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arXiv · 2402.13975

A sublinear-time randomized algorithm for column and row subset selection based on strong rank-revealing QR factorizations

Alice Cortinovis·Lexing Ying
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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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Alice Cortinovis, Lexing Ying. 2024-02-21. A sublinear-time randomized algorithm for column and row subset selection based on strong rank-revealing QR factorizations. https://arxiv.org/abs/2402.13975

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