The DOI matches its Crossref record; 27 of the 27 references it cites were found in a registry or an index.
A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
Abstract
A new method for sparse LU factorization is presented that combines a column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The column ordering is selected to give a good a priori upper bound on fill-in and then refined during numerical factorization (while preserving the bound). Pivot rows are selected to maintain numerical stability and to preserve sparsity. The method analyzes the matrix and automatically selects one of three pre-ordering and pivoting strategies. The number of nonzeros in the LU factors computed by the method is typically less than or equal to those found by a wide range of unsymmetric sparse LU factorization methods, including left-looking methods and prior multifrontal methods.
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Cites
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
Karypis, G., & Kumar, V. (1998) · SIAM Journal on Scientific Computing · doi:10.1137/s1064827595287997 · Cited by 5,762
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
Amestoy, P. R., Duff, I. S., L'Excellent, J.-Y., & Koster, J. (2001) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479899358194 · Cited by 2,287
Computer Solution of Large Sparse Positive Definite Systems.
Pasciak, J. E., George, A., & Liu, J. W. (1982) · Mathematics of Computation · doi:10.2307/2007640 · Cited by 1,874
A set of level 3 basic linear algebra subprograms
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Direct Methods for Sparse Matrices
Duff, I. S., Erisman, A. M., & Reid, J. K. (2017) · doi:10.1093/acprof:oso/9780198508380.001.0001 · Cited by 1,604
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
Davis, T. A. (2004) · ACM Transactions on Mathematical Software · doi:10.1145/992200.992206 · Cited by 1,422
Self-citationA Supernodal Approach to Sparse Partial Pivoting
Demmel, J. W., Eisenstat, S. C., Gilbert, J. R., Li, X. S., & Liu, J. W. H. (1999) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479895291765 · Cited by 840
An Approximate Minimum Degree Ordering Algorithm
Amestoy, P. R., Davis, T. A., & Duff, I. S. (1996) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479894278952 · Cited by 731
Self-citationSparse Matrices in MATLAB: Design and Implementation
Gilbert, J. R., Moler, C., & Schreiber, R. (1992) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/0613024 · Cited by 591
An Unsymmetric-Pattern Multifrontal Method for Sparse LU Factorization
Davis, T. A., & Duff, I. S. (1997) · SIAM Journal on Matrix Analysis and Applications · doi:10.1137/s0895479894246905 · Cited by 520
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Cited by
On the spatial statistics of optical flow
Roth, S., & Black, M. J. (2005) · Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 · doi:10.1109/iccv.2005.180 · Cited by 95
Metadata
- Authors
- Davis, T. A.
- Venue
- ACM Transactions on Mathematical Software
- Published
- 2004-06
- Volume
- 30
- Issue
- 2
- Pages
- 165-195
- ISSN
- 0098-3500 (ISSN-L)
- 1557-7295
- OpenAlex
- W1987902628
- Cited by
- 419
- References
- 27
- FWCI
- 19.05
- Type
- journal article
- Language
- en
- Open access
- closed
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