Cited by 467Matrix Theory and AlgorithmsParallel Computing and Optimization TechniquesAdvanced Optimization Algorithms Research

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An overview of SuperLU: Algorithms, implementation, and user interface

Li, Xiaoye S.·2005·ACM Transactions on Mathematical Software

Abstract

We give an overview of the algorithms, design philosophy, and implementation techniques in the software SuperLU, for solving sparse unsymmetric linear systems. In particular, we highlight the differences between the sequential SuperLU (including its multithreaded extension) and parallel SuperLU_DIST. These include the numerical pivoting strategy, the ordering strategy for preserving sparsity, the ordering in which the updating tasks are performed, the numerical kernel, and the parallelization strategy. Because of the scalability concern, the parallel code is drastically different from the sequential one. We describe the user interfaces of the libraries, and illustrate how to use the libraries most efficiently depending on some matrix characteristics. Finally, we give some examples of how the solver has been used in large-scale scientific applications, and the performance.

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Research works printed but not linked: 31

  1. Alvarado F. L. Pothen A. and Schreiber R. 1993. Highly parallel sparse triangular solution. In Graph Theory and Sparse Matrix Computation A. George J. R. Gilbert and J. W. Liu Eds. Springer-Verlag New York NY 159--190. Alvarado F. L. Pothen A. and Schreiber R. 1993. Highly parallel sparse triangular solution. In Graph Theory and Sparse Matrix Computation A. George J. R. Gilbert and J. W. Liu Eds. Springer-Verlag New York NY 159--190. · DOI
  2. 10.1137/S0895479894278952 · DOI
  3. Anderson E. Bai Z. Bischof C. Blackford S. Demmel J. Dongarra J. Du Croz J. Greenbaum A. Hammarling S. McKenney A. and Sorensen D. 1999. LAPACK Users' Guide Release 3.0. SIAM Press Philadelphia PA. Anderson E. Bai Z. Bischof C. Blackford S. Demmel J. Dongarra J. Du Croz J. Greenbaum A. Hammarling S. McKenney A. and Sorensen D. 1999. LAPACK Users' Guide Release 3.0. SIAM Press Philadelphia PA. · DOI
  4. Arioli M., 1989, Solving sparse linear systems with sparse backward error, SIAM J. Matrix Anal. Appl., 10, 2, 10.1137/0610013 · DOI
  5. Ashcraft C., Proceedings of the Ninth SIAM Conference on Parallel Processing for Scientific Computing
  6. Baertschy M., 2034, Proceedings of SC2001: High Performance Networking and Computing Conference
  7. Baertschy M., 2001, Electron-impact ionization of atomic hydrogen, Phys. Rev. A, 63, 022712, 10.1103/PhysRevA.63.022712 · DOI
  8. Baertschy M., 2001, Accurate amplitudes for electron-impactionization, Phys. Rev. Lett., 64, 022709
  9. 10.1145/1024074.1024079 · DOI
  10. Demmel J. W. 1997. Applied Numerical Linear Algebra. SIAM Press Philadelphia PA. Demmel J. W. 1997. Applied Numerical Linear Algebra. SIAM Press Philadelphia PA. · DOI
  11. 10.1137/S0895479895291765 · DOI
  12. 10.1137/S0895479897317685 · DOI
  13. Demmel J. W. Gilbert J. R. and Li X. S. 1999c. SuperLU users' guide. Tech. rep. LBNL-44289. Lawrence Berkeley National Laboratory Berkeley CA. Software is available online at http://crd.lbl.gov/~xiaoye/SuperLU. Demmel J. W. Gilbert J. R. and Li X. S. 1999c. SuperLU users' guide. Tech. rep. LBNL-44289. Lawrence Berkeley National Laboratory Berkeley CA. Software is available online at http://crd.lbl.gov/~xiaoye/SuperLU. · DOI
  14. 10.1137/S0895479897317661 · DOI
  15. 10.1137/0613017 · DOI
