{
  "abstract": "We study explicit lightning-plus-polynomial (LP) approximation of $g(z)z^α(\\log z)^m$ on a closed unit-radius sector, where $0<α<1$, $m$ is fixed, and $g$ is analytic nearby. Since the basic sector root-exponential rate is already known, we address three finer questions. First, a one-sided Abel--Poisson formula and a pole-free notched contour give a branchwise error bound that is uniform for grid shifts in compact subsets of $(0,1)$ and valid for every fixed logarithmic power. Second, for $z^α$ in the dense and balanced regimes, an exact vertex-scale rescaling identifies a positive finite leading constant for a specified shifted sequence. Third, a rate-matched band of additional representation poles followed by polynomial compression gives the explicit representation dimension $N+2\\sqrt{2αλ_σN}+O(1)$ while leaving the first $N$ tapered poles unchanged. A slightly overresolved hybrid sequence also preserves the exact leading constant. Matched-dimension experiments, including reentrant sectors, illustrate the allocation. These exact-asymptotic and dimension statements concern the stated constructions, not sector minimax approximation or total computational complexity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09256",
  "author_total": 2,
  "authors": [
    {
      "name": "Fei Xue"
    },
    {
      "name": "Tianqi Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c22x7v4fe014x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09256",
  "fulltext_url": null,
  "id": "c22x7v4fe014x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09256",
  "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.NA"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7220940934",
  "pdf_url": "https://arxiv.org/pdf/2610.09256",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c22x7v4fe014x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09256",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09256"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Shifted tapered-pole approximation on finite sectors: an exact asymptotic and dimension control",
  "title_text": "Shifted tapered-pole approximation on finite sectors: an exact asymptotic and dimension control",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/c22x7v4fe014x",
  "venue": "arXiv",
  "versions": []
}