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International Conference on Parallel Processing and Applied Mathematics

PPAM 2015: Parallel Processing and Applied Mathematics pp 505–514Cite as

Revisiting the Gauss-Huard Algorithm for the Solution of Linear Systems on Graphics Accelerators

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9573))

Abstract

In 1979, P. Huard presented an efficient variant of the Gauss-Jordan elimination for the solution of linear systems. In particular, this alternative algorithm exhibits the same computational cost as the traditional LU-based solver, and is considerably cheaper than the Gauss-Jordan algorithm, but there exist no recent high performance implementations of the Gauss-Huard (GH) variant that allow a comparison of these approaches. In this paper we present a reliable GH solver for hybrid platforms equipped with conventional multi-core technology and a graphics processing unit (GPU). The experimental results show that the GH algorithm can beat high performance versions of the LU solver, from tuned libraries for CPU-GPU servers such as MAGMA, for problems of small to moderate scale.

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References

  1. Balay, S., Gropp, W., McInnes, L.C., Smith, B.: PETSc 2.0 users manual. Technical report ANL-95/11, Argonne National Laboratory, October 1996

    Google Scholar 

  2. Barrachina, S., Castillo, M., Igual, F.D., Mayo, R., Quintana-Ortí, E.S.: Solving dense linear systems on graphics processors. In: Luque, E., Margalef, T., Benítez, D. (eds.) Euro-Par 2008. LNCS, vol. 5168, pp. 739–748. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  3. Benner, P., Ezzatti, P., Quintana-Ortí, E.S., Remón, A.: Using hybrid CPU-GPU platforms to accelerate the computation of the matrix sign function. In: Lin, H.-X., Alexander, M., Forsell, M., Knüpfer, A., Prodan, R., Sousa, L., Streit, A. (eds.) Euro-Par 2009. LNCS, vol. 6043, pp. 132–139. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  4. Benner, P., Ezzatti, P., Quintana-Ortí, E.S., Remón, A.: Matrix inversion on CPU-GPU platforms with applications in control theory. Concur. Comput. Pract. Exp. 25(8), 1170–1182 (2013)

    Article  Google Scholar 

  5. Dekker, T.J., Hoffmann, W., Potma, K.: Stability of the Gauss-Huard algorithm with partial pivoting. Computing 58, 225–244 (1997)

    Article  MathSciNet  Google Scholar 

  6. Demmel, J.W.: Applied Numerical Linear Algebra. Society for Industrial and Applied Mathematics, Philadelphia (1997)

    Book  Google Scholar 

  7. Dufrechou, E., Ezzatti, P., Quintana-Ortí, E., Remón, A.: Solving linear systems on the Intel Xeon-Phi accelerator via the Gauss-Huard algorithm. In: Osthoff, C., Navaux, P.O.A., Hernandez, C.J.B., Silva Dias, P.L. (eds.) High Performance Computing. CCIS, vol. 565, pp. 107–117. Springer International Publishing, Switzerland (2015)

    Chapter  Google Scholar 

  8. EM Photonics. http://www.culatools.com/

  9. Golub, G.H., Van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore (1996)

    MATH  Google Scholar 

  10. 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)

    Article  Google Scholar 

  11. Hoffmann, W., Potma, K., Pronk, G.: Solving dense linear systems by Gauss-Huard’s method on a distributed memory system. Future Gener. Comput. Syst. 10(2–3), 321–325 (1994)

    Article  Google Scholar 

  12. Huard, P.: La méthode simplex sans inverse explicite. EDB Bull. Direction Études Rech. Sér. C Math. Inform. 2, 79–98 (1979)

    Google Scholar 

  13. Quintana-Ortí, E.S., Quintana-Ortí, G., Sun, X., van de Geijn, R.A.: A note on parallel matrix inversion. SIAM J. Sci. Comput. 22, 1762–1771 (2001)

    Article  MathSciNet  Google Scholar 

  14. Silva, J.P., Dufrechou, E., Quintana-Ortí, E., Remón, A., Benner, P.: Solving dense linear systems with hybrid CPU-GPU platforms. In: Proceedings of the XLI Latin American Computing Conference (2015) (to appear)

    Google Scholar 

  15. TOP500.org. http://www.top500.org/

  16. TU Wien and FASTMathSciDAC Institute. http://viennacl.sourceforge.net/

  17. Univ. of Tennessee. http://icl.cs.utk.edu/magma/

  18. Volkov, V., Demmel, J.: LU, QR and Cholesky factorizations using vector capabilities of GPUs. Technical report UCB/EECS-2008-49, EECS Department, University of California, Berkeley, May 2008

    Google Scholar 

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Acknowledgments

The researcher from the Universidad Jaime I was supported by the CICYT projects TIN2011-23283 and TIN2014-53495-R of the Ministerio de Economía y Competitividad and FEDER.

Author information

Authors and Affiliations

  1. Max Planck Institute for Dynamics of Complex Technical Systems, 39106, Magdeburg, Germany

    Peter Benner & Alfredo Remón

  2. Instituto de Computación, Universidad de la República, 11300, Montevideo, Uruguay

    Pablo Ezzatti

  3. Dep. de Ingeniería y Ciencia de la Computación, Universidad Jaime I, 12701, Castellón, Spain

    Enrique S. Quintana-Ortí

Authors
  1. Peter Benner
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  2. Pablo Ezzatti
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  3. Enrique S. Quintana-Ortí
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  4. Alfredo Remón
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Corresponding author

Correspondence to Alfredo Remón .

Editor information

Editors and Affiliations

  1. Czestochowa University of Technolog, Czestochowa, Poland

    Roman Wyrzykowski

  2. Department of Computer Science, University of Southern California, Marina Del Rey, California, USA

    Ewa Deelman

  3. Electrical Engineering & Comput. Science, University of Tennessee, Knoxville, Tennessee, USA

    Jack Dongarra

  4. Czestochowa University of Technology, Institute of Computer & Information Sci., Czestochowa, Poland

    Konrad Karczewski

  5. Department of Computer Science, AGH University of Science and Technology, Krakow, Poland

    Jacek Kitowski

  6. Systèmes d’informations, Big Data et Rec, AGH University of Science and Technology, Krakow, Poland

    Kazimierz Wiatr

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Benner, P., Ezzatti, P., Quintana-Ortí, E.S., Remón, A. (2016). Revisiting the Gauss-Huard Algorithm for the Solution of Linear Systems on Graphics Accelerators. In: Wyrzykowski, R., Deelman, E., Dongarra, J., Karczewski, K., Kitowski, J., Wiatr, K. (eds) Parallel Processing and Applied Mathematics. PPAM 2015. Lecture Notes in Computer Science(), vol 9573. Springer, Cham. https://doi.org/10.1007/978-3-319-32149-3_47

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  • DOI: https://doi.org/10.1007/978-3-319-32149-3_47

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32148-6

  • Online ISBN: 978-3-319-32149-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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