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PreprintCC BY 4.0arXiv

Smallest Singular Value Estimates for Nonuniform Fourier Matrices via Periodic Nonuniform Sampling

  • Liang Chen
  • Rongrong Lin
  • Haizhang Zhang
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Abstract

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≤ L<1/2, our result confirms the conjecture of Austin and Trefethen on the 2-norm Lebesgue constant up to a logarithmic factor.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026smallest,
  title = {{Smallest Singular Value Estimates for Nonuniform Fourier Matrices via Periodic Nonuniform Sampling}},
  author = {Liang Chen and Rongrong Lin and Haizhang Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.21960},
  eprint = {2608.21960},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.21960},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Smallest Singular Value Estimates for Nonuniform Fourier Matrices via Periodic Nonuniform Sampling
AU  - Liang Chen
AU  - Rongrong Lin
AU  - Haizhang Zhang
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2608.21960
UR  - https://arxiv.org/abs/2608.21960
AB  - 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≤ L<1/2, our result confirms the conjecture of Austin and Trefethen on the 2-norm Lebesgue constant up to a logarithmic factor.
ER  -