Updating an LU factorization with pivoting

ACM Transactions on Mathematical Software

Volumn 35, Issue 2, 2008, Pages 1-16

  Quintana Ortí, Enrique S ^a   Van De Geijn, Robert A ^b  

^a UNIVERSITAT JAUME I   (Spain)

^b University of Texas at Austin   (United States)

Author keywords

Linear systems; LU factorization; Pivoting; Updating

Indexed keywords

FACTORIZATION; LINEAR ALGEBRA; LINEAR SYSTEMS;

FORMAL LINEAR ALGEBRA METHODS ENVIRONMENTS; INTEL ITANIUM2; LU FACTORIZATION; PIVOTING; SUBMATRIX; UPDATING;

APPLICATION PROGRAMMING INTERFACES (API);

EID: 48849086742     PISSN: 00983500     EISSN: 15577295     Source Type: Journal    
DOI: 10.1145/1377612.1377615     Document Type: Article

References (23)

1. BIENTINESI, P., GUNNELS, J. A., MYERS, M. E., QUINTANA-ORTÍ, E. S., AND VAN DE GEIJN, R. A. 2005. The science of deriving dense linear algebra algorithms. ACM Trans. Math. Softw. 31, 1 (Mar.), 1-26.
2. BIENTINESI, P. AND VAN DE GEIJN, R. 2006. Representing dense linear algebra algorithms: A farewell to indices. Tech. Rep. FLAME Working Note 17, CS-TR-2006-10, Department of Computer Sciences, The University of Texas at Austin.
3. CWIK, T., VAN DE GEIJN, R., AND PATTERSON, J. 1994. The application of parallel computation to integral equation models of electromagnetic scattering. J. Optic. Soc. Amer. A 11, 4 (Apr.), 1538-1545.
4. DEMMEL, J. AND DONGARRA, J. 2005. LAPACK 2005 prospectus: Reliable and scalable software for linear algebra computations on high end computers. LAPACK Working Note 164 UT-CS-05-546, University of Tennessee. February.
5. GENG, P., ODEN, J. T., AND VAN DE GEIJN, R. 1996. Massively parallel computation for acoustical scattering problems using boundary element methods. J. Sound Vibra. 191, 1, 145-165.
6. GOTO, K. 2004. TACC software and tools. http://www.tacc.utexas. edu/resources/software/.
7. GOTO, K. AND VAN DE GEIJN, R. A. 2008. Anatomy of a high-performance matrix multiplication. ACM Trans. Math. Softw. 34, 3 (to appear).
8. GUNNELS, J. A., HENRY, G. M., AND VAN DE GEIJN, R. A. 2001. A family of high-performance matrix multiplication algorithms. In Proceedings of the International Conference on Computational Science (ICCS), Part I, V. N. Alexandrov et al., eds. Lecture Notes in Computer Science, vol. 2073. Springer, 51-60.
9. GUNTER, B. AND VAN DE GEIJN, R. 2005. Parallel out-of-core computation and updating of the QR factorization. ACM Trans. Math. Softw. 31, 1 (Mar.), 60-78.
10. GUSTAVSON, F., HENRIKSSON, A., JONSSON, I., K̊AGSTRÖM, B., AND LING, P. 1998. Superscalar GEMM-based level 3 BLAS - The on-going evolution of a portable and high-performance library. In Proceedings of the Workshop Applied Parallel Computing (PARA), Large Scale Scientific and Industrial Problems, B. K. et al., eds. Lecture Notes in Computer Science, vol. 1541. Springer, 207-215.
11. HIGHAM, N. J. 2002. Accuracy and Stability of Numerical Algorithms, 2nd ed. Society for Industrial and Applied Mathematics, Philadelphia, PA.
12. JOFFRAIN, T., QUINTANA-ORTÍ, E. S., AND VAN DE GEIJN, R. A. 2005. Rapid development of high-performance out-of-core solvers. In Proceedings of the Workshop on Applied Parallel Computing (PARA 2004), J. Dongarra et al., eds. Lecture Notes in Computer Science, vol. 3732. Springer, 413-422.
13. K̊AGSTRÖM, B., LING, P., AND LOAN, C. V. 1995. Gemm-Based level 3 blas: High-Performance model, implementations and performance evaluation benchmark. LAPACK Working Note no. 107 CS-95-315, University of Tennessee. November.
14. K̊AGSTRÖM, B., LING, P., AND LOAN, C. V. 1998. GEMM-Based level 3 BLAS: High performance model implementations and performance evaluation benchmark. ACM Trans. Math. Softw. 24, 3, 268-302.
15. KLIMKOWSKI, K. AND VAN DE GEIJN, R. 1995. Anatomy of an out-of-core dense linear solver. In Proceedings of the International Conference on Parallel Processing. vol. III - Algorithms and Applications, 29-33.
16. SORENSEN, D. C. 1985. Analysis of pairwise pivoting in Gaussian elimination. IEEE Trans. Comput. C-34, 3, 274-278.
17. STEWART, G. W. 1998. Matrix Algorithms. Volume I: Basic Decompositions. SIAM, Philadelphia, PA.
18. TOLEDO, S. 1997. Locality of reference in LU decomposition with partial pivoting. SIAM J. Matrix Anal. Appl. 18, 4, 1065-1081.
19. TOLEDO, S. 1999. A survey of out-of-core algorithms in numerical linear algebra. In External Memory Algorithms and Visualization, J. Abello and J. S. Vitter, eds. American Mathematical Society Press, Providence, RI, 161-180.
20. TOLEDO, S. AND GUSTAVSON, F. 1996. The design and implementation of SOLAR, a portable library for scalable out-of-core linear algebra computations. In Proceedings of the 4th Workshop on I/O in Parallel and Distributed Systems, 28-40.
21. TREFETHEN, L. N. AND SCHREIBER, R. S. 1990. Average-Case stability of Gaussian elimination. SIAM J. Matrix Anal. Appl. 11, 3, 335-360.
22. WILKINSON, J. H. 1965. The Algebraic Eigenvalue Problem. Oxford University Press, London.
23. YIP, E. L. 1979. Fortran subroutines for out-of-core solutions of large complex linear systems. Tech. Rep. CR-159142, NASA.