{
  "abstract": "We present a novel numerical integration method for non-periodic functions over the high-dimensional unit cube $[0,1]^s$ by a specially crafted (unequally-)weighted quadrature rule using transformed lattice points, with the additional option of subsampling. The method is designed for integrands whose mixed derivatives up to order $α$ are square-integrable with respect to a product Chebyshev density. The ingredients are (i) periodizing the integrand, (ii) approximating the smooth periodic function by a kernel interpolant at lattice points, (iii) integrating exactly the product of the kernel interpolant and the nonsmooth density, together with subsampling alternatives for (ii) and~(iii). With $|J|$ corresponding to the number of function evaluations, we achieve the convergence rate close to the order $|J|^{-(α-1/2)}$ and $|J|^{-α}\\,($1.110721$)^s$, where the implied constants are independent of $s$ under favorable conditions. We can interpolate these two results to trade between the convergence rate and the growth in $s$. We provide numerical experiments to demonstrate our theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01113",
  "author_total": 5,
  "authors": [
    {
      "name": "Felix Bartel"
    },
    {
      "name": "Alexander D. Gilbert"
    },
    {
      "name": "Michael Griebel"
    },
    {
      "name": "Frances Y. Kuo"
    },
    {
      "name": "Ian H. Sloan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ed8fd3pj3nc5v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01113",
  "fulltext_url": null,
  "id": "ed8fd3pj3nc5v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01113",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2612|Mathematical Approximation and Integration"
    ]
  ],
  "openalex": "W7215802178",
  "pdf_url": "https://arxiv.org/pdf/2610.01113",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ed8fd3pj3nc5v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01113",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01113"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A higher order lattice-based method for high-dimensional numerical integration using periodization",
  "title_text": "A higher order lattice-based method for high-dimensional numerical integration using periodization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/ed8fd3pj3nc5v",
  "venue": "arXiv",
  "versions": []
}