{
  "abstract": "We present a root isolation algorithm for an analytic function. The method combines interval subdivision with a heuristic test based on local cubic Hermite interpolation. Whenever the function is sufficiently close to its cubic Hermite interpolant at a few sample points, we assume that the critical points of the cubic interpolant give a valid root isolation for the original function. Such an algorithm cannot, in general, provide a rigorous certification of the computed intervals. Nevertheless, extensive numerical experiments show that it is highly efficient and almost always produces the correct results. We hope that a probabilistic or exact algorithm can be derived from this work.",
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  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02934",
  "author_total": 1,
  "authors": [
    {
      "name": "Christophe Raffalli"
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  "bibtex": "https://research.draconitic.com/paper/7kp8n7e8q7qd5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02934",
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  "id": "7kp8n7e8q7qd5",
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  "landing_url": "https://hal.science/hal-05765782v1",
  "language": "en",
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      "1703|Polynomial and algebraic computation"
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  "pdf_url": "https://hal.science/hal-05765782/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7kp8n7e8q7qd5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "hal-05765782",
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      "url": "https://hal.science/hal-05765782v1"
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      "native_id": "2610.02934",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02934"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "ROOT ISOLATION FOR ANALYTIC FUNCTIONS USING CUBIC HERMITE INTERPOLATION.",
  "title_text": "ROOT ISOLATION FOR ANALYTIC FUNCTIONS USING CUBIC HERMITE INTERPOLATION.",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/7kp8n7e8q7qd5",
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