Abstract
In recent times the work on networks of processors has become very important, due to the low cost and the availability of these systems. This is why it is interesting to study algorithms on networks of processors. In this paper we study on networks of processors different Eigenvalue Solvers. In particular, the Power method, deflation, Givens algorithm, Davidson methods and Jacobi methods are analized using PVM and MPI. The conclusion is that the solution of Eigenvalue Problems can be accelerated by using networks of processors and typical parallel algorithms, but the high cost of communications in these systems gives rise to small modifications in the algorithms to achieve good performance.
Partially supported by Comisióon Interministerial de Ciencia y Tecnología, project TIC96-1062-C03-02, and Consejería de Cultura y Educación de Murcia, Dirección General de Universidades, project COM-18/96 MAT.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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. SIAM, Philadelphia (1995)
Blackford, L.S., Choi, J., Cleary, A., D’Azevedo, E., Demmel, J., Dhillon, I., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D., Whaley, R.C.: ScaLAPACK User’s Guide. SIAM, Philadelphia (1997)
Demmel, J., Stanley, K.: The Performance of Finding Eigen values and Eigenvectors of Dense Symmetric Matrices on Distributed Memory Computers. In: Bailey, D.H., Bjørstad, P.E., Gilbert, J.R., Mascagni, M.V., Schreiber, R.S., Simon, H.D., Torczon, V.J., Watson, L.T. (eds.) Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing, pp. 528–533. SIAM, Philadelphia (1995)
Giménez, D., Majado, M.J., Verdú, I.: Solving the Symmetric Eigenvalue Problem on Distributed Memory Systems. In: Arabnia, H.R. (ed.) Proceedings of the International Conference on Parallel and Distributed Processing Techniques and Applications. PDPTA 1997, pp. 744–747 (1997)
Huang, K.-C., Wang, F.-J., Wu, P.-C.: Parallelizing a Level 3 BLAS Library for LAN-ConnectedWorkstations. Journal of Parallel and Distributed Computing 38, 28–36 (1996)
Lo, G.-C., Saad, Y.: Iterative solution of general sparse linear systemson clusters of workstations (May 1996)
Geist, A., Begelin, A., Dongarra, J., Jiang, W., Manchek, R., Sunderam, V.: Parallel Virtual Machine. A User’s Guide and Tutorial for Networked Parallel Computing (1995)
Message Passing Interface Forum. A Message-Passing Interface Standard. International Journal of Supercomputer Applications 3 (1994)
Users guide to mpich. preprint
García, F.J., Giménez, D.: Resolución de sistemas triangulares de ecuaciones lineales en redes de ordenadores. Facultad de Informática, Universidad de Murcia (1997)
Edelman, A.: Large dense linear algebra in 1993: The parallel computing influence. The International Journal of Supercomputer Applications 7(2), 113–128 (1993)
Golub, G.H., Van Loan, C.F.: Matrix Computations. The Johns Hopkins University Press, Baltimore (1989) Segunda Edición
Trefethen, L.N., Bau III, D.: Numerical Linear Algebra. SIAM, Philadelphia (1997)
Watkins, D.S.: Matrix Computations. John Wiley & Sons, Chichester (1991)
Wilkinson, J.H.: The Algebraic Eigenvalue Problem. Clarendon Press, Oxford (1965)
Kumar, V., Grama, A., Gupta, A., Karypis, G.: Introduction to Parallel Computing. Design and Analysis of Algorithms. The Benjamin Cummings Publishing Company (1994)
Davidson, E.R.: The Iterative Calculation of a Few of the Lowest Eigenvalues and Corresponding Eigenvectors of Large Real-Symmetric Matrices. Journal of Computational Physics 17, 87–94 (1975)
Bradbury, W.W., Fletcher, R.: New Iterative Methods for Solution of theEigenproblem. Numerische Mathematik 9, 259–267 (1966)
Edelman, A., Smith, S.T.: On conjugate gradient-like methods for eigenvalue like problems. BIT 36(3), 494–508 (1996)
Badía, J.M., Vidal, A.M.: Exploiting the Parallel Divide-and-Conquer Methodto Solve the Symmetric Tridiagonal Eigenproblem. In: Proceedings of the Sixth Euromicro Workshop on Parallel and Distributed Processing, Madrid, January 21-23 (1998)
Giménez, D., Hernández, V., Vidal, A.M.: A unified approach to parallel block-jacobi methods for the symmetric eigenvalue problem. In: Hernández, V., Palma, J.M.L.M., Dongarra, J. (eds.) VECPAR 1998. LNCS, vol. 1573, pp. 29–42. Springer, Heidelberg (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Giménez, D., Jiménez, C., Majado, M.J., Marín, N., Martín, A. (1999). Solving Eigenvalue Problems on Networks of Processors. In: Hernández, V., Palma, J.M.L.M., Dongarra, J.J. (eds) Vector and Parallel Processing – VECPAR’98. VECPAR 1998. Lecture Notes in Computer Science, vol 1573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10703040_8
Download citation
DOI: https://doi.org/10.1007/10703040_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66228-0
Online ISBN: 978-3-540-48516-2
eBook Packages: Springer Book Archive