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A Supernodal Approach to Sparse Partial Pivoting
Abstract
We investigate several ways to improve the performance of sparse LU factorization with partial pivoting, as used to solve unsymmetric linear systems. We introduce the notion of unsymmetric supernodes to perform most of the numerical computation in dense matrix kernels. We introduce unsymmetric supernode-panel updates and two-dimensional data partitioning to better exploit the memory hierarchy. We use Gilbert and Peierls's depth-first search with Eisenstat and Liu's symmetric structural reductions to speed up symbolic factorization. We have developed a sparse LU code using all these ideas. We present experiments demonstrating that it is significantly faster than earlier partial pivoting codes. We also compare its performance with UMFPACK, which uses a multifrontal approach; our code is very competitive in time and storage requirements, especially for large problems.
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Citations
Cited by
(2006) · Cited by 1,979
Solving unsymmetric sparse systems of linear equations with PARDISO
Schenk, O., & Gärtner, K. (2004) · Future Generation Computer Systems · doi:10.1016/j.future.2003.07.011 · Cited by 1,467
SBA: A software package for generic sparse bundle adjustment
Lourakis, M. I. A., & Argyros, A. A. (2009) · ACM Transactions on Mathematical Software · doi:10.1145/1486525.1486527 · Cited by 788
An overview of SuperLU: Algorithms, implementation, and user interface
Li, X. S. (2005) · ACM Transactions on Mathematical Software · doi:10.1145/1089014.1089017 · Cited by 467
Self-citationA column pre-ordering strategy for the unsymmetric-pattern multifrontal method
Davis, T. A. (2004) · ACM Transactions on Mathematical Software · doi:10.1145/992200.992205 · Cited by 419
Metadata
- Authors
- Demmel, J. W., Eisenstat, S. C., Gilbert, J. R., Li, X. S., & Liu, J. W. H.
- Venue
- SIAM Journal on Matrix Analysis and Applications
- Published
- 1999-01
- Volume
- 20
- Issue
- 3
- Pages
- 720-755
- ISSN
- 0895-4798 (ISSN-L)
- 1095-7162
- OpenAlex
- W2038205735
- Cited by
- 840
- References
- 0
- FWCI
- 25.24
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: A Supernodal Approach to Sparse Partial Pivoting. https://app.cochat.ai/papers/10.1137/s0895479895291765
- The paper
- Demmel, J. W., Eisenstat, S. C., Gilbert, J. R., Li, X. S., & Liu, J. W. H. (1999). A Supernodal Approach to Sparse Partial Pivoting. SIAM Journal on Matrix Analysis and Applications. https://doi.org/10.1137/s0895479895291765
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