Submatrices with the best-bounded inverses: an asymptotically tight upper bound for $\mathbb{C}^{n \times 2}$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913064564031488 |
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| author | Nesterenko, Yuri |
| author_facet | Nesterenko, Yuri |
| contents | The long-standing hypothesis formulated by Goreinov, Tyrtyshnikov and Zamarashkin \cite{GTZ1997} has recently been solved affirmatively in the case of real two-column matrices by Sengupta and Pautov \cite{SP2026}. In this paper, we consider the complex variant of this problem and prove the asymptotically tight upper bound for spectral norms of the best-bounded inverse $2 \times 2$ submatrices of an arbitrary complex $n \times 2$ matrix with orthonormal columns. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_24087 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Submatrices with the best-bounded inverses: an asymptotically tight upper bound for $\mathbb{C}^{n \times 2}$ Nesterenko, Yuri Numerical Analysis The long-standing hypothesis formulated by Goreinov, Tyrtyshnikov and Zamarashkin \cite{GTZ1997} has recently been solved affirmatively in the case of real two-column matrices by Sengupta and Pautov \cite{SP2026}. In this paper, we consider the complex variant of this problem and prove the asymptotically tight upper bound for spectral norms of the best-bounded inverse $2 \times 2$ submatrices of an arbitrary complex $n \times 2$ matrix with orthonormal columns. |
| title | Submatrices with the best-bounded inverses: an asymptotically tight upper bound for $\mathbb{C}^{n \times 2}$ |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2604.24087 |