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Smallest Singular Value Estimates for Nonuniform Fourier Matrices via Periodic Nonuniform Sampling — arXiv:2608.21960

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.21960
License (as archived): CC0-1.0
Archived: 2026-10-18T08:27:28.861Z
SHA-256 of the archived text: c298ca5139226979e369a4934830a02a31cc1bbb969d712a98a43e0d0f2e6142
Stable URL of this page: https://metraipolis.com/documento/dc_c170d950a70d

How to cite

Smallest Singular Value Estimates for Nonuniform Fourier Matrices via Periodic Nonuniform Sampling — arXiv:2608.21960 — arXiv (en), https://arxiv.org/abs/2608.21960 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_c170d950a70d (Metraipolis archive dc_c170d950a70d, sha256 c298ca5139226979e369a4934830a02a31cc1bbb969d712a98a43e0d0f2e6142)

BibTeX

@misc{dcc170d950a70d,
  title = {Smallest Singular Value Estimates for Nonuniform Fourier Matrices via Periodic Nonuniform Sampling — arXiv:2608.21960},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.21960},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_c170d950a70d; sha256 c298ca5139226979e369a4934830a02a31cc1bbb969d712a98a43e0d0f2e6142},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.21960. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We study the smallest singular value of nonuniform Fourier matrices in two settings: clustered nodes and perturbations of an equispaced grid. By reducing the problem to spectral norm estimates for periodic nonuniform interpolation matrices, we obtain nearly optimal bounds in both cases. For clustered nodes, we derive the first local separation condition in which each required gap depends only on the sizes of the two neighboring clusters. For perturbations with the bound \(1/4\leq L<1/2\), our result confirms the conjecture of Austin and Trefethen on the \(2\)-norm Lebesgue constant up to a logarithmic factor.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-25 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2608.21960 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-18T08:27:23.834Z dalla pagina https://arxiv.org/catchup/math.NA/2026-08-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).