References

1

M. ABOELAZE, N. CHRISOCHOIDES, AND E. HOUSTIS, The Parallelization of Level 2 and 3 BLAS Operations on Distributed Memory Machines, Tech. Rep. CSD-TR-91-007, Purdue University, West Lafayette, IN, 1991.

2

R. AGARWAL, F. GUSTAVSON, AND M. ZUBAIR, Improving Performance of Linear Algebra Algorithms for Dense Matrices Using Algorithmic Prefetching, IBM J. Res. Dev., 38 (1994), pp. 265-275.

3

E. ANDERSON, Z. BAI, C. BISCHOF, J. DEMMEL, J. DONGARRA, J. DUCROZ, A. GREENBAUM, S. HAMMARLING, A. MCKENNEY, S. OSTROUCHOV, AND D. SORENSEN, ``LAPACK Users' Guide, Second Edition'', SIAM, Philadelphia, PA, 1995.

4

C. ASHCRAFT, The Distributed Solution of Linear Systems Using the Torus-wrap Data mapping, Tech. Rep. ECA-TR-147, Boeing Computer Services, Seattle, WA, 1990.

5

L. S. BLACKFORD, J. CHOI, A. CLEARY, J. DEMMEL, I. DHILLON, J. DONGARRA, S. HAMMARLING, G. HENRY, A. PETITET, D. WALKER, AND R. C. WHALEY, `` ScaLAPACK: A Portable Linear Algebra Library for Distributed Memory Computers - Design Issues and Performance '', in Proceedings of the Supercomputer 96 Conference, IEEE Computer Society Press, November 1996.

6

R. BRENT, The LINPACK Benchmark on the AP 1000, in Frontiers, 1992, McLean, VA, 1992, pp. 128-135.

7

R. BRENT AND P. STRAZDINS, Implementation of BLAS Level 3 and LINPACK Benchmark on the AP1000, Fujitsu Scientific and Technical Journal, 5 (1993), pp. 61-70.

8

J. CHOI, J. DEMMEL, I. DHILLON, J. DONGARRA, S. OSTROUCHOV, A. PETITET, K. STANLEY, D. WALKER, AND R. C. WHALEY, ScaLAPACK: A Portable Linear Algebra Library for Distributed Memory Computers - Design Issues and Performance, Computer Physics Communications, 97 (1996), pp. 1-15. (also LAPACK Working Note #95).

9

J. CHOI, J. DONGARRA, S. OSTROUCHOV, A. PETITET, D. WALKER, AND R. C. WHALEY, A proposal for a set of parallel basic linear algebra subprograms, LAPACK Working Note #100 Technical report UT CS-95-292, University of Tennessee, 1995.

10

J. CHOI, J. DONGARRA, R. POZO, AND D. WALKER, ``ScaLAPACK: A Scalable Linear Algebra Library for Distributed Memory Concurrent Computers'', Tech. Rep. UT CS-92-181, LAPACK Working Note #55, University of Tennessee, 1992.

11

J. CHOI, J. DONGARRA, AND D. WALKER, PB-BLAS: A Set of Parallel Block Basic Linear Algebra Subroutines, Concurrency: Practice and Experience, 8 (1996), pp. 517-535.

12

A. CHTCHELKANOVA, J. GUNNELS, G. MORROW, J. OVERFELT, AND R. VAN DE GEIJN, Parallel Implementation of BLAS: General Techniques for Level 3 BLAS, Tech. Rep. TR95-49, Department of Computer Sciences, UT-Austin, 1995. Submitted to Concurrency: Practice and Experience.

13

E. CHU AND A. GEORGE, QR Factorization of a Dense Matrix on a Hypercube Multiprocessor, SIAM Journal on Scientific and Statistical Computing, 11 (1990), pp. 990-1028.

14

M. DAYDE, I. DUFF, AND A. PETITET, A Parallel Block Implementation of Level 3 BLAS for MIMD Vector Processors, ACM Trans. Math. Softw., 20 (1994), pp. 178-193.

15

J. DONGARRA, J. DUCROZ, I. DUFF, AND S. HAMMARLING, ``A Set of Level 3 Basic Linear Algebra Subprograms'', ACM Trans. Math. Softw., 16 (1990), pp. 1-28.

