Abstract
A generalized eigensystem problem is usually transformed, utilizing Cholesky decomposition, to a standard eigenproblem. The latter is then solved efficiently by a matrix reduction approach based on Householder tridiagonalization method. We present parallel implementation of an integrated transformation-reduction algorithm on GPU accelerator using CUBLAS. Experimental results clearly demonstrate the potential of data-parallel coprocessors for scientific computations. When comparing against the CPU implementation, the GPU implementations achieve above 16-fold and 26-fold speedups in double precision for reduction and transformation respectively.
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Anderson, E., Bai, Z., Bischof, C., Blackford, S., Demmel, J., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., et al.: LAPAck Users’ Guide SIAM (1999)
Blackford, L., Cleary, A., Choi, J., d’Azevedo, E., Demmel, J., Dhillon, I., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., et al.: ScaLAPACK users’ guide. Society for Industrial Mathematics (1997)
Volkov, V., Demmel, J.W.: Using GPUs to accelerate the bisection algorithm for finding eigenvalues of symmetric tridiagonal matrices, Department of Computer Science, University of Tennessee, Knoxville, LAPACK Working Note 197 (January 2008)
Bientinesi, P., Dhillon, I.S., van de Geijn, R.A.: A parallel eigensolver for dense symmetric matrices based on multiple relatively robust representations. SIAM J. Scientific Computing 27(1), 43–66 (2005)
Dhillon, I.S., Parlett, B.N.: Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices. Linear Algebra and its Applications 387, 1–28 (2004)
Lessig, C., Bientinesi, P.: On Parallelizing the MRRR Algorithm for Data-Parallel Coprocessors. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds.) PPAM 2009, Part I. LNCS, vol. 6067, pp. 396–402. Springer, Heidelberg (2010)
Nvidia, C.: CUBLAS Library, NVIDIA Corporation, Santa Clara, California (2008)
Cao, X.-Q., Chi, X.-B., Gu, N.: Parallel solving symmetric eigenproblems. In: 5th International Conference on Algorithms and Architectures for Parallel Processing. IEEE, Beijing (2002)
Tomov, S., Nath, R., Dongarra, J.: Accelerating the reduction to upper Hessenberg, tridiagonal, and bidiagonal forms through hybrid GPU-based computing. Parallel Computing 36(12), 645–654 (2010)
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Zhao, Y., Zhang, J., Chi, X. (2012). Implementations of Main Algorithms for Generalized Eigenproblem on GPU Accelerator. In: Tan, Y., Shi, Y., Ji, Z. (eds) Advances in Swarm Intelligence. ICSI 2012. Lecture Notes in Computer Science, vol 7332. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31020-1_56
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DOI: https://doi.org/10.1007/978-3-642-31020-1_56
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31019-5
Online ISBN: 978-3-642-31020-1
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