{
  "abstract": "The Padé-based method for subgroup parameter calculation in resonance self-shielding analysis is ill-posed: the truncated overdetermined system, the Vandermonde-type coefficient matrix, and the unenforced pole–residue structure jointly produce unstable poles and subgroup parameters that violate non-negativity or the probability normalization. This paper proposes the regularized overdetermined Padé approximation (ROPA), a two-stage, structure-preserving procedure that resolves this ill-posedness at the level of the mathematical problem rather than the numerical workflow. In stage one, the overdetermined least-squares Padé system is built on a normalized background cross-section variable with column equilibration and Tikhonov regularization, the poles are computed as eigenvalues of a companion matrix, and a reflection gate maps them onto the positive real axis. In stage two, the subgroup probabilities are recovered by a convex quadratic program enforcing non-negativity and unit sum, with non-negative least squares for partial probability channels. The well-posedness of the regularized problem is established theoretically, including an explicit stability bound with respect to perturbations of the resonance integral data. Validation against OpenMC Monte Carlo references on ENDF/B-VIII.0 data for 235U, 238U, and 240Pu over 16 resonance groups, together with VERA pin-cell and lattice benchmarks, demonstrates that ROPA achieves accuracy comparable to or higher than existing methods while guaranteeing admissible parameters in all tested cases.",
  "abstract_shown": true,
  "affiliations": [
    "Naval University of Engineering, Wuhan 430033, China",
    "China Nuclear Data Center, China Institute of Atomic Energy, Beijing 102413, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 6,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Song Li"
    },
    {
      "affs": [
        0
      ],
      "name": "Lei Liu",
      "orcid": "0009-0007-5009-7057"
    },
    {
      "affs": [
        0
      ],
      "name": "Yongfa Zhang"
    },
    {
      "affs": [
        0
      ],
      "name": "Jianli Hao"
    },
    {
      "affs": [
        0
      ],
      "name": "Zouzhe Li"
    },
    {
      "affs": [
        1
      ],
      "name": "Ying Chen",
      "orcid": "0009-0005-1991-3488"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8a7wzty5cagbf.bib",
  "cited_by": 0,
  "doi": "10.3390/math14193636",
  "fulltext_url": null,
  "id": "8a7wzty5cagbf",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/19/3636",
  "language": null,
  "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": [
    [
      "openalex",
      "2202|Nuclear reactor physics and engineering"
    ]
  ],
  "openalex": "W7220944763",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/8a7wzty5cagbf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14193636",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/19/3636"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Mathematical Resolution of Ill-Posedness in Padé-Based Subgroup Parameter Calculation via Regularization and Pole–Residue Constraints",
  "title_text": "Mathematical Resolution of Ill-Posedness in Padé-Based Subgroup Parameter Calculation via Regularization and Pole–Residue Constraints",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/8a7wzty5cagbf",
  "venue": "Mathematics",
  "versions": []
}