Scalability issues affecting the design of a dense linear algebra library

Journal of Parallel and Distributed Computing

Volumn 22, Issue 3, 1994, Pages 523-537

  Dongarra, Jack J ^a,b   Vandegeijn, Robert A ^c   Walker, David W ^b  

^a UNIVERSITY OF TENNESSEE   (United States)

^b OAK RIDGE NATIONAL LABORATORY   (United States)

^c UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000778168     PISSN: 07437315     EISSN: None     Source Type: Journal    
DOI: 10.1006/jpdc.1994.1108     Document Type: Article

References (49)

1. Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J. J., DuCroz, J., Greenbaum, A., Hammarling, S., McKenney, A., and Sorensen, D. Lapack: A portable linear algebra library for high-performance computers. Proceedings of Supercomputing '90, IEEE Press, 1990. pp. 1-10.
2. Anderson, E., Bai, Z., Demmel, J., Dongarra, J., DuCroz, J., Greenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., and Sorensen, D. LAPACK Users' Guide. SIAM, Philadelphia, 1992.
3. Anderson, E., Benzoni, A., Dongarra, J., Moulton, S., Ostrouchov, S., Tourancheau, B., and van de Geijn, R. Basic linear algebra communication subprograms. Sixth Distributed Memory Computing Conference Proceedings. IEEE Comput. Soc. Press. 1991, pp. 287-290.
4. Anderson, E., Benzoni, A., Dongarra, J. J., Moulton, S., Ostrouchov, S., Tourancheau, B., and van de Geijn, R. LAPACK for distributed memory architectures: Progress report. Parallel Processing for Scientific Computing, Fifth SIAM Conference. SIAM, 1991.
5. Ashcraft, C. C. The distributed solution of linear systems using the torus wrap data mapping. Engineering Computing and Analysis Technical Report ECA-TR-147, Boeing Computer Services. 1990.
6. Ashcraft, C. C. A taxonomy of distributed dense LU factorization methods. Engineering Computing and Analysis Technical Report ECA-TR-161, Boeing Computer Services. 1991.
7. Bai, Z., and Demmel, J. Design of a parallel nonsymmetric eigenroutine toolbox. In Sincovec, R. (Ed.), Proceedings of Sixth SIAM Conference on Parallel Processing for Scientific Computing. SIAM Press, 1993.
8. Bailey, D. H., Lee, K., and Simon, H. D. Using Strassen’s algorithm to accelerate the solution of linear systems. J. Supercomputing 4 (1990), 357-371.
9. Brent, R. P. The LINPACK benchmark on the AP 1000: Preliminary report. Proceedings of the 2nd CAP Workshop. Nov. 1991.
10. Choi, J., Dongarra, J. J., Pozo, R., and Walker, D. W. 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.
11. Choi, J., Dongarra, J. J., and Walker, D. W. The design of scalable software libraries for distributed memory concurrent computers. Proceedings of the CNRS-NSF Workshop on Environments and Tools for Parallel Scientific Computing. Elsevier, Amsterdam, 1993.
12. Cwik, T., Patterson, J., and Scott, D. Electromagnetic scattering calculations on the Intel Touchstone Delta. Proceedings of Supercomputing '92. IEEE Comput. Soc. Press, 1992. pp. 538-542.
13. Demmel, J., Dongarra, J. J., Du Croz, J., Greenbaum, A., Hammarling, S., and Sorensen, D. Prospectus for the development of a linear algebra library for high performance computers. Technical Report 97, Argonne National Laboratory, Mathematics and Computer Science Division, Sept. 1987.
14. Dongarra, J. J. LINPACK benchmark: Performance of various computers using standard linear equations software. Supercomputing Rev. 5, 3 (March 1992), 54-63.
15. Dongarra, J. J., Bunch, J., Moler, C., and Stewart, G. W. LINPACK User's Guide. SIAM, Philadelphia, 1979.
16. Dongarra, J. J., Du Croz, J., Duff, L. and Hammarling, S. A proposal for a set of level 3 basic linear algebra subprograms. Technical Report 88, Argonne National Laboratory. Mathematics and Computer Science Division, Apr. 1987.
17. Dongarra, J. J., Duff, L, Du Croz, J., and Hammarling, S. A set of level 3 basic linear algebra subprograms. ACM Trans. Math. Software 16 (March 1990), 1-17.
18. Dongarra, J. J., Duff, I. S., Sorensen, D. C., and van der Vorst, H. A. Solving Linear Systems on Vector and Shared Memory Computers. SIAM, Philadelphia, 1990.
19. Dongarra, J. J., Hempel, R., Hey, A. J. G., and Walker, D. W. A proposal for a user-level message passing interface in a distributed memory environment. Technical Report TM-12231. Oak Ridge National Laboratory. Feb. 1993.
20. Dongarra, J. J., and Ostrouchov, S. LAPACK block factorization algorithms on the Intel iPSC/860. Technical Report CS-90-115, University of Tennessee at Knoxville, Computer Science Department, Oct. 1990.
21. Dongarra, J. J., Pozo, R., and Walker, D. W. An object oriented design for high performance linear algebra on distributed memory architectures. Proceedings of Object Oriented Numerics Conference. 1993.
22. Dongarra, J. J., and van de Geijn, R. A. Two-dimensional basic linear algebra communication subprograms. Technical Report LAPACK working note 37, Computer Science Department, University of Tennessee. Knoxville, TN, Oct. 1991.
