{
  "abstract": "We study a local graph-based interpolation framework for data defined on graph vertices embedded in a metric space. The resulting interpolants are constructed from variational graph splines defined on small neighborhoods, yielding continuous-domain extensions of the graph data. We analyze their behavior through energy estimates, Lipschitz continuity, and stability properties, and compare them with $k$-Nearest Neighbor ($k$NN) interpolation as a natural baseline due to its simplicity and widespread use. Numerical experiments on the manifold of symmetric positive definite matrices illustrate the relative performance of the proposed local interpolation schemes and $k$NN interpolation across varying levels of smoothness and noise.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15172",
  "author_total": 3,
  "authors": [
    {
      "name": "E. Fuselier"
    },
    {
      "name": "J. P. Ward"
    },
    {
      "name": "J. Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3qpcfr4qb5v0s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15172",
  "fulltext_url": null,
  "id": "3qpcfr4qb5v0s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15172",
  "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",
      "1703|Topological and Geometric Data Analysis"
    ]
  ],
  "openalex": "W7221790734",
  "pdf_url": "https://arxiv.org/pdf/2610.15172",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3qpcfr4qb5v0s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15172",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15172"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Interpolation in path-connected metric spaces using splines on embedded graphs",
  "title_text": "Interpolation in path-connected metric spaces using splines on embedded graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/3qpcfr4qb5v0s",
  "venue": "arXiv",
  "versions": []
}