An improved error analysis of CholeskyQR with the randomized model
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915448358961152 |
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| author | Guan, Haoran Fan, Yuwei |
| author_facet | Guan, Haoran Fan, Yuwei |
| contents | This work is about an improved error analysis of CholeskyQR with the randomized model for the tall-skinny $X \in \mathbb{R}^{m\times n}$. Due to the structure of CholeskyQR, we utilize the randomized model in the first step of CholeskyQR with a weak assumption. We receive a better sufficient condition of $κ_{2}(X)$ and a tighter upper bound of residual for CholeskyQR2, together with a probabilistic shifted item $s$ for Shifted CholeskyQR3 based on $\norm{X}_{F}$ after improved error analysis. Numerical experiments demonstrate the effectiveness of our new theoretical results. The probabilistic $s$ for Shifted CholeskyQR3 can enhance the applicability of Shifted CholeskyQR3 while maintaining numerical stability. It is also robust enough after numerous experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09389 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An improved error analysis of CholeskyQR with the randomized model Guan, Haoran Fan, Yuwei Numerical Analysis 65F30, 15A23, 65F25, 65G50 This work is about an improved error analysis of CholeskyQR with the randomized model for the tall-skinny $X \in \mathbb{R}^{m\times n}$. Due to the structure of CholeskyQR, we utilize the randomized model in the first step of CholeskyQR with a weak assumption. We receive a better sufficient condition of $κ_{2}(X)$ and a tighter upper bound of residual for CholeskyQR2, together with a probabilistic shifted item $s$ for Shifted CholeskyQR3 based on $\norm{X}_{F}$ after improved error analysis. Numerical experiments demonstrate the effectiveness of our new theoretical results. The probabilistic $s$ for Shifted CholeskyQR3 can enhance the applicability of Shifted CholeskyQR3 while maintaining numerical stability. It is also robust enough after numerous experiments. |
| title | An improved error analysis of CholeskyQR with the randomized model |
| topic | Numerical Analysis 65F30, 15A23, 65F25, 65G50 |
| url | https://arxiv.org/abs/2410.09389 |