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http://dx.doi.org/10.14372/IEMEK.2013.8.3.171

Implementation and Performance Evaluation of the Faddev-Leverrier Algorithm using GPGPU  

Park, Yong-Hun (University of Ulsan)
Kim, Cheol-Hong (Chonnam National University)
Kim, Jong-Myon (University of Ulsan)
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Abstract
In this paper, we implement the Faddev-Leverier algorithm using GPGPU (General-Purpose Graphics Processing Unit) to accelerate singular value decomposition. In addition, we compare the performance of the algorithm using CPU and CPU plus GPGPU for eleven ${\times}n$ matrix sizes in order to decompose singular values, where =4, 8, 16, 32, 64, 128, 256, 512, 1,024, 2,048, and 4,096. Experimental results indicate that CPU achieves better performance than CPU plus GPGPU for $n{\leq}64$ because of a large number of read and write operations between CPU and GPGPU. However, CPU plus GPGPU outperforms CPU exponentially in the execution time for $n{\geq}64$.
Keywords
GPGPU; OpenCL; Singular value decomposition; Faddev-Leverrier algorithm;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 A. Rajwade, A. Rangarajan, and A. Banerjee. "Image Denoising using the Higher Order Singular Value Decomposition," Proceedings on Technical Report REP-2011-515, Department of CISE, University of Florida, Gainesville, Florida, 2011.
2 J.-Y. Lyu, J.-S. You, D.-W. Kim, D.-G. Kim, "An Invisible Watermarking Scheme Using the SVD," The Journal of Korea Information and Communications Society, Vol. 28, No. 11, pp.1118-1122, 2003 (in Korean).
3 C.-S. Yang, H.-J. Jeong, "A Study on Dipole Modeling Method for Ship's Magnetic Anomaly using Singular Value Decomposition Technique," Journal of the Korean Magnetics Society, Vol. 17, No. 6, pp.259-264, 2007 (in Korean).   DOI   ScienceOn
4 Z. Gu, W. Lin, B. Lee, C. Lau, "Low-Complexity Video Coding Based on Two-Dimensional Singular Value Decomposition," IEEE Trans. Image Processing, Vol. 21, No. 2, pp.674-687, 2012.   DOI   ScienceOn
5 G.H. Golub, C. Reinshch, "Singular Value Decomposition and Least Squares Solutions," Numer. Math., Vol. 14, No. 5, pp.403-441, 1970.   DOI
6 Khronos Group, "OpenCL-The Open Standard for Parallel Programming of Heterogeneous Systems," 2008.
7 J.E. Stone, D. Gohara, G. Shi, "OpenCL : A Parallel Programming Standard for Heterogeneous Computing Systems," Computing in Science and Eng., Vol. 12, No. 3, pp.66-73, 2010.
8 J.C. Gower, "A modified Leverrier-Faddeev algorithm for matrixes with multiple eigenvalues," Linear Algebra and its Applications, Vol. 31, pp.61-70, 1980.   DOI   ScienceOn
9 NVIDIA Corporation. NVIDA CUDA Visual Profiler, 4.1 edition. 2011.