23. Dongarra, J. J. and van de Geijn, R. A. Reduction to condensed form for the eigenvalue problem on distributed memory architectures. Parallel Comput. 18 (1992), 973-982.
24. Dongarra, J. J., van de Geijn, R. A., and Walker, D. W. A look at scalable dense linear algebra libraries. InJ. H. Saltz (Ed.), Proceedings of the 1992 Scalable High Performance Computing Conference. IEEE Press, 1992.
25. Douglas, C. C., Heroux, M., Slishman, G., and Smith, R. M. GEMMW: A portable level 3 BLAS Winograd variant of Strassen's matrix-matrix multiply algorithm. J. Comput. Phys. 110 (1994), 1-10.
26. Edelman, A. Large dense numerical linear algebra in 1993: The parallel computing influence. Int. J. Supercomputing Appl. 7, 2 (1993).
27. Fox, G. C., Hiranandani, S., Kennedy, K., Koelbel, C., Kremer, U., Tseng, C-W., and Wu, M-Y. Fortran D language specification. Technical Report CRPC-TR90079. Center for Research on Parallel Computation, Rice University, Dec. 1990.
28. Fox, G. C., Johnson, M. A., Lyzenga, G. A., Otto, S. W., Salmon, J. K., and Walker, D. W. Solving Problems on Concurrent Processors. Vol. 1. Prentice-Hall, Englewood Cliffs, NJ, 1988.
29. Garbow, B. S., Boyle, J. M., Dongarra, J. J., and Moler, C. B. Matrix Eigensystem Routines—EISPACK Guide Extension. Lecture Notes in Computer Science. Vol. 51. Springer-Verlag, Berlin. 1977.
30. Geist, G. A., Heath, M. T., Peyton, B. W., and Worley, P. H. A user's guide to PICL: A portable instrumented communication library. Technical Report TM-11616, Oak Ridge National Laboratory, Oct. 1990.
31. Gupta, A., and Kumar, V. The scalability of FFT on parallel computers. IEEE Trans. Parallel Distrib. Systems 4, 7 (July 1993). A detailed version is available as Technical Report TR 90-53, Department of Computer Science, University of Minnesota. MN 55455.
32. Gustafson, J. Reevaluating Amdahl's law. Comm. ACM 31, 5 (1988), 532-533.
33. Gustafson, J., Rover, D., Elbert, S., and Carter, M. The design of a scalable, fixed-time computer benchmark. J. Parallel Distrib. Corn-put. 12 (1991), 388-401.
34. Hendrickson, B., and Womble, D. The torus-wrap mapping for dense matrix computations on massively parallel computers. Technical Report SAND92-0792, Sandia National Laboratories, Apr. 1992.
35. High Performance Fortran Forum. High Performance Fortran Language Specification, Version 0.4. Nov. 1992.
36. Higham, N. J. Exploiting fast matrix multiplication within the level 3 BLAS. ACM Trans. Math. Software 16, 4 (1990), 352-368.
37. Ho, C.-T., and Johnsson, S. L. Distributed routing algorithms for broadcasting and personalized communication in hypercubes. Proceedings of the 1986 International Conference on Parallel Processing. IEEE. 1986, pp. 640-648.
38. Hockney, R. W., and Jesshope, C. R. Parallel Computers. Hilger, Bristol, 1981.
39. Kumar, V., and Gupta, A. Analyzing scalability of parallel algorithms and architectures. Technical report, TR-91-18. Computer Science Department, University of Minnesota. June 1991. J. Parallel Distrib. Comput. 22, 3 (1994) 379-391. A short version of the paper appears in the Proceedings of the 1991 International Conference on Supercomputing. Germany, and as an invited paper in the Proceedings of the 29th Annual Allerton Conference on Communication, Control and Computing. Urbana, IL, Oct. 1991.
40. Lichtenstein, W., and Johnsson, S. L. Block-cyclic dense linear algebra. Technical Report TR-04-92. Harvard University. Center for Research in Computing Technology, Jan. 1992.
41. Saad, Y., and Schultz, M. H. Parallel direct methods for solving banded linear systems. Technical Report YALEU/DCS/RR-387. Department of Computer Science, Yale University, 1985.
42. Skjellum, A. J., and Baldwin, C. The multicomputer toolbox: Scalable parallel libraries for large-scale concurrent applications. Technical report. Numerical Mathematics Group. Lawrence Livermore National Laboratory, Dec. 1991.
43. Skjellum, A. J., and Leung, A. LU factorization of sparse, unsym-metric, Jacobian matrices on multicomputers. In Walker, D. W. and Stout, Q. F. (Eds.). Proceedings of the Fifth Distributed Memory Concurrent Computing Conference. IEEE Press. 1990, pp. 328-337.
44. Smith, B. T., Boyle, J. M., Dongarra, J. J., Garbow, B. S., Ikebe, Y., Klema, V. C., and Moler, C. B. Matrix Eigensyslem Routines—EISPACK Guide, Lecture Notes in Computer Science, Vol. 6. Springer-Verlag, Berlin, 1976.
45. Strassen, V. Gaussian elimination is not optimal. Ntuner. Math. 13 (1969), 354-356.
46. Sun, X.-H., and Ni, L. Scalable problems and memory-bounded speedup. J. Parallel Distrib. Computing 19, 1 (1993). 27-37.
47. Thinking Machines Corporation. CMS Technical Summary. Cambridge, MA, 1991.
48. van de Geijn, R. A. Massively parallel LINPACK benchmark on the Intel Touchstone Delta and iPSC/860 systems. Computer Science Report TR-91-28, Univ. of Texas, 1991.
49. Van de Velde, E. F. Data redistribution and concurrency. Parallel Comput. 16 (Dec 1990).