A sublinear-time randomized algorithm for column and row subset selection based on strong rank-revealing QR factorizations
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909115327971328 |
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| author | Cortinovis, Alice Ying, Lexing |
| author_facet | Cortinovis, Alice Ying, Lexing |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13975 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A sublinear-time randomized algorithm for column and row subset selection based on strong rank-revealing QR factorizations Cortinovis, Alice Ying, Lexing Numerical Analysis 65F30 (Primary) 15A23 (Secondary) 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. |
| title | A sublinear-time randomized algorithm for column and row subset selection based on strong rank-revealing QR factorizations |
| topic | Numerical Analysis 65F30 (Primary) 15A23 (Secondary) |
| url | https://arxiv.org/abs/2402.13975 |