The Journal of Supercomputing

, Volume 58, Issue 2, pp 145–150 | Cite as

Using desktop computers to solve large-scale dense linear algebra problems

  • M. Marqués
  • G. Quintana-Ortí
  • E. S. Quintana-Ortí
  • R. van de Geijn
Article

Abstract

We provide experimental evidence that current desktop computers feature enough computational power to solve large-scale dense linear algebra problems. While the high computational cost of the numerical methods for solving these problems can be tackled by the multiple cores of current processors, we propose to use the disk to store the large data structures associated with these applications. Our results also show that the limited amount of RAM and the comparatively slow disk of the system pose no problem for the solution of very large dense linear systems and linear least-squares problems. Thus, current desktop computers are revealed as an appealing, cost-effective platform for research groups that have to deal with large dense linear algebra problems but have no direct access to large computing facilities.

Keywords

Dense linear algebra Out-of-core algorithms LU factorization High-performance computing 

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References

  1. 1.
    Baboulin M (2006) Solving large dense linear least squares problems on parallel distributed computers. application to the Earth’s gravity field computation. Ph.D. dissertation, INPT. TH/PA/06/22 Google Scholar
  2. 2.
    Geng P, Oden JT, van de Geijn R (1996) Massively parallel computation for acoustical scattering problems using boundary element methods. J Sound Vib 191(1):145–165 CrossRefGoogle Scholar
  3. 3.
    Gunter BC (2004) Computational methods and processing strategies for estimating Earth’s gravity field. Ph.D. thesis, The University of Texas at Austin Google Scholar
  4. 4.
    Gunter BC, van de Geijn RA (2005) Parallel out-of-core computation and updating the QR factorization. ACM Trans Math Softw 31(1):60–78. http://doi.acm.org/10.1145/1055531.1055534 MATHCrossRefGoogle Scholar
  5. 5.
    Gunter BC, Reiley WC, van de Geijn RA (2001) Parallel out-of-core Cholesky and QR factorizations with POOCLAPACK. In: Proceedings of the 15th international parallel and distributed processing symposium (IPDPS). IEEE Computer Society, Los Alamitos Google Scholar
  6. 6.
    Joffrain T, Quintana-Ortí ES, van de Geijn RA (2005) Rapid development of high-performance out-of-core solvers. In: Proceedings of PARA 2004. Lecture notes in computer science, vol 3732. Springer, Berlin, Heidelberg, pp 413–422 Google Scholar
  7. 7.
    Marqués M, Quintana-Ortí G, Quintana-Ortí ES, van de Geijn R (2009) Out-of-core computation of the QR factorization on multi-core processors. In: Proceedings of Euro-Par 2009. Lecture notes in computer science, vol 5704. Springer, Berlin, Heidelberg, pp 809–820 CrossRefGoogle Scholar
  8. 8.
    Marqués M, Quintana-Ortí G, Quintana-Ortí ES, van de Geijn R (2009) Solving “large” dense matrix problems on multi-core processors. In: 10th IEEE international workshop on parallel and distributed scientific and engineering computing—PDSEC’09. (CD–DROM), pp 1–8 Google Scholar
  9. 9.
    Quintana-Ortí ES, van de Geijn RA (2008) Updating an LU factorization with pivoting. ACM Trans Math Soft 35(2):11:1–11:16 CrossRefGoogle Scholar
  10. 10.
    Quintana-Ortí G, Quintana-Ortí ES, van de Geijn R, Zee FV, Chan E (2009) Programming matrix algorithms-by-blocks for thread-level parallelism. ACM Trans Math Soft 36(3):14:1–14:26. Available at http://doi.acm.org/10.1145/1527286.1527288 CrossRefGoogle Scholar
  11. 11.
    Schafer N, Serban R, Negrut D (2008) Implicit integration in molecular dynamics simulation. In: ASME international mechanical engineering congress & exposition, 2008 (IMECE2008-66438) Google Scholar
  12. 12.
    Watkins DS (2002) Fundamentals of matrix computations, 2nd edn. Wiley, New York MATHCrossRefGoogle Scholar
  13. 13.
    Zhang Y, Sarkar TK, van de Geijn RA, Taylor MC (2008) Parallel MoM using higher order basis function and PLAPACK in-core and out-of-core solvers for challenging EM simulations. In: IEEE AP-S & USNC/URSI symposium, 2008 Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • M. Marqués
    • 1
  • G. Quintana-Ortí
    • 1
  • E. S. Quintana-Ortí
    • 1
  • R. van de Geijn
    • 2
  1. 1.Depto. de Ingeniería y Ciencia de ComputadoresUniversidad Jaime ICastellónSpain
  2. 2.Dept. of Computer SciencesThe University of Texas at AustinAustinUSA

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