Abstract
In this paper, we discuss a more scalable OOC implementation of a dense linear system solver via LU factorization that presents numerical stability similar to that of the LU factorization with partial pivoting. Our implementation builds on the Formal Linear Algebra Methods Environment (FLAME), the Parallel Linear Algebra Package (PLAPACK), and the Parallel Out-of-Core Linear Algebra Package (POOCLAPACK) infrastructures. Experimental results on an Intel Itanium2 (R) platform demonstrate the high performance of this approach.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Anderson, E., Bai, Z., Demmel, J., Dongarra, J.E., DuCroz, J., Greenbaum, A., Hammarling, S., McKenney, A.E., Ostrouchov, S., Sorensen, D.: LAPACK Users’ Guide. SIAM, Philadelphia (1992)
Bientinesi, P., Gunnels, J.A., Myers, M.E., Quintana-Ortí, E.S., van de Geijn, R.A.: The science of deriving dense linear algebra algorithms. ACM Trans. Math. Soft. (to appear)
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 Users’ Guide. SIAM, Philadelphia (1997)
Cwik, T., van de Geijn, R., Patterson, J.: The application of parallel computation to integral equation models of electromagnetic scattering. Journal of the Optical Society of America A 11(4), 1538–1545 (1994)
D’Azevedo, E.F., Dongarra, J.J.: The design and implementation of the parallel out-ofcore scalapack LU, QR, and Cholesky factorization routines. LAPACK Working Note 118 CS-97-247, University of Tennessee, Knoxville (January 1997)
Dongarra, J.J., Bunch, J.R., Moler, C.B., Stewart, G.W.: LINPACK Users’ Guide. SIAM, Philadelphia (1979)
Geng, P., Tinsley Oden, J., van de Geijn, R.: Massively parallel computation for acoustical scattering problems using boundary element methods. Journal of Sound and Vibration 191(1), 145–165 (1996)
Golub, G., Van Loan, C.: Matrix Computations, 3rd edn. The Johns Hopkins University Press (1996)
Gunnels, J.A., Gustavson, F.G., Henry, G.M., van de Geijn, R.A.: FLAME: Formal Linear Algebra Methods Environment. ACM Transactions on Mathematical Software 27(4), 422–455 (2001)
Gunter, B., van de Geijn, R.A.: Parallel out-of-core computation and updating of the QR factorization. ACM Transactions on Mathematical Software (2004) (to appear)
Higham, N.J.: Accuracy and Stability of Numerical Algorithms, 2nd edn. Society for Industrial and Applied Mathematics, Philadelphia (2002)
Kågström, B., Ling, P., Van Loan, C.: GEMM-based level 3 BLAS: High-performance model, implementations and performance evaluation benchmark. LAPACK Working Note #107 CS-95-315, Univ. of Tennessee (November 1995)
Reiley, W.C., van de Geijn, R.A.: POOCLAPACK: Parallel Out-of-Core Linear Algebra Package. Technical Report CS-TR-99-33, Department of Computer Sciences, The University of Texas at Austin (November 1999)
Toledo, S.: Locality of reference in LU decomposition with partial pivoting. SIAM J. Matrix Anal. and Appl. 18(4), 1065–1081 (1997)
Toledo, S.: A survey of out-of-core algorithms in numerical linear algebra. In: DIMACS Series in Discrete Mathematics and Theoretical Computer Science (1999)
Toledo, S., Gustavson, F.G.: The design and implementation of SOLAR, a portable library for scalable out-of-core linear algebra computation. In: Proceedings of IOPADS 1996 (1996)
Trefethen, L.N., Schreiber, R.S.: Average-case stability of Gaussian elimination. SIAM J. Matrix Anal. and Appl. 11(3), 335–360 (1990)
van de Geijn, R.A.: Using PLAPACK: Parallel Linear Algebra Package. The MIT Press, Cambridge (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Joffrain, T., Quintana-Ortí, E.S., van de Geijn, R.A. (2006). Rapid Development of High-Performance Out-of-Core Solvers. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004. Lecture Notes in Computer Science, vol 3732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558958_49
Download citation
DOI: https://doi.org/10.1007/11558958_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29067-4
Online ISBN: 978-3-540-33498-9
eBook Packages: Computer ScienceComputer Science (R0)