{
  "abstract": "This paper integrates the multivariate Arnoldi process into tangent space Hermite interpolation for manifold-valued data. A G-Arnoldi recurrence constructs a discrete orthogonal polynomial basis, improving numerical conditioning for high-degree approximation. The analysis uses a Markov inequality with a geometry-dependent exponent r; for the convex parameter domains considered here, r = 2 is available. Under suitable regularity and sampling assumptions, we establish C^0 and C^1 error bounds and analyze their propagation through the exponential map. When only function values are sampled, these bounds are O(sqrt(M) n^{-m}) and O(sqrt(M) n^{2-m}), respectively. When first derivatives are also sampled, the C^1 bound improves to O(sqrt(M(d+1)) n^{1-m}). Here n is the polynomial degree, d the parameter dimension, m the target regularity, and M the number of sampling points. For sampling sequences satisfying the fill distance condition with M \\asymp n^{2d}, the corresponding bounds become O(n^{d-m}), O(n^{d+2-m}), and O(n^{d+1-m}), yielding superalgebraic convergence for targets admitting smooth extensions. Numerical experiments on SO(3) and S^2 compare the accuracy and computational cost of the Arnoldi-enhanced method with THI+Kriging, with supplementary experiments demonstrating approximation without derivative samples.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.25176",
  "author_total": 3,
  "authors": [
    {
      "name": "Yuxuan Li"
    },
    {
      "name": "Qiang Niu"
    },
    {
      "name": "Wubin Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9c2hffa6xh0kd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.25176",
  "fulltext_url": null,
  "id": "9c2hffa6xh0kd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.25176",
  "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",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7162421126",
  "pdf_url": "https://arxiv.org/pdf/2605.25176",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9c2hffa6xh0kd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2605.25176",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.25176"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Arnoldi-Enhanced Multivariate Hermite Interpolation of Manifold-Valued Data",
  "title_text": "Arnoldi-Enhanced Multivariate Hermite Interpolation of Manifold-Valued Data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/9c2hffa6xh0kd",
  "venue": "arXiv",
  "versions": []
}