Abstract
We first present data parallel algorithms for classical linear algebra methods. We analyze some of the main problems that a user has to solve. As examples, we propose data parallel algorithms for the Gauss and Gauss-Jordan methods. Thus, we introduce some criteria, such as the average data parallel computation ratio, to evaluate and compare data parallel algorithms. Our studies include both dense and sparse matrix computations. We describe in detail a data parallel structure to map general sparse matrices and we present data parallel sparse matrixvector multiplication. Then, we propose a data parallel preconditioned conjugate gradient algorithm using these matrix vector operations.
Preview
Unable to display preview. Download preview PDF.
References
S. Asby. Polynomial Preconditioning for Conjugate Gradient Methods. PhD thesis, University of Illinois at Urbana Champaign, 1987.
F. Chatelin. Valeurs propres de matrices. Masson, 1989.
D. Dahl. Mapping and compiled communications on the Connection Machine system. In Proceeding of the Fifth Distributed Memory Computing Conference, 1990.
T. dekker and W. Hoffman. Rehabilitation of the Gauss-Jordan algorithm. Technical report, Instituut Universiteit van Amsterdam, 1986.
N. Emad. Data parallel Lanczos and Padé-Rayleigh-Ritz on the CM-5. In Jean-Michel Alimi et al., editor, Science on the Connection Machine System. Thinking Machine Coorp., 1995.
N. Emad. The Padé-Rayleigh-Ritz method for solving large symetric eigenproblem. Journal of Numerical Analysis, 11, 1996.
N. Emad and S. Petiton. Numerical behavior of iterative Arnoldi's method for sparse eigenproblems on massively parallel architectures. In Iterative Methods in Linear Algebra. North Holland, 1992.
G. Golub and C. Van Loan. Matrix Computation. North Oxford Academic Oxford, second edition, 1989.
H. Golub and G. Meurant. Résolution numérique des grands systèmes linéaires. Eyrolles, 1983.
S. Hammond. Mapping unstructured grid computation to massively parallel computers. Technical Report 14, RIACS/NASA Ames, 1992.
W.D. Hillis and G.L. Steele. Data parallel algorithms. Communication of the ACM, 29, 1986.
S. L. Johnsson and K. Mathur. Data structures and algorithms for the finite element method on a data parallel supercomputer. International Journal for Numerical Methods in Engineering, 29, 1990.
S. Petiton and G. Edjlali. Data parallel structures and algorithms for sparse matrix computation. In Advances in Parallel Computing. North Holland, 1993.
S. Petiton. Du Développement de Logiciels Numériques en Environnements Parallèles. PhD thesis, University P. and M. Curie, Paris VI, 1988.
S. Petiton. Parallel QR algorithm for iterative subspace methods on the Connection Machine (CM2). In J. Dongarra, P. Messina, D. Sorensen, and R. Voigt, editors, Parallel Processing for Scientific Computing. SIAM, 1990.
S. Petiton. Parallel subspace method for non-hermitian eigenproblems on the Connection Machine (CM2). Applied Numerical Mathematics, 9, 1992.
S. Petiton, Y. Saad, K. Wu, and W. Ferng. Basic sparse matrix computation on the CM-5. International Journal of Modern Physics C, 4, 1993.
S. Petiton and C. Weill-Duflos. Very sparse preconditioned conjugate gradient on massively parallel architectures. In Proceeding of 13th World Congress on Computation and Applied Mathematics, 1991.
Y. Saad. Practical use of polynomial preconditionings for the conjugate gradient method. SIAM J. SCI. STAT. COMP., 6, 1985.
Y. Saad. SPARSKIT: a basic tool kit for sparse matrix computations. Technical Report 20, RIACS, NASA Ames Research Center, 90.
J. Saltz, S. Petiton, H. Berryman, and A. Rifkin. Performance effects of irregular communications patterns on massively parallel multiprocessors. Journal of Parallel and Distributed Computing, 8, 1991.
C. Tong. The preconditioned conjugate gradient method on the Connection Machine. In Scientific Applications of the Connection Machine. World Scientific, 1989.
J. Wilkinson. The Algebric Eigenvalue Problem. Oxford University Press, 65.
J. Zdenek. Data Parallel Finite Element Techniques for Large-Scale Computational Fuild Dynamics. PhD thesis, Stanford University, 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Petiton, S.G., Emad, N. (1996). A data parallel scientific computing introduction. In: Perrin, GR., Darte, A. (eds) The Data Parallel Programming Model. Lecture Notes in Computer Science, vol 1132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61736-1_42
Download citation
DOI: https://doi.org/10.1007/3-540-61736-1_42
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61736-5
Online ISBN: 978-3-540-70646-5
eBook Packages: Springer Book Archive