallel Banded Preconditioners for Iterative Linear System Solvers
SIAM Journal on Scientific Computing
A domain-decomposing parallel sparse linear system solver
Journal of Computational and Applied Mathematics
Improved Balanced Incomplete Factorization
SIAM Journal on Matrix Analysis and Applications
Maximum-weighted matching strategies and the application to symmetric indefinite systems
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
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ScalA '13 Proceedings of the Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems
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Standard preconditioners, like incomplete factorizations, perform well when the coefficient matrix is diagonally dominant, but often fail on general sparse matrices. We experiment with nonsymmetric permutations and scalings aimed at placing large entries on the diagonal in the context of preconditioning for general sparse matrices. The permutations and scalings are those developed by Olschowka and Neumaier [Linear Algebra Appl., 240 (1996), pp. 131--151] and by Duff and Koster [SIAM J. Matrix Anal. Appl., 20 (1999), pp. 889--901; Tech. report Ral-Tr-99-030, Rutherford Appleton Laboratory, Chilton, UK, 1999]. We target highly indefinite, nonsymmetric problems that cause difficulties for preconditioned iterative solvers. Our numerical experiments indicate that the reliability and performance of preconditioned iterative solvers are greatly enhanced by such preprocessing.