Abstract
In this article, a fully scalable parallel algorithm is presented for solving symmetric tridiagonal eigenvalue problems using quasi-Laguerre's method. The algorithm is implemented using PVM and tested on a variety of matrices with a load balancing scheme. Test results show that the algorithm has high parallel efficiency. Compared with other existing algorithms, our algorithm seems to be the best for distributed memory parallel architecture.
The research was supported in part by NSF under Grant DMS-9504953 and a Guggenheim Fellowship.
Chapter PDF
References
E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorenson, LAPACK User's Guide, SIAM, Philadelphia, 1992.
Q. Du, M. Jin, T. Y. Li and Z. Zeng, The Quasi-Laguerre iteration, to appear: Math. Comp.
Q. Du, M. Jin, T.Y. Li and Z. Zeng Quasi-Laguerre iteration in solving symmetric tridiagonal eigenvalue problems, to appear: SIAM J. Sci. Comput.
A. Geist, A. Beguelin, J. Dongarra, W. Jiang, R. Manchek, V. Sunderam, PVM 3 User's Guide and Reference Manual, September, 1994.
G. H. Golub and C. F. Van Loan, Matrix Computations, 2nd Ed., The Johns Hopkins University Press, Baltimore, MD, 1989.
C. Trefftz, P. McKinley, T. Y. Li, and Z. Zeng, A scalable eigenvalue solver for symmetric tridiagonal matrices, Parallel Computing, 21(1995), pp. 1213–1240.
T. Y. Li and Z. Zeng, Laguerre's iteration in solving the symmetric tridiagonal eigenproblem — revisited, SIAM J. Sci. Comput., Vol. 15, No. 5 (1994), pp. 1145–1173.
J. H. Wilkinson, The Algebraic Eigenvalue Problem, Oxford University Press, Oxford, 1965.
X. Zou, Quasi-Laguerre's method and its parallel implementation on solving symmetric tridiagonal eigenvalue problems, Ph.D thesis, Michigan State University, 1995.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Li, T.Y., Zou, X. (1996). Implementing the parallel quasi-Laguerre's algorithm for symmetric tridiagonal eigenproblems. In: Bougé, L., Fraigniaud, P., Mignotte, A., Robert, Y. (eds) Euro-Par'96 Parallel Processing. Euro-Par 1996. Lecture Notes in Computer Science, vol 1124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024683
Download citation
DOI: https://doi.org/10.1007/BFb0024683
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61627-6
Online ISBN: 978-3-540-70636-6
eBook Packages: Springer Book Archive