Formal methods for high-performance linear algebra libraries

IFIP Advances in Information and Communication Technology

Volumn 60, Issue , 2001, Pages 193-208

  Gunnels, John A ^a   van de Geijn, Robert A ^a  

^a University of Texas at Austin   (United States)

Author keywords

Algorithms; FLAME; Formal methods; Linear algebra; LU factorization

Indexed keywords

ALGORITHMS; CODES (SYMBOLS); COMPUTER SOFTWARE; FORMAL METHODS; FORTRAN (PROGRAMMING LANGUAGE); LIBRARIES; LINEAR ALGEBRA; MEMORY ARCHITECTURE;

CONVENTIONAL APPROACH; FLAME; FORMAL LINEAR ALGEBRA METHODS ENVIRONMENTS; LANGUAGE INDEPENDENTS; LINEAR ALGEBRA LIBRARIES; LU FACTORIZATION; PERFORMANCE ANALYSIS; PROGRAM CORRECTNESS;

C++ (PROGRAMMING LANGUAGE);

EID: 84901946998     PISSN: 18684238     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-0-387-35407-1_12     Document Type: Conference Paper

References (20)

1. Robert Allen and David Garlan. A formal basis for architectural connection. ACM TOSEM, 6(3):213-249, 1997.
2. E. Anderson, Z. Bai, J. Demmel, J. E. Dongarra, J. DuCroz, A. Greenbaum, S. Hammarling, A. E. McKenney, S. Ostrouchov, and D. Sorensen. LAPACK Users' Guide. SIAM, Philadelphia, 1992.
3. J. Choi, J. J. Dongarra, R. Pozo, and D. W. Walker. Scalapack: A scalable linear algebra library for distributed memory concurrent computers. In Proceedings of the Fourth Symposium on the Frontiers of Massively Parallel Computation, pages 120-127. IEEE Comput. Soc. Press, 1992.
4. J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart. LINPACK Users' Guide. SIAM, Philadelphia, 1979.
5. Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, and lain Duff. A set of level 3 basic linear algebra subprograms. A CM 'nuns. Math. Soft., 16(1):1-17, March 1990.
6. Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, and Richard J. Hanson. An extended set of FORTRAN basic linear algebra subprograms. ACM Trans. Math. Soft., 14(1):1-17, March 1988.
7. Jack J. Dongarra, lain S. Duff, Danny C. Sorensen, and Henk A. van der Vorst. Solving Linear Systems on Vector and Shared Memory Computers. SIAM, Philadelphia, PA, 1991.
8. David Gries. The Science of Programming. Springer-Verlag, 1981.
9. John Gunnels, Greg Henry, and Robert van de Geijn. Toward dynamic high-performance matrix multiplication kernels. Technical report, Department of Computer Sciences, The University of Texas at Austin, in preparation.
10. John Gunnels, Calvin Lin, Greg Morrow, and Robert van de Geijn. A flexible class of parallel matrix multiplication algorithms. In Proceedings of First Merged International Parallel Processing Symposium and Symposium on Parallel and Distributed Processing (1998 IPPS/SPDP '98), pages 110-116, 1998.
11. John A. Gunnels, Greg M. Henry, and Robert A. van de Geijn. Formal linear algebra methods environment (flame):overview. FLAME Working Note #1 CS-TR-00-28, Department of Computer Sciences, The University of Texas at Austin, NOV 2000.
12. F. Gustavson, A. Henriksson, I. Jonsson, B. Kagstrom, and P. Ling. Recursive blocked data formats and bIas's for dense linear algebra algorithms. In B. Kagstrom et al., editor, Applied Parallel Computing, Large Scale Scientific and Industrial Problems, volume 1541 of Lecture Notes in Computer Science, pages 195-206. SpringerVerlag, 1998.
13. F. G. Gustavson. Recursion leads to automatic variable blocking for dense linear-algebra algorithms. IBM Journal of Research and Development, 41(6):737-755, November 1997.
14. B. Kagstrom, P. Ling, and C. Van Loan. GEMM-based level 3 BLAS: High performance model implementations and performance evaluation benchmark. TOMS, 24(3):268-302, 1998.
15. C. L. Lawson, R. J. Hanson, D. R. Kincaid, and F. T. Krogh. Basic linear algebra subprograms for Fortran usage. ACM Trans. Math. Soft., 5(3):308-323, Sept. 1979.
16. Wesley C. Reiley and Robert A. van de Geijn. POOCLAPACK: Parallel Out-of-Core Linear Algebra Package. Technical Report CS-TR-99-33, Department of Computer Sciences, The University of Texas at Austin, Nov. 1999.
17. B. T. Smith et al. Matrix Eigensystem Routines-EISPACK Guide. Lecture Notes in Computer Science 6. Springer-Verlag, New York, second edition, 1976.
18. Marc Snir, Steve W. Otto, Steven Huss-Lederman, David W. Walker, and Jack Dongarra. MPI: The Complete Reference. The MIT Press, 1996.
19. G. W. Stewart. Matrix Algorithms Volume 1: Basic Decompositions. SIAM, 1998.
20. Robert A. van de Geijn. Using PLAPACK: Parallel Linear Algebra Package. The MIT Press, 1997.