Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2603.01191 |
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Inhaltsangabe:
- 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.