Abstract
Multishift QR algorithms are efficient for solving the symmetric tridiagonal eigenvalue problem on a parallel computer. In this paper, we focus on three variants of the multishift QR algorithm, namely, the conventional multishift QR algorithm, the deferred shift QR algorithm and the fully pipelined multishift QR algorithm, and construct performance models for them. Our models are designed for shared-memory parallel machines, and given the basic performance characteristics of the target machine and the problem size, predict the execution time of these algorithms. Experimental results show that our models can predict the relative performance of these algorithms to the accuracy of 10% in many cases. Thus our models are useful for choosing the best algorithm to solve a given problem in a specified computational environment, as well as for finding the best value of the performance parameters.
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
Golub, G.H., van Loan, C.F.: Matrix Computations. Johns Hopkins University Press (1996)
Demmel, J.W.: Applied Numerical Linear Algebra. SIAM, Philadelphia (1997)
Sameh, A.H., Kuck, D.J.: A parallel QR algorithm for symmetric tridiagonal matrices. IEEE Trans. Comput. C-26, 147–153 (1977)
Bai, Z., Demmel, J.: On a block implementation of Hessenberg QR iteration. Int. J. of High Speed Computing 1, 97–112 (1989)
Kaufman, L.: A parallel QR algorithm for the symmetric tridiagonal eigenvalue problem. J. Parallel and Distributed Comput. 3, 429–434 (1994)
Bar-On, I., Codenotti, B.: A fast and stable parallel QR algorithm for symmetric tridiagonal matrices. Linear Algebra Appl. 220, 63–95 (1995)
Van de Geijn, R.A.: Deferred shifting schemes for parallel QR methods. SIAM J. Matrix Anal. Appl. 14, 180–194 (1993)
Miyata, T., Yamamoto, Y., Zhang, S.-L.: A fully pipelined multishift QR algorithm for parallel solution of symmetric tridiagonal eigenproblems. IPSJ Trans. Advanced Computing Systems 1, 14–27 (2008)
Dackland, K., Kågström, B.: A hierarchical approach for performance analysis of ScaLAPACK-based routines using the distributed linear algebra machine. In: Madsen, K., Olesen, D., Waśniewski, J., Dongarra, J. (eds.) PARA 1996. LNCS, vol. 1184, pp. 187–195. Springer, Heidelberg (1996)
Cuenca, J., Gimenez, D., Gonzalez, J.: Architecture of an automatically tuned linear algebra library. Parallel Computing 30, 187–210 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Miyata, T., Yamamoto, Y., Zhang, SL. (2010). Performance Modeling of Multishift QR Algorithms for the Parallel Solution of Symmetric Tridiagonal Eigenvalue Problems. In: Hsu, CH., Yang, L.T., Park, J.H., Yeo, SS. (eds) Algorithms and Architectures for Parallel Processing. ICA3PP 2010. Lecture Notes in Computer Science, vol 6082. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13136-3_41
Download citation
DOI: https://doi.org/10.1007/978-3-642-13136-3_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13135-6
Online ISBN: 978-3-642-13136-3
eBook Packages: Computer ScienceComputer Science (R0)