Abstract
We present several algorithms to compute the solution of a linear system of equations on a GPU, as well as general techniques to improve their performance, such as padding and hybrid GPU-CPU computation. We also show how iterative refinement with mixed-precision can be used to regain full accuracy in the solution of linear systems. Experimental results on a G80 using CUBLAS 1.0, the implementation of BLAS for NVIDIA® GPUs with unified architecture, illustrate the performance of the different algorithms and techniques proposed.
This research was supported by the CICYT project TIN2005-09037-C02-02 and FEDER, and project No. P1-1B2007-32 of the Fundación Caixa-Castellón/Bancaixa and UJI. Francisco Igual is supported by a research fellowship from the UJI (PREDOC/2006/02).
Chapter PDF
Similar content being viewed by others
Keywords
References
Galoppo, N., Govindaraju, N.K., Henson, M., Manocha, D.: LU-GPU: Efficient algorithms for solving dense linear systems on graphics hardware. In: SC 2005: Proceedings of the 2005 ACM/IEEE conference on Supercomputing, p. 3. IEEE Computer Society, Los Alamitos (2005)
Junk, J.H., O’Leary, D.P.: Cholesky decomposition and linear programming on a GPU. Master’s thesis, University of Maryland, College Park
NVIDIA: Nvidia CUDA Compute Unified Device Architecture. Programming Guide. NVIDIA (2007)
NVIDIA: CUBLAS Library. NVIDIA (2007)
Watkins, D.S.: Fundamentals of Matrix Computations, 2nd edn. John Wiley and Sons, Inc., New York (2002)
Gunnels, J.A., Gustavson, F.G., Henry, G.M., van de Geijn, R.A.: FLAME: Formal Linear Algebra Methods Environment. ACM Trans. Math. Soft. 27(4), 422–455 (2001)
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. 31(1), 1–26 (2005)
Barrachina, S., Castillo, M., Igual, F.D., Mayo, R., Quintana-Ortí, E.S.: Evaluation and tuning of the level 3 CUBLAS for graphics processors. In: 9th IEEE International Workshop on Parallel and Distributed Scientific and Engineering Computing – PDSEC 2008 (2008)
Buttari, A., Dongarra, J., Langou, J., Langou, J., Luszczek, P., Kurzak, J.: Mixed precision iterative refinement techniques for the solution of dense linear systems. Int. J. High Perform. Comput. Appl. 21(4), 457–466 (2007)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Barrachina, S., Castillo, M., Igual, F.D., Mayo, R., Quintana-Ortí, E.S. (2008). Solving Dense Linear Systems on Graphics Processors. In: Luque, E., Margalef, T., Benítez, D. (eds) Euro-Par 2008 – Parallel Processing. Euro-Par 2008. Lecture Notes in Computer Science, vol 5168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85451-7_79
Download citation
DOI: https://doi.org/10.1007/978-3-540-85451-7_79
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85450-0
Online ISBN: 978-3-540-85451-7
eBook Packages: Computer ScienceComputer Science (R0)