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A sublinear-time randomized algorithm for column and row subset selection based on strong rank-revealing QR factorizations (2402.13975v1)
Published 21 Feb 2024 in math.NA and cs.NA
Abstract: In this work, we analyze a sublinear-time algorithm for selecting a few rows and columns of a matrix for low-rank approximation purposes. The algorithm is based on an initial uniformly random selection of rows and columns, followed by a refinement of this choice using a strong rank-revealing QR factorization. We prove bounds on the error of the corresponding low-rank approximation (more precisely, the CUR approximation error) when the matrix is a perturbation of a low-rank matrix that can be factorized into the product of matrices with suitable incoherence and/or sparsity assumptions.
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