Exploiting mixed precision floating point hardware in scientific computations

Advances in Parallel Computing

Volumn 16, Issue , 2008, Pages 19-36

  Buttari, Alfredo ^a   Dongarra, Jack ^a,b   Kurzak, Jakub ^a   Langou, Julie ^a   Langou, Julien ^c   Luszczek, Piotr ^a   Tomov, Stanimire ^a  

^a University of Tennessee   (United States)

^b OAK RIDGE NATIONAL LABORATORY   (United States)

^c UNIVERSITY OF COLORADO   (United States)

Author keywords

factorization; Iterative refinement; Krylov methods

Indexed keywords

EID: 84884666121     PISSN: 09275452     EISSN: None     Source Type: Book Series    
DOI: None     Document Type: Conference Paper

References (28)

1. G. W. Stewart. Introduction to Matrix Computations. Academic Press, 1973.
2. J. W. Demmel. Applied Numerical Linear Algebra. SIAM, 1997.
3. J. H. Wilkinson. Rounding Errors in Algebraic Processes. Prentice-Hall, 1963.
4. C. B. Moler. Iterative refinement in floating point. J. ACM, 14(2):316-321, 1967.
5. N. J. Higham. Accuracy and Stability of Numerical Algorithms. SIAM, 1996.
6. J. Langou, J. Langou, P. Luszczek, J. Kurzak, A. Buttari, and J. J. Dongarraa. Exploiting the performance of 32 bit floating point arithmetic in obtaining 64 bit accuracy. In Proceedings of the 2006 ACM/IEEE Conference on Supercomputing, 2006.
7. J. Kurzak and J. J. Dongarra. Implementation of mixed precision in solving systems of linear equations on the CELL processor. Concurrency Computat. Pract. Exper. to appear.
8. J. Kurzak and J. J. Dongarra. Mixed precision dense linear system solver based on cholesky factorization for the CELL processor. Concurrency Computat. Pract. Exper. in preparation.
9. Iain S. Duff and John K. Reid. The multifrontal solution of indefinite sparse symmetric linear equations. 9(3):302-325, September 1983.
10. Cleve Ashcraft, R. Grimes, J. Lewis, Barry W. Peyton, and Horst Simon. Progress in sparse matrix methods in large sparse linear systems on vector supercomputers. Intern. J. of Supercomputer Applications, 1:10-30, 1987.
11. Alfredo Buttari, Jack Dongarra, Jakub Kurzak, Piotr Luszczek, and Stanmire Tomov. Computations to enhance the performance while achieving the 64-bit accuracy. Technical Report UT-CS-06-584, University of Tennessee Knoxville, November 2006. LAPACK Working Note 180.
12. Patrick R. Amestoy, Iain S. Duff, and J.-Y. L'Excellent. Multifrontal parallel distributed symmetric and unsymmetric solvers. Comput. Methods Appl. Mech. Eng., 184:501-520, 2000.
13. Patrick R. Amestoy, Iain S. Duff, J.-Y. L'Excellent, and Jacko Koster. A fully asynchronous multifrontal solver using distributed dynamic scheduling. 23:15-41, 2001.
14. Patrick R. Amestoy, A. Guermouche, J.-Y. L'Excellent, and S. Pralet. Hybrid scheduling for the parallel solution of linear systems. Parallel Comput., 32:136-156, 2006.
15. Timothy A. Davis Iain S. Duff. An unsymmetric-pattern multifrontal method for sparse LU factorization. 18:140-158, 1997.
16. Timothy A. Davis. A combined unifrontal/multifrontal method for unsymmetric sparse matrices. 25:1-19, 1999.
17. Timothy A. Davis. A column pre-ordering strategy for the unsymmetric-pattern multifrontal method. 30:196-199, 2004.
18. R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. M. Donato, Jack Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. V. der Vorst. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. Philadalphia: Society for Industrial and Applied Mathematics., 1994. Also available as postscript file at http://www.netlib.org/templates/Templates.html.
19. Y. Saad. Iterative Methods for Sparse Linear Systems. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2003.
20. Kathryn Turner and Homer F. Walker. Efficient high accuracy solutions with gmres( m). SIAM J. Sci. Stat. Comput., 13(3):815-825, 1992.
21. Gene H. Golub and Qiang Ye. Inexact preconditioned conjugate gradient method with inner-outer iteration. SIAM Journal on Scientific Computing, 21(4):1305-1320, 2000.
22. Y. Saad. A flexible inner-outer preconditioned GMRES algorithm. Technical Report 91-279, Department of Computer Science and Egineering, University of Minnesota, Minneapolis, Minnesota, 1991.
23. Valeria Simoncini and Daniel B. Szyld. Flexible inner-outer Krylov subspace methods. SIAM J. Numer. Anal., 40(6):2219-2239, 2002.
24. O. Axelsson and P. S. Vassilevski. A black box generalized conjugate gradient solver with inner iterations and variable-step preconditioning. SIAM J.Matrix Anal. Appl., 12(4):625-644, 1991.
25. Y. Notay. Flexible conjugate gradients. SIAM Journal on Scientic Computing, 22:1444-1460, 2000.
26. C. Vuik. New insights in gmres-like methods with variable preconditioners. J. Comput. Appl. Math., 61(2):189-204, 1995.
27. J. van den Eshof, G. L. G. Sleijpen, and M .B. van Gijzen. Relaxation strategies for nested Krylov methods. Technical Report TR/PA/03/27, CERFACS, Toulouse, France, 2003.
28. H. A. van der Vorst and C. Vuik. GMRESR: a family of nested GMRES methods. Numerical Linear Algebra with Applications, 1(4):369-386, 1994.