{
  "abstract": "We study deterministic approximation of the Lebesgue volume of compact unit sublevel sets of positive quasi-homogeneous polynomials. Pushing the uniform measure on a bounding box through the polynomial reduces the problem to a univariate moment problem. Weighted homogeneity determines the moments of its restriction to the unit interval up to the unknown volume. Two algorithms provide upper and lower bounds using polynomial arithmetic and linear algebra. CHEB integrates Chebyshev polynomial approximations of a continuous piecewise-linear function and converges algebraically. GEVP uses two generalized eigenvalue problems and converges exponentially, with a rate governed by an upper bound on the polynomial over the box. Moment preprocessing depends on the dimension, polynomial structure and approximation order. Explicit Stokes dual certificates yield corresponding convergence bounds for the multivariate moment-sums-of-squares hierarchy.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.29269",
  "author_total": 2,
  "authors": [
    {
      "name": "Didier Henrion"
    },
    {
      "name": "Jean B Lasserre"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1vg7vwsc8qf8m.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "1vg7vwsc8qf8m",
  "issns": [],
  "landing_url": "https://hal.science/hal-05708227v2",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-oc"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05708227/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1vg7vwsc8qf8m.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:20:53Z",
      "native_id": "hal-05708227",
      "source": "hal",
      "url": "https://hal.science/hal-05708227v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-oc",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Volume of quasi-homogeneous sublevel sets: Two linear algebra deterministic algorithms with convergence rates",
  "title_text": "Volume of quasi-homogeneous sublevel sets: Two linear algebra deterministic algorithms with convergence rates",
  "type": "preprint",
  "updated_at": "2026-11-05T12:20:12Z",
  "url": "https://research.draconitic.com/paper/1vg7vwsc8qf8m",
  "venue": "HAL",
  "versions": []
}