A GPU-based Approximate SVD Algorithm

Blake Foster, Sridhar Mahadevan, Rui Wang
Department of Computer Science, University of Massachusetts, Amherst, MA 01003, USA
9th International Conference on Parallel Processing and Applied Mathematics, 2011


   title={A GPU-based Approximate SVD Algorithm},

   author={Foster, B. and Mahadevan, S. and Wang, R.},



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Approximation of matrices using the Singular Value Decomposition (SVD) plays a central role in many science and engineering applications. However, the computation cost of an exact SVD is prohibitively high for very large matrices. In this paper, we describe a GPU-based approximate SVD algorithm for large matrices. Our method is based on the QUIC-SVD introduced by [6], which exploits a tree-based structure to efficiently discover a subset of rows that spans the matrix space. We describe how to map QUIC-SVD onto the GPU, and improve its speed and stability using a blocked Gram-Schmidt orthogonalization method. Results show that our GPU algorithm achieves 6~7 times speedup over an optimized CPU version of QUIC-SVD, which itself is orders of magnitude faster than exact SVD methods. Using a simple matrix partitioning scheme, we have extended our algorithm to out-of-core computation, suitable for very large matrices that exceed the main memory size.
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