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.
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References
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
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
Gunter BC (2004) Computational methods and processing strategies for estimating Earth’s gravity field. Ph.D. thesis, The University of Texas at Austin
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
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
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
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
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
Quintana-Ortí ES, van de Geijn RA (2008) Updating an LU factorization with pivoting. ACM Trans Math Soft 35(2):11:1–11:16
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
Schafer N, Serban R, Negrut D (2008) Implicit integration in molecular dynamics simulation. In: ASME international mechanical engineering congress & exposition, 2008 (IMECE2008-66438)
Watkins DS (2002) Fundamentals of matrix computations, 2nd edn. Wiley, New York
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
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Marqués, M., Quintana-Ortí, G., Quintana-Ortí, E.S. et al. Using desktop computers to solve large-scale dense linear algebra problems. J Supercomput 58, 145–150 (2011). https://doi.org/10.1007/s11227-010-0394-2
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DOI: https://doi.org/10.1007/s11227-010-0394-2