Robust Blockwise Random Pivoting: Fast and Accurate Adaptive Interpolative Decomposition
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| Publicado en: | arXiv.org (Dec 19, 2024), p. n/a |
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| Autor principal: | |
| Otros Autores: | , , |
| Publicado: |
Cornell University Library, arXiv.org
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| Materias: | |
| Acceso en línea: | Citation/Abstract Full text outside of ProQuest |
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| 001 | 2870189021 | ||
| 003 | UK-CbPIL | ||
| 022 | |a 2331-8422 | ||
| 035 | |a 2870189021 | ||
| 045 | 0 | |b d20241219 | |
| 100 | 1 | |a Dong, Yijun | |
| 245 | 1 | |a Robust Blockwise Random Pivoting: Fast and Accurate Adaptive Interpolative Decomposition | |
| 260 | |b Cornell University Library, arXiv.org |c Dec 19, 2024 | ||
| 513 | |a Working Paper | ||
| 520 | 3 | |a The interpolative decomposition (ID) aims to construct a low-rank approximation formed by a basis consisting of row/column skeletons in the original matrix and a corresponding interpolation matrix. This work explores fast and accurate ID algorithms from comprehensive perspectives for empirical performance, including accuracy in both skeleton selection and interpolation matrix construction, efficiency in terms of asymptotic complexity and hardware efficiency, as well as rank adaptiveness. While many algorithms have been developed to optimize some of these aspects, practical ID algorithms proficient in all aspects remain absent. To fill in the gap, we introduce robust blockwise random pivoting (RBRP) that is asymptotically fast, hardware-efficient, and rank-adaptive, providing accurate skeletons and interpolation matrices comparable to the best existing ID algorithms in practice. Through extensive numerical experiments on various synthetic and natural datasets, we demonstrate the appealing empirical performance of RBRP from the aforementioned perspectives, as well as the robustness of RBRP to adversarial inputs. | |
| 653 | |a Parallel processing | ||
| 653 | |a Tolerances | ||
| 653 | |a Mathematical analysis | ||
| 653 | |a Matrices (mathematics) | ||
| 653 | |a Interpolation | ||
| 653 | |a Optimization | ||
| 653 | |a Approximation | ||
| 653 | |a Algorithms | ||
| 653 | |a Asymptotic properties | ||
| 653 | |a Robustness (mathematics) | ||
| 653 | |a Complexity | ||
| 653 | |a Error detection | ||
| 653 | |a Decomposition | ||
| 700 | 1 | |a Chen, Chao | |
| 700 | 1 | |a Martinsson, Per-Gunnar | |
| 700 | 1 | |a Pearce, Katherine | |
| 773 | 0 | |t arXiv.org |g (Dec 19, 2024), p. n/a | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/2870189021/abstract/embedded/ZKJTFFSVAI7CB62C?source=fedsrch |
| 856 | 4 | 0 | |3 Full text outside of ProQuest |u http://arxiv.org/abs/2309.16002 |