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An Approximate Minimum Degree Ordering Algorithm
Abstract
Abstract. An approximate minimum degree (AMD), ordering algorithm for preordering a symmetric sparse matrix prior to numerical factorization is presented. We use techniques based on the quotient graph for matrix factorization that allow us to obtain computationally cheap bounds for the minimum degree. We show that these bounds are often equal to the actual degree. The resulting algorithm is typically much faster than previous minimum degree ordering algorithms and produces results that are comparable in quality with the best orderings from other minimum degree algorithms.
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Cited by
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
Square Root SAM: Simultaneous Localization and Mapping via Square Root Information Smoothing
Dellaert, F., & Kaess, M. (2006) · The International Journal of Robotics Research · doi:10.1177/0278364906072768 · Cited by 922
Andersen, E. D., & Andersen, K. D. (2000) · Applied Optimization · doi:10.1007/978-1-4757-3216-0_8 · Cited by 766
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
A 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
Self-citation
Metadata
- Authors
- Amestoy, P. R., Davis, T. A., & Duff, I. S.
- Venue
- SIAM Journal on Matrix Analysis and Applications
- Published
- 1996-10
- Volume
- 17
- Issue
- 4
- Pages
- 886-905
- ISSN
- 0895-4798 (ISSN-L)
- 1095-7162
- OpenAlex
- W2014730252
- Cited by
- 731
- References
- 0
- FWCI
- 21.13
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: An Approximate Minimum Degree Ordering Algorithm. https://app.cochat.ai/papers/10.1137/s0895479894278952
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- Amestoy, P. R., Davis, T. A., & Duff, I. S. (1996). An Approximate Minimum Degree Ordering Algorithm. SIAM Journal on Matrix Analysis and Applications. https://doi.org/10.1137/s0895479894278952
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