{
  "abstract": "Let $S:X\\to Y$ be a bounded linear operator between real Banach spaces, and let $F\\subset X$ be nonempty, bounded and convex. We prove $$a_{2n-1}(S,F)\\le 27n\\min \\{ e^{\\rm ran}_n (S,F), e^{\\rm ada}_n (S,F)\\}.$$ Here $a_k$ is the minimal worst-case error of continuous affine algorithms of rank at most $k$, and $e_n^{\\rm ran}$ and $e_n^{\\rm ada}$ are the minimal errors of adaptive randomized and deterministic algorithms using at most $n$ continuous linear measurements. This shows that the gain of adaption and randomization, and even nonlinearity, is limited by a factor $27n$ for approximation in convex sets. We discuss the optimality of the result by examples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33733",
  "author_total": 3,
  "authors": [
    {
      "name": "David Krieg"
    },
    {
      "name": "Erich Novak"
    },
    {
      "name": "Mario Ullrich"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cp7cf89p9ebsv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33733",
  "fulltext_url": null,
  "id": "cp7cf89p9ebsv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33733",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7224024197",
  "pdf_url": "https://arxiv.org/pdf/2610.33733",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cp7cf89p9ebsv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33733",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33733"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "On the power of adaption and randomization 2: Non-symmetric convex sets",
  "title_text": "On the power of adaption and randomization 2: Non-symmetric convex sets",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/cp7cf89p9ebsv",
  "venue": "arXiv",
  "versions": []
}