Low cost high performance uncertainty quantification

Proceedings of the 2nd Workshop on High Performance Computational Finance, WHPCF '09

Volumn , Issue , 2009, Pages

  Bekas, C ^a   Curioni, A ^a   Fedulova, I ^b  

^a IBM RESEARCH ZURICH   (Switzerland)

^b IBM Systems and Technology Group   (Russian Federation)

Author keywords

Inverse covariance matrices; Iterative refinement; Iterative solvers; Massive parallelism; Quadratic cost; Stochastic estimation

Indexed keywords

INVERSE COVARIANCE; ITERATIVE REFINEMENT; ITERATIVE SOLVERS; MASSIVE PARALLELISM; QUADRATIC COSTS; STOCHASTIC ESTIMATION;

COVARIANCE MATRIX; ESTIMATION; FACTORIZATION; LINEAR SYSTEMS; RISK ANALYSIS; RISK ASSESSMENT; SAFETY FACTOR; STOCHASTIC SYSTEMS; UNCERTAINTY ANALYSIS;

COSTS;

EID: 74049083297     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1645413.1645421     Document Type: Conference Paper

References (21)

1. C. Bekas, E. Kokiopoulou, and Y. Saad. An estimator for the diagonal of a matrix. Applied Numerical Mathematics, 57(11-12):1214-1229, November 2007.
2. G. Bhanot, A. Gara, P. Heidelberger, E. Lawless, J C. Sexton and R. Walkup. Optimizing task layout on the Blue Gene/L supercomputer. IBM Journal of Research and Development, Vol. 49, No. 2/3 , p. 489-500, 2005
3. L. Blackford, J. Choi, A. Cleary, E. D'Azevedo, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, and R. Whaley. ScaLAPACK User's Guide. SIAM, Philadelphia, 1997. See also www.netlib.org/scalapack.
4. A. Buttari, J. Dongarra, J. Langou, J. Langou, P. Luszczek, and J. Kurzak. Mixed precision iterative refinement techniques for the solution of dense linear systems. International Journal of High Performance Computing Applications, 21(4):457-466, November 2007.
5. J. J. Dongarra, I. Duff, D. C. Sorensen, and H. van der Vorst. Numerical Linear Algebra for High-Performance Computers. SIAM, 1998.
6. I. Fedulova. Parallel task mapping method for block-diagonal communication matrices. In preparation, 2009.
7. D. Girard. Un algorithme simple et rapide pour la validation croissee generalisee sur des problemes de grande taillee. RR 669-M, Grenoble, France: Informatique et Mathématiques Appliquées de Grenoble., 1987.
8. G. H. Golub and C. F. V. Loan. Matrix Computations. The Johns Hopkins University Press, Baltimore, 3d edition, 1996.
9. W. Gropp, S. Huss-Lederman, A. Lumsdaine, E. Lusk, B. Nitzberg, W. Saphir, and M. Snir. MPI - The complete Reference, Volume 2, The MPI Extensions. MIT Press, 1998.
10. J. Hartlap, P. Simon, and P. Schneider. Eso 2007 astronomy astrophysics, 2006.
11. N. J. Higham. Accuracy and Stability of Numerical Algorithms. SIAM, Philadelphia, 1996.
12. M. F. Hutchinson. A stochastic estimator of the trace of the influence matrix for laplacian smoothing splines. J. Commun. Statist. Simula., 19(2):433-450, 1990.
13. IBM. Blue Gene/P Solution. www-03.ibm.com/systems/deepcomputing/bluegene.
14. Jugene. Jülich Supercomputer Center. http://www.fz-juelich.de/jsc/ jugene
15. D. S. Oliver. Calculation of the inverse of the covariance. Mathematical Geology, 30(7):911-933, October 1998.
16. Y. Saad. Numerical Methods for Large Eigenvalue Problems. Halstead Press, New York, 1992.
17. Y. Saad. Iterative Methods for Sparse Linear Systems. SIAM, 2nd edition, 2003.
18. M. Snir, S. Otto, S. Huss-Lederman, D. Walker, and J. Dongarra. MPI - The complete Reference, Volume 1, The MPI Core. MIT Press, 1998.
19. G. V. G. Stevens. On the inverse of the covariance matrix in portfolio analysis. The Journal of Finance, 53:1821-1827, 1998.
20. K. Visweswariah, P. Olsen, R. Gopinath, and S. Axelrod. Maximum likelihood training of subspaces for inverse covariance modeling. In in Proc. ICASSP, 2003.
21. J. H. Wilkinson. Rounding errors in algebraic processes. Notes on Applied Science No. 32. Her Majesty's Stationary Office, London, 1963.