{
  "abstract": "For every reproducing kernel Hilbert space $\\mathcal{H}_K$ with bounded kernel $K$, we prove that the linear sampling widths $g_m^{\\text{lin}}$ and Gelfand widths $c_n$ in the uniform norm satisfy $$ g_m^{\\text{lin}}(B_{\\mathcal H_K})_\\infty \\leq \\frac{m+1}{m-n+1}\\, c_n(B_{\\mathcal H_K})_\\infty\\quad , \\quad m\\ge n. $$ In a certain sense, the leading factor $(m+1)/(m-n+1)$ on the right-hand side is sharp. We transfer the problem into the selection of a maximal volume subset of kernel translates (kernel $D$-optimal design). Apart from basic linear algebra, our proof employs low rank approximation techniques and a version of the Eckart-Young-Mirsky theorem. The same argument gives corresponding bounds for the selection of a reduced basis in Hilbert spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15556",
  "author_total": 2,
  "authors": [
    {
      "name": "Sebastian Neumayer"
    },
    {
      "name": "Tino Ullrich"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7x97zzk2xk3tk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15556",
  "fulltext_url": null,
  "id": "7x97zzk2xk3tk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15556",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2612|Mathematical Approximation and Integration"
    ]
  ],
  "openalex": "W7213302390",
  "pdf_url": "https://arxiv.org/pdf/2609.15556",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7x97zzk2xk3tk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15556",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15556"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A sharp bound for sampling widths in the uniform norm: kernel $D$-optimal designs and oversampling",
  "title_text": "A sharp bound for sampling widths in the uniform norm: kernel D-optimal designs and oversampling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/7x97zzk2xk3tk",
  "venue": "arXiv",
  "versions": []
}