SUMMA: Scalable universal matrix multiplication algorithm

Concurrency Practice and Experience

Volumn 9, Issue 4, 1997, Pages 255-274

  Van De Geijn, R A ^a   Watts, J ^b  

^a University of Texas at Austin   (United States)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; MATRIX ALGEBRA;

MESSAGE PASSING INTERFACE (MPI) IMPLEMENTATIONS;

PARALLEL ALGORITHMS;

EID: 0031123769     PISSN: 10403108     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1096-9128(199704)9:4<255::AID-CPE250>3.0.CO;2-2     Document Type: Article

References (23)

1. G. H. Golub and C. F. Van Loan, Matrix Computations, Johns Hopkins University Press, 2nd edn., 1989.
2. L. E. Cannon, A Cellular Computer to Implement the Kalman Filter Algorithm, Ph.D. thesis, Montana State University, 1969.
3. G. C. Fox, M. A. Johnson, G. A. Lyzenga, S. W. Otto, J. K. Salmon and D. W. Walker, Solving Problems on Concurrent Processors, vol. 1, Prentice Hall, Englewood Cliffs, N.J., 1988.
4. G. Fox, S. Otto and A. Hey, 'Matrix algorithms on a hypercube I: matrix multiplication', Parallel Comput., 3, 17-31 (1987).
5. C. Lin and L. Snyder, 'A matrix product algorithm and its comparative performance on hypercubes', in Q. Stout and M. Wolfe (Eds.) Proceedings of Scalable High Performance Computing Conference, IEEE Press, Los Alamitos, CA, 1992, pp. 190-193.
6. J. Choi, J. J. Dongarra and D. W. Walker, 'PUMMA: Parallel universal matrix multiplication algorithms on distributed memory concurrent computers', Concurrency, Pract. Exp., 6, (7), 543-570 (1994).
7. S. Huss-Lederman, E. Jacobson and A. Tsao, 'Comparison of scalable parallel matrix multiplication libraries', in Proceedings of the Scalable Parallel Libraries Conference, Starksville, MS, Oct. 1993.
8. S. Huss-Lederman, E. Jacobson, A. Tsao and G. Zhang, 'Matrix multiplication on the Intel Touchstone DELTA', Concurrency, Pract. Exp., 6, (7), 571-594 (1994).
9. W. Gropp, E. Lusk and A. Skjellum, Using MPI: Portable Programming with the MessagePassing Interface, The MIT Press, 1994.
10. R. C. Agarwal, F. Gustavson and M. Zubair, 'A high-performance matrix multiplication algorithm on a distributed memory parallel computer using overlapped communication', IBM J. Res. Dev., 38, (6), (1994).
11. K. Klimkowski and R. van de Geijn, 'Anatomy of a parallel out-of-core dense linear solver', Vol III - Algorithms and applications, Proceedings of the 1995 International Conference on Parallel Processing, pp. 29-33.
12. J. J. Dongarra, J. Du Croz, S. Hammarling and I. Duff, 'A set of level 3 basic linear algebra subprograms', TOMS, 16, (1), 1-16 (1990).
13. M. Barnett, S. Gupta, D. Payne, L. Shuler, R. van de Geijn and J. Watts, 'Interprocessor collective communication library (InterCom)', Scalable High Performance Computing Conference 1994.
14. M. Barnett, D. G. Payne, R. van de Geijn and J. Watts, 'Broadcasting on meshes with worm-hole routing', J. Parallel Distrib. Comput., 35, (2), 111-122 (1996).
15. J. Watts and R. van de Geijn, 'A pipelined broadcast for multidimensional meshes', Parallel Process. Lett., 5, (2), 281-292 (1995).
16. A. Chtchelkanova, J. Gunnels, G. Morrow, J. Overfelt and R. van de Geijn, 'Parallel implementation of BLAS: General techniques for level 3 BLAS', TR-95-40, Department of Computer Sciences, University of Texas, October 1995.
17. J. J. Dongarra, R. A. van de Geijn and D. W. Walker, 'Scalability issues affecting the design of a dense linear algebra library', J. Parallel Distrib. Comput., 22, (3), 523-537 (1994).
18. E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. DuCroz, A. Greenbaum, S. Hammarling, A. McKenney and D. Sorensen, 'Lapack: A portable linear algebra library for high performance computers', Proceedings of Supercomputing '90, IEEE Press, 1990, pp. 1-10.
19. E. Anderson, Z. Bai, J. Demmel, J. Dongarra, J. DuCroz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov and D. Sorensen, LAPACK Users' Guide, SIAM, Philadelphia, 1992.
20. J. Choi, J. J. Dongarra, R. Pozo and D. W. Walker, 'Scalapack: A scalable linear algebra library for distributed memory concurrent computers', Proceedings of the Fourth Symposium on the Frontiers of Massively Parallel Computation, IEEE Comput. Soc. Press, 1992, pp. 120-127.
21. J. Choi, J. J. Dongarra and D. W. Walker, 'Level 3 BLAS for distributed memory concurrent computers', CNRS-NSF Workshop on Environments and Tools for Parallel Scientific Computing, Saint Hilaire du Touvet, France, Sept. 7-8, 1992, Elsevier Science Publishers, 1992.
22. J. J. Dongarra, I. S. Duff, D. C. Sorensen and H. A. van der Vorst, Solving Linear Systems on Vector and Shared Memory Computers, SIAM, Philadelphia, 1991.
23. C.-T. Ho and S. L. Johnsson, 'Distributed routing algorithms for broadcasting and personalized communication in hypercubes', in Proceedings of the 1986 International Conference on Parallel Processing, IEEE, 1986, pp. 640-648.