Minimal data copy for dense linear algebra factorization

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4699 LNCS, Issue , 2007, Pages 540-549

  Gustavson, Fred G ^a   Gunnels, John A ^a   Sexton, James C ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BLOCK CODES; COMPUTER HARDWARE; DATA STRUCTURES; FACTORIZATION; MATRIX ALGEBRA;

CHOLESKY FACTORIZATION; HARDWARE STREAMING; SUBMATRICES;

DATA PROCESSING;

EID: 38049054439     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-75755-9_66     Document Type: Conference Paper

References (25)

1. Agarwal, R.C., Gustavson, F.G., Zubair, M.: Exploiting functional parallelism of POWER2 to design high-performance numerical algorithms. IBM Journal of Research and Development 38(5), 563-576 (1994)
2. Andersen, B.S., Gustavson, F.G., Wasnieski, J.: A Recursive Formulation of Cholesky Factorization of a Matrix in Packed Storage. ACM TOMS 27(2), 214-244 (2001)
3. Andersen, B.S., Gunnels, J.A., Gustavson, F.G., Reid, J.K., Wasnieski, J.: A Fully Portable High Performance Minimal Storage Hybrid Cholesky Algorithm. ACM TOMS 31(2), 201-227 (2005)
4. Anderson, E., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., Sorensen, D.: LAPACK Users' Guide Release 3.0, SIAM, Philadelphia (1999), http://www.netlib. org/lapack/lug/lapack.lug.html
5. Bilmes, J., Asanovic, K., Whye Chin, C., Demmel, J.: Optimizing Matrix Multiply Using PHiPAC: A Portable, High-Performance, ANSI C Coding Methodology. In: Proceedings of International Conference on Supercomputing, Vienna, Austria (1997)
6. Chatterjee, S., et al.: Design and Exploitation of a High-performance SIMD Floating-point Unit for Blue Gene/L. IBM Journal of Research and Development 49(2-3), 377-391 (2005)
7. Dongarra, J.J., Moler, C.B., Bunch, J.R., Stewart, G.W.: LINPACK Users' Guide Release 2.0. SIAM, Philadelphia (1979)
8. Dongarra, J.J., Gustavson, F.G., Karp, A.: Implementing Linear Algebra Algorithms for Dense Matrices on a Vector Pipeline Machine. SIAM Review 26(1), 91-112 (1984)
9. Dongarra, J.J., Du Croz, J., Hammarling, S., Hanson, R.J.: An Extended Set of FORTRAN Basic Linear Algebra Subprograms. TOMS 14(1), 1-17 (1988)
10. Dongarra, J.J., Du Croz, J., Hammarling, S., Duff, I.: A Set of Level 3 Basic Linear Algebra Subprograms. TOMS 16(1), 1-17 (1990)
11. Elmroth, E., Gustavson, F.G., Kagstrom, B., Jonsson, I.: Recursive Blocked Algorithms and Hybrid Data Structures for Dense Matrix Library Software. SIAM Review 46(1), 3-45 (2004)
12. Gunnels, J., Gustavson, F.G., Henry, G., van de Geijn, R.: Formal linear algebra methods environment (FLAME). ACM TOMS 27(4), 422-455 (2001)
13. Gunnels, J.A., Gustavson, F.G.: A New Array Format for Symmetric and Triangular Matrices. In: Dongarra, J.J., Madsen, K., Waśniewski, J. (eds.) PARA 2004. LNCS, vol. 3732, pp. 247-255. Springer, Heidelberg (2006)
14. Gunnels, J.A., Gustavson, F.G., Henry, G.M., van de Geijn, R.A.: A Family of High-Performance Matrix Multiplication Algorithms. In: Dongarra, J.J., Madsen, K., Waśniewski, J. (eds.) PARA 2004. LNCS, vol. 3732, pp. 256-265. Springer, Heidelberg (2006)
15. Gustavson, F.G.: Recursion Leads to Automatic Variable Blocking for Dense Linear-Algebra Algorithms. IBM Journal of Research and Development 41(6), 737-755 (1997)
16. Gustavson, F.G., Jonsson, I.: Minimal Storage High Performance Cholesky via Blocking and Recursion. IBM Journal of Research and Development 44(6), 823-849 (2000)
17. Gustavson, F.G.: High Performance Linear Algebra Algorithms using New Generalized Data Structures for Matrices. IBM Journal of Research and Development 47(1), 31-55 (2003)
18. Gustavson, F.G.: New Generalized Data Structures for Matrices Lead to a Variety of High performance Dense Linear Algorithms. In: Dongarra, J.J., Madsen, K., Waániewski, J. (eds.) PARA 2004, LNCS, vol. 3732, pp. 11-20. Springer, Heidelberg (2006)
19. Gustavson, F.G., Wasniewski, J.: Rectangular Full Packed Format for LAPACK Algorithms Timings on Several Computers. In: Kågström, B., Elmroth, E., Dongarra, J., Wasniewski, J. (eds.) PARA 2006. LNCS, vol. 4699, pp. 570-579. Springer, Heidelberg (2007)
20. IBM: IBM Engineering and Scientific Subroutine Library for AIX Version 3, Release 3. IBM Pub. No. SA22-7272-04 (December 2001)
21. Kalla, R., Sinharoy, B., Tendler, J.: Power 5. HotChips-15, August 17-19, 2003, Stanford, CA (2003)
22. Lawson, C.L., Hanson, R.J., Kincaid, D.R., Krogh, F.T.: Basic Linear Algebra Subprograms for Fortran Usage. TOMS 5(3), 308-323 (1979)
23. Park, N., Hong, B., Prasanna, V.K.: Tiling, Block Data Layout, and Memory Hierarchy Performance. IEEE Trans. Parallel and Distributed Systems 14(7), 640-654 (2003)
24. Sinharoy, B., Kalla, R.N., Tendler, J.M, Kovacs, R.G., Eickemeyer, R.J., Joyner, J.B.: POWER5 System Microarchitecture. IBM Journal of Research and Development 49(4/5), 505-521 (2005)
25. Whaley, R.C., Petitet, A., Dongarra, J.J.: Automated Empirical Optimization of Software and the ATLAS Project. Parallel Computing (1-2), 3-35 (2001)