Multifrontal QR factorization in a multiprocessor environment

Numerical Linear Algebra with Applications

Volumn 3, Issue 4, 1996, Pages 275-300

  Amestoy, P R ^a   Duff, I S ^b,c   Puglisi, C ^c  

^a IRIT   (France)

^b RUTHERFORD APPLETON LABORATORY   (United Kingdom)

^c CERFACS   (France)

Author keywords

Multifrontal method; Parallelism; Sparse QR factorization

Indexed keywords

EID: 21344466930     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1506(199607/08)3:4<275::AID-NLA83>3.0.CO;2-7     Document Type: Article

References (27)

1. P. R. Amestoy. Factorization of large sparse matrices based on a multifrontal approach in a multiprocessor environment. Phd thesis, Institut National Polytechnique de Toulouse, 1991. Available as CERFACS report TH/PA/91/2.
2. P. R. Amestoy, M. J. Daydé and I. S. Duff. Use of Level 3 BLAS kernels in the solution of full and sparse linear equations. Proceedings of the European Symposium on High Performance Computing, pages 19-31. Elsevier Science Publishers B.V., 1989.
3. P. R. Amestoy and I. S. Duff. Memory allocation issues in sparse multiprocessor multifrontal methods. Int Journal of Supercomputer Applications, 7, 64-82, 1993.
4. J. H. Argyris and O. E. Bronlund. The natural factor formulation of the stiffness for the matrix displacement method. Comput. Meth. Appl. Mech. Engrg., 5,97-119, 1975.
5. T. F. Coleman, A. Edenbrandt and J. R. Gilbert. Predicting fill for sparse orthogonal factorization. Journal of the Association for Computing Machinery, 33, 517-532, 1986.
6. K. Dackland, E. Elmroth and B. Kågström. Parallel block matrix factorizations on the shared-memory multiprocessor IBM 3090 VF/600J. Int Journal of Supercomputer Applications, 6, 69-97, 1992.
7. I. S. Duff. Pivot selection and row orderings in Givens reduction on sparse matrices. Computing, 13, 239-248, 1974.
8. I. S. Duff. Full matrix techniques in sparse Gaussian elimination. In G. Watson, editor, Numerical Analysis Proceedings, Dundee 1981, Lecture Notes in Mathematics 912, pages 71-84. Springer-Verlag, Berlin, 1981.
9. I. S. Duff. Parallel implementation of multifrontal schemes. Parallel Computing, 3, 193-204, 1986.
10. I. S. Duff. Multiprocessing a sparse matrix code on the Alliant FX/8. J. Comput. Appl. Math., 27, 229-239, 1989.
11. I. S. Duff and J. K. Reid. The multifrontal solution of indefinite sparse symmetric linear systems. ACM Transactions on Mathematical Software, 9, 302-325, 1983.
12. I. S. Duff and J. K. Reid. The multifrontal solution of unsymmetric sets of linear systems. SIAM Journal on Scientific and Statistical Computing, 5, 633-641, 1984.
13. W. M. Gentleman. Row elimination for solving sparse linear systems and least squares problems. In Proceedings of the 6th Dundee Conference on Numerical Analysis, pages 122-133. Springer Verlag, 1976.
14. J. A. George and M. T. Heath. Solution of sparse linear least squares problems using Givens rotations. Linear Algebra and its Applications, 34, 69-83, 1980.
15. J. A. George and J. H. W. Liu. Householder reflections versus Givens rotations in sparse orthogonal decomposition. Linear Algebra and its Applications, 88/89, 223-238, 1987.
16. M. Hegland. Description and use of animal breeding data for large least squares problems. Technical Report TR/PA/93/50, CERFACS, Toulouse, France, 1993.
17. A. Hofer. Schätzung von Zuchtwerten feldgeprüfter Schweine mit einem Mehrmerkmals-Tiermodell. PhD thesis, EHT-Zurich, 1990.
18. J. G. Lewis, D. J. Pierce and D. C. Wah. A multifrontal Householder QR factorization. Technical Report ECA-TR-127, Engineering and Scientific Services Division, Boeing Computer Services, 1989.
19. J. H. W. Liu. On general row merging schemes for sparse Givens transformations. SIAM Journal on Scientific and Statistical Computing, 7, 1190-1211, 1986.
20. J. H. W. Liu. The role of elimination trees in sparse factorization. SIAM Journal on Matrix Analysis and Applications, 11, 134-172, 1990.
21. P. Matstoms. Sparse QR Factorization with Applications to Linear Least Squares Problems. PhD thesis, Linköping University, 1994.
22. P. Matstoms. Parallel sparse QR factorization on shared memory architectures. Parallel Computing, 21, 473-486, 1995.
23. C. Puglisi. Modification of the Householder method based on the compact WY representation. SIAM Journal on Scientific and Statistical Computing, 13, 723-726, 1992.
24. C. Puglisi. QR Factorization of large sparse overdetermined and square matrices using a multifrontal method in a multiprocessor environment. Phd thesis, Institut National Polytechnique de Toulouse, 1993. Available as CERFACS report TH/PA/93/33.
25. J. K. Reid. A note on the least squares solution of a band system of linear equations by Householder reductions. The Computer J., 10, 188-189, 1967.
26. R. Schreiber and C. F. Van Loan. A storage efficient WY representation for products of Householder transformations. SIAM J. Sci. Stat. Comput., 10, 53-57, 1989.
27. R. S. Schreiber. A new implementation of sparse Gaussian elimination. ACM Transactions on Mathematical Software, 8, 256-276, 1982.