{
  "abstract": "We investigate the recovery of an unknown number of stationary point heat sources, together with their locations and constant positive strengths, from temperature histories recorded by a few sensors. The reconstruction combines candidate selection by orthogonal matching pursuit or least angle regression with continuous constrained fitting. A noise-based discrepancy rule selects the smallest accepted source count among those tested. The analysis distinguishes source-count selection, individual-parameter recovery, and aggregate estimation. For a close pair, the local single-source residual is quadratic in separation when the projected curvature is nonzero, whereas a compensating unit parameter direction produces a linearized response bounded by a constant times the cube of separation. This difference explains why a pair may be distinguishable from a single source while its individual parameters remain poorly determined. A conditional stability bound controls errors in total strength and the strength-weighted center, and a local Gaussian approximation relates single-source rejection to noise and separation. Numerical experiments assess sensor configuration, temporal sampling, noise, separation, and initialization, with additional tests using independently generated finite-plate data and a three-dimensional model. Correct source-count selection need not imply accurate individual parameters, whereas unresolved pairs can retain accurate aggregate estimates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21301",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiaomei Yang"
    },
    {
      "name": "Zhiliang Deng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fmqs0y4rcbhx6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21301",
  "fulltext_url": null,
  "id": "fmqs0y4rcbhx6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21301",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2610|Numerical methods in inverse problems"
    ]
  ],
  "openalex": "W7222590345",
  "pdf_url": "https://arxiv.org/pdf/2610.21301",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fmqs0y4rcbhx6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.21301",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21301"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Reconstructing constant point heat sources from few temperature sensors: sparse selection and spatial resolution",
  "title_text": "Reconstructing constant point heat sources from few temperature sensors: sparse selection and spatial resolution",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:59Z",
  "url": "https://research.draconitic.com/paper/fmqs0y4rcbhx6",
  "venue": "arXiv",
  "versions": []
}