Beyond singular value gaps in randomized subspace approximation
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911476346781696 |
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| author | Wang, Christopher Townsend, Alex |
| author_facet | Wang, Christopher Townsend, Alex |
| contents | The success of randomized range finders (RRFs) is typically analyzed via the singular value gaps of a target matrix $A$. In this work, we show that the so-called Frobenius singular value ratio provides a sharper analysis of an RRF's subspace quality under Gaussian sketching. For any matrix $A$ and any integer $k\ge0$, we derive an explicit, closed-form expression for the cumulative distribution function of the largest principal angle between the $k$-dominant singular subspace of $A$ and the approximate RRF subspace, expressing it in terms of a hypergeometric function. We obtain definitive probabilistic guarantees for RRFs that are strictly stronger than those obtained previously. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01191 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Beyond singular value gaps in randomized subspace approximation Wang, Christopher Townsend, Alex Numerical Analysis 65F55, 15A18, 68W20 (Primary) 60B20, 62H10, 62R30 (Secondary) The success of randomized range finders (RRFs) is typically analyzed via the singular value gaps of a target matrix $A$. In this work, we show that the so-called Frobenius singular value ratio provides a sharper analysis of an RRF's subspace quality under Gaussian sketching. For any matrix $A$ and any integer $k\ge0$, we derive an explicit, closed-form expression for the cumulative distribution function of the largest principal angle between the $k$-dominant singular subspace of $A$ and the approximate RRF subspace, expressing it in terms of a hypergeometric function. We obtain definitive probabilistic guarantees for RRFs that are strictly stronger than those obtained previously. |
| title | Beyond singular value gaps in randomized subspace approximation |
| topic | Numerical Analysis 65F55, 15A18, 68W20 (Primary) 60B20, 62H10, 62R30 (Secondary) |
| url | https://arxiv.org/abs/2603.01191 |