Performances of Methods for Solving a Linear System of Equations in the Architecture of GPU Accelerator
Keywords:
LU factorization, linear system of equations, Random Butterfly Transformation, GEPP, GENP, MAGMA, GPU acceleratorAbstract
We consider some important issues related to the solution of linear system of equations that arise in multi-processor and graphics processing unit architecture. A more effective method for solving a linear system of equations is considered through the LU factorization. Investigations are conducted in case of general complex matrices, because for those matrices the random butterfly transformation is used. The paper presents performances of several ways of solving methods on the graphic processor NVIDIA K40c.
References
R. Nath, S. Tomov and J. Dongarra, “An improved MAGMA GEMM for Fermi GPUs”, International Journal of High Performance Computing Applications, vol. 24, no. 4, pp. 511–515, 2010.
S. Tomov, J. Dongarra and M. Baboulin, “Towards dense linear algebra for hybrid GPU accelerated manycore systems”, Parallel Computing, vol. 36(5&6), pp. 232– 240, 2010.
S. Tomov, R. Nath and J. Dongarra, “Accelerating the reduction to upper Hessenberg, tridiagonal, and bidiagonal forms through hybrid GPU-based computing”, Parallel Computing, vol. 36, no. 12, pp. 645–654, 2010.
M. Baboulin, D. Becker and J. J. Dongarra, “A parallel tiled solver for dense symmetric indefinite systems on multicore architectures”, Parallel & Distributed Processing Symposium (IPDPS), 2012.
M. Baboulin, D. Becker, G. Bosilca, A. Danalis and J. J. Dongarra, “An efficient distributed randomized algorithm for solving large dense symmetric indefinite linear systems”, Parallel Computing, vol. 40, no. 7 , pp. 212--223, 2014.
J. W. Demmel, Applied Numerical Linear Algebra, SIAM, 1997. ISBN: 0898713897
J. Kurzak, P. Luszczek, M. Faverge, and J. Dongarra, “LU factorization with partial pivoting for a multicore system with accelerators”, IEEE Transactions on Parallel and Distributed Systems, vol. 24, no. 8, pp. 1613—1621, 2013.
E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney and D. Sorensen, LAPACK User’s Guide, SIAM, 1999, Third edition.
K. Goto, GotoBLAS. Texas Advanced Computing Center, University of Texas at Austin, USA. http: // www. otc. utexas. edu/ ATdisplay. jsp, 2007.
Intel. Math Kernel Library (MKL). http://www.intel.com/software/products/mkl/.
AMD. AMD Core Math Library (ACML). [Online]. Available: http://developer. amd. com/acml. jsp, 2012.
IBM Corporation. IBM Parallel Engineering and Scientific Subroutine Library. Guide and Reference. (GC23-3836), 1995.
R. C. Whaley and J. Dongarra. Automatically Tuned Linear Algebra Software. Technical Report UT-CS-97-366, University of Tennessee, December 1997. [Online]. Available: http://www.netlib.org/lapack/lawns/lawn131.ps.
D. S. Parker, “Random butterfly transformations with applications in computational linear algebra”, Technical Report CSD-950023, UCLA Computer Science Department, 1995.
D. S. Parker and B. Pierce, “The randomizing FFT: an alternative to pivoting in Gaussian elimination”, Technical Report CSD-950037, Computer Science Department, UCLA, 1995.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
