Efficient and optimal parallel algorithms for cholesky decomposition

Journal of Mathematical Modelling and Algorithms

Volumn 2, Issue 3, 2003, Pages 217-234

  Santos, Eunice E ^a   Chu, Pei Yue ^b  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

^b Lehigh University   (United States)

Author keywords

Algorithms and complexity; Cholesky decomposition; LogP model; Numerical linear algebra; Parallel complexity

Indexed keywords

EID: 78049308441     PISSN: 15701166     EISSN: 15729214     Source Type: Journal    
DOI: 10.1023/B:JMMA.0000015832.41014.ed     Document Type: Article

References (20)

1. Agarwal, R. C., Gustavson, F. G. and Zubair, M.: Improving performance of linear algebra algorithms for dense matrices using algorithmic prefetch, IBM J. Res. Develop. 38(3) (1994), 265-275.
2. Arioli, M., Duff, I. S., Noailles, J. and Ruiz, D.: A block projection method for sparse matrices, SIAM J. Sci. Statist. Comput. 13 (1992), 47-70.
3. Ashcraft, C.: The fan-both family of column-based distributed Cholesky factorization algorithms, Technical Report ECA-TR-208, Boeing Computer Services, 1992.
4. Culler, D., Karp, R., Patterson, D., Sahay, A., Santos, E. E., Schauser, K., Subramonian, R. and von Eicken, T.: LogP: A practical model for parallel computation, Comm. ACM 37(11) (1996).
5. Demmel, J. W., Heath, M. T. and van der Vorst, H. A.: Parallel numerical linear algebra, Acta Numer. 2 (1993).
6. Dongarra, J. J., Gustavson, F. G. and Karp, A.: Implementing linear algebra algorithms for dense matrices on a vector pipeline machine, SIAM Rev. 26 (1986), 91-112.
7. Dumitrescu, B., Doreille, M., Roch, J. L. and Trystram, D.: Two-dimensional block partitioning for the parallel sparse Cholesky factorization, Numer. Algorithms 16 (1997), 17-38.
8. Edelman, A.: Large dense numerical linear algebra in 1993: The parallel computing influence, Int. J. Supercomput. Appl. 7 (1994).
9. Eswar, K., Huang, C.-H. and Sadayappan, P.: On mapping data and computation for parallel sparse Cholesky factorization, Proceedings of the Fifth Symposium on the Frontiers of Massively Parallel Computation, 1995.
10. Gravannis, G. A.: Explicit preconditioned methods for solving 3D boundary value problems by approximate inverse finite element matrix techniques, Int. J. Comp. Math. 56 (1995).
11. Gravvanis, G. A.: A three-dimensional symmetric linear equation solver, Comm. Numer. Methods Engrg. 10(9) (1994).
12. Gustavson, F. G.: Recursive leads to automatic variable blocking for dense linear-algebra algorithms, IBM J. Res. Develop. 41(6) (Nov. 1997).
13. Lichtenstein, W. and Johnsson, S. L.: Block-cyclic dense linear algebra, SIAM J. Sci. Comput. 14(6) (1993).
14. Ng, E. G. and Peyton, B. W.: Block sparse Cholesky algorithms on advanced uniprocessor computers, SIAM J. Sci. Statist. Comput. 14 (1993), 1034-1056.
15. Ortega, J. M.: Introduction to Parallel and Vector Solutions of Linear Systems, Plenum Press, New York, 1988.
16. Rothberg, E. and Gupta, A.: The performance impact of data reuse in parallel dense Cholesky factorization, Technical Report CS-TR-92-1401, Stanford University, Jan. 1992.
17. Rothberg, E. and Gupta, A.: An efficient block-oriented approach to parallel sparse Cholesky factorization, SIAM J. Sci. Comput. 15(6) (1994), 1413-1439.
18. Santos, E. E. and Chu, P.: Efficient parallel algorithms for dense Cholesky factorizition, In: Lecture Notes in Comput. Sci. 1557, Springer, New York, 1999, pp. 600-602.
19. Santos, E. E. and Chu, P.: Optimal and efficient parallel algorithms for dense Cholesky decomposition, Technical Report LCID-03-102, Laboratory for Computation, Information, & Distributed Processing, Virginia Polytechnic Institute & State University, 2003.
20. Strazdins, P. E.: High performance dense linear systems solution on a beowulf cluster, In: 5th International Conference on High Performance Computing in Asia, 2001.