On the Upper Bounds for the Matrix Spectral Norm
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911012360290304 |
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| author | Naumov, Alexey Rakhuba, Maxim Ryapolov, Denis Samsonov, Sergey |
| author_facet | Naumov, Alexey Rakhuba, Maxim Ryapolov, Denis Samsonov, Sergey |
| contents | We consider the problem of estimating the spectral norm of a matrix using only matrix-vector products. We propose a new Counterbalance estimator that provides upper bounds on the norm and derive probabilistic guarantees on its underestimation. Compared to standard approaches such as the power method, the proposed estimator produces significantly tighter upper bounds in both synthetic and real-world settings. Our method is especially effective for matrices with fast-decaying spectra, such as those arising in deep learning and inverse problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15660 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Upper Bounds for the Matrix Spectral Norm Naumov, Alexey Rakhuba, Maxim Ryapolov, Denis Samsonov, Sergey Numerical Analysis Machine Learning Statistics Theory 65F35 We consider the problem of estimating the spectral norm of a matrix using only matrix-vector products. We propose a new Counterbalance estimator that provides upper bounds on the norm and derive probabilistic guarantees on its underestimation. Compared to standard approaches such as the power method, the proposed estimator produces significantly tighter upper bounds in both synthetic and real-world settings. Our method is especially effective for matrices with fast-decaying spectra, such as those arising in deep learning and inverse problems. |
| title | On the Upper Bounds for the Matrix Spectral Norm |
| topic | Numerical Analysis Machine Learning Statistics Theory 65F35 |
| url | https://arxiv.org/abs/2506.15660 |