  16. 10.1137/0909008 · DOI
  17. 10.1137/0908072 · DOI
  18. Gilbert J. R., 1988, Sparse partial pivoting in time proportional to arithmetic operations, SIAM J. Sci. Stat. Comput., 9, 862, 10.1137/0909058 · DOI
  19. Grigori L., Proceedings of SC2002
  20. Hendrickson B. and Leland R. 1993. The CHACO user's guide version 1.0. Tech. rep. SAND93-2339 &bul1; UC-405. Sandia National Laboratories Albuquerque NM. Available online at http://www.cs.sandia.gov/~bahendr/chaco.html. Hendrickson B. and Leland R. 1993. The CHACO user's guide version 1.0. Tech. rep. SAND93-2339 &bul1; UC-405. Sandia National Laboratories Albuquerque NM. Available online at http://www.cs.sandia.gov/~bahendr/chaco.html. · DOI
  21. Higham N. J. 1996. Accuracy and Stability of Numerical Algorithms. SIAM Press Philadelphia PA. Higham N. J. 1996. Accuracy and Stability of Numerical Algorithms. SIAM Press Philadelphia PA.
  22. Husbands P., SIAM Annual Meeting (June) Montreal, P.Q., Canada.
  23. Li X. S., Proceedings of SC98: High Performance Networking and Computing Conference
  24. 10.1145/779359.779361 · DOI
  25. 10.1145/567806.567808 · DOI
  26. Li X. S. and Wang Y. 2003. Performance evaluation and enhancement of SuperLU_DIST 2.0. Tech. rep. LBNL-53624. Lawrence Berkeley National Laboratory Berkeley CA. Li X. S. and Wang Y. 2003. Performance evaluation and enhancement of SuperLU_DIST 2.0. Tech. rep. LBNL-53624. Lawrence Berkeley National Laboratory Berkeley CA. · DOI
  27. 10.1145/214392.214398 · DOI
  28. Markowitz H. M., 1957, The elimination form of the inverse and its application to linear programming, Management Sci., 3, 255, 10.1287/mnsc.3.3.255 · DOI
  29. Oettli W., 1964, Compatibility of approximate solution of linear equations with given error bounds for coefficients and right hand sides, Num. Math., 6, 405, 10.1007/BF01386090 · DOI
  30. Rescigno T. N., 1999, Collisional breakup in a quantum system of three charged particles, Science, 286, 5449, 10.1126/science.286.5449.2474 · DOI
  31. Sun Y. 2003. The filter algorithm for solving large-scale eigenproblems from accelerator simulations. Ph.D. dissertation. Department of Computer Science Stanford University Stanford CA. Sun Y. 2003. The filter algorithm for solving large-scale eigenproblems from accelerator simulations. Ph.D. dissertation. Department of Computer Science Stanford University Stanford CA.

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Metadata

Authors
Li, X. S.
Corresponding author
Li, Xiaoye S.
Venue
ACM Transactions on Mathematical Software
Published
2005-09
Volume
31
Issue
3
Pages
302-325
ISSN
  • 0098-3500 (ISSN-L)
  • 1557-7295
OpenAlex
W1970009422
Cited by
467
References
0
Citations by year
2026: 24 · 2025: 24 · 2024: 30 · 2023: 31 · 2022: 33 · 2021: 28 · 2020: 38 · 2019: 43 · 2018: 37 · 2017: 38 · 2016: 28 · 2015: 31 · 2014: 21 · 2013: 14 · 2012: 14
FWCI
5.42
Type
journal article
Language
en
Open access
closed
Locations
ACM Transactions on Mathematical Software (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
  • Physical Sciences › Computer Science › Hardware and Architecture › Parallel Computing and Optimization Techniques
  • Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
Keywords
SuperLU, sparse LU factorization, sparse matrix reordering, parallel linear solvers, solver scalability

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Li, X. S. (2005). An overview of SuperLU: Algorithms, implementation, and user interface. ACM Transactions on Mathematical Software. https://doi.org/10.1145/1089014.1089017