Matrix perturbation bounds via contour bootstrapping
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910657633320960 |
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| author | Tran, Phuc Vu, Van |
| author_facet | Tran, Phuc Vu, Van |
| contents | Matrix perturbation bounds play an essential role in the design and analysis of spectral algorithms. In this paper, we use a "contour bootstrapping" argument to derive several new perturbation bounds. As applications, we discuss new bounds on the error occurring when one uses matrix sparsification to speed up the computation of spectral parameters. Another potential application is the estimation of the trade-off in computing with privacy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05230 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Matrix perturbation bounds via contour bootstrapping Tran, Phuc Vu, Van Numerical Analysis Statistics Theory 68W40, 47A55 Matrix perturbation bounds play an essential role in the design and analysis of spectral algorithms. In this paper, we use a "contour bootstrapping" argument to derive several new perturbation bounds. As applications, we discuss new bounds on the error occurring when one uses matrix sparsification to speed up the computation of spectral parameters. Another potential application is the estimation of the trade-off in computing with privacy. |
| title | Matrix perturbation bounds via contour bootstrapping |
| topic | Numerical Analysis Statistics Theory 68W40, 47A55 |
| url | https://arxiv.org/abs/2407.05230 |