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Subspace-Orbit Randomized Decomposition for Low-rank Matrix Approximation
An efficient, accurate and reliable approximation of a matrix by one of lower
rank is a fundamental task in numerical linear algebra and signal processing
applications. In this paper, we introduce a new matrix decomposition approach
termed Subspace-Orbit Randomized singular value decomposition (SOR-SVD), which
makes use of random sampling techniques to give an approximation to a low-rank
matrix. Given a large and dense data matrix of size with numerical
rank , where , the algorithm requires a few passes
through data, and can be computed in floating-point operations.
Moreover, the SOR-SVD algorithm can utilize advanced computer architectures,
and, as a result, it can be optimized for maximum efficiency. The SOR-SVD
algorithm is simple, accurate, and provably correct, and outperforms previously
reported techniques in terms of accuracy and efficiency. Our numerical
experiments support these claims