Abstract
In this paper we present two parallel routines for the LU factorization of band matrices arising in model reduction problems that target SMP architectures. The special properties of these problems often allows the elimination of pivoting during the factorization, and results in a higher efficiency of the parallel routines. Also, the routines aggregate operations during the iteration, exposing a coarser-grain parallelism than their LAPACK counterpart. Experimental results on two different parallel platforms show the benefits of the new approach.
This research was supported by the CICYT project TIN2005-09037-C02-02 and FEDER, and the DAAD programme Acciones Integradas HA2005-0081.
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.
Similar content being viewed by others
References
Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Sorensen, D.: LAPACK Users’ Guide, 3rd edn. SIAM, Philadelphia (1999)
Antoulas, A.C.: Lectures on the Approximation of Large-Scale Dynamical Systems. SIAM, Philadelphia (2005)
Cheng, C.-K., Lillis, J., Lin, S., Chang, N.H.: Interconnect Analysis and Synthesis. John Wiley & Sons, NY (2000)
Golub, G.H., Van Loan, C.: Unsymmetric positive definite linear systems. Linear Algebra Appl. 28, 85–97 (1979)
Lancaster, P., Rodman, L.: The Algebraic Riccati Equation. Oxford University Press, Oxford (1995)
Li, J.-R., White, J.: Low rank solution of Lyapunov equations. SIAM J. Matrix Anal. Appl. 24(1), 260–280 (2002)
Lienemann, J., Billger, D., Rudnyi, E.B., Greiner, A., Korvink, J.G.: Mems compact modeling meets model order reduction: Examples of the application of arnoldi methods to microsystem devices. In: Technical Proceedings of the 2004 Nanotechnology Conference and Trade Show, Nanotech 2004 (2004)
Mathias, R.: Matrices with positive definite Hermitian part: Inequalities and linear systems. SIAM J. Matrix Anal. Appl. 13(2), 640–654 (1992)
Penzl, T.: A cyclic low rank Smith method for large sparse Lyapunov equations. SIAM J. Sci. Comput. 21(4), 1401–1418 (2000)
Remón, A., Quintana-Ortí, E.S., Quintana-Ortí, G.: Parallel LU factorization of band matrices on SMP systems. In: Gerndt, M., Kranzlmüller, D. (eds.) HPCC 2006. LNCS, vol. 4208, pp. 110–118. Springer, Heidelberg (2006)
Remón, A., Quintana-Ortí, E.S., Quintana-Ortí, G.: Cholesky factorization of band matrices using multithreaded BLAS. In: Kågström, B., Elmroth, E., Dongarra, J., Waśniewski, J. (eds.) PARA 2006. LNCS, vol. 4699, pp. 608–616. Springer, Heidelberg (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Remón, A., Quintana-Ortí, E.S., Quintana-Ortí, G. (2008). Parallel Solution of Band Linear Systems in Model Reduction. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2007. Lecture Notes in Computer Science, vol 4967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68111-3_71
Download citation
DOI: https://doi.org/10.1007/978-3-540-68111-3_71
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68105-2
Online ISBN: 978-3-540-68111-3
eBook Packages: Computer ScienceComputer Science (R0)