16

J. DONGARRA, J. DUCROZ, S. HAMMARLING, AND R. HANSON, ``An Extended Set of Fortran Basic Linear Algebra Subprograms'', ACM Trans. Math. Softw., 14 (1988), pp. 1-32.

17

J. DONGARRA, R. VAN DE GEIJN, AND D. WALKER, ``A Look at Scalable Dense Linear Algebra Librairies'', Tech. Rep. UT CS-92-155, LAPACK Working Note #43, University of Tennessee, 1992.

18

J. DONGARRA AND D. WALKER, Software Libraries for Linear Algebra Computations on High Performance Computers, SIAM Review, 37 (1995), pp. 151-180.

19

J. DONGARRA AND R. C. WHALEY, ``A User's Guide to the BLACS v1.0'', Tech. Rep. UT CS-95-281, LAPACK Working Note #94, University of Tennessee, 1995.

20

R. FALGOUT, A. SKJELLUM, S. SMITH, AND C. STILL, The Multicomputer Toolbox Approach to Concurrent BLAS and LACS, in Proceedings of the Scalable High Performance Computing Conference SHPCC-92, IEEE Computer Society Press, 1992.

21

G. FOX, M. JOHNSON, G. LYZENGA, S. OTTO, J. SALMON, AND D. WALKER, ``Solving Problems on Concurrent Processors'', vol. 1, Prentice Hall, Englewood Cliffs, N.J, 1988.

22

A. GEIST, A. BEGUELIN, J. DONGARRA, W. JIANG, R. MANCHEK, AND V. SUNDERAM, PVM : Parallel Virtual Machine. A Users' Guide and Tutorial for Networked Parallel Computing, The MIT Press Cambridge, Massachusetts, 1994.

23

G. GEIST AND C. ROMINE, LU Factorization Algorithms on Distributed Memory Multiprocessor Architectures, SIAM Journal on Scientific and Statistical Computing, 9 (1988), pp. 639-649.

24

B. HENDRICKSON AND D. WOMBLE, The Torus-wrap Mapping for Dense Matrix Calculations on Massively Parallel Computers, SIAM Journal on Scientific and Statistical Computing, 15 (1994), pp. 1201-1226.

25

G. HENRY AND R. VAN DE GEIJN, Parallelizing the QR Algorithm for the Unsymmetric Algebraic Eigenvalue problem: Myths and Reality, Tech. Rep. UT CS-94-244, LAPACK Working Note #79, University of Tennessee, 1994.

26

S. HUSS-LEDERMAN, E. JACOBSON, A. TSAO, AND G. ZHANG, Matrix Multiplication on the Intel Touchstone DELTA, Concurrency: Practice and Experience, 6 (1994), pp. 571-594.

27

B. KAGSTRfOM, P. LING, AND C. VAN LOAN, GEMM-Based Level 3 BLAS: High-Performance Model Implementations and Performance Evaluation Benchmark, Tech. Rep. UMINF 95-18, Department of Computing Science, Umea University, 1995. Submitted to ACM TOMS.

28

V. KUMAR, A. GRAMA, A. GUPTA, AND G. KARYPIS, Introduction to Parallel Computing, The Benjamin/Cummings Publishing Company, Inc., Redwood City, CA, 1994.

29

C. LAWSON, R. HANSON, D. KINCAID, AND F. KROGH, ``Basic Linear Algebra Subprograms for Fortran Usage'', ACM Trans. Math. Softw., 5 (1979), pp. 308-323.

30

W. LICHTENSTEIN AND S. L. JOHNSSON, Block-Cyclic Dense Linear Algebra, SIAM Journal on Scientific and Statistical Computing, 14 (1993), pp. 1259-1288.

31

R. SCHREIBER AND C. VAN LOAN, A storage efficient WY representation for products of Householder transformations, SIAM J. Sci. Stat. Comput., 10 (1989), pp. 53-57.

32

M. SNIR, S. W. OTTO, S. HUSS-LEDERMAN, D. W. WALKER, AND J. J. DONGARRA, MPI: The Complete Reference, MIT Press, Cambridge, Massachusetts, 1996.