{
  "abstract": "This paper studies extensions of adaptive randomized pivoting (ARP), recently introduced for matrix column subset selection, to tensors in the t-product framework. We propose two constructions. ARP-T-CUR applies matrix ARP-cross at the nonredundant Fourier frequencies and uses conjugate symmetry to preserve real-valued tensors. Assuming that the selected intersections are nonsingular almost surely, the matrix theory gives a direct expected-error bound for this Fourier-slicewise approximation. T-ARP instead selects common lateral and horizontal slices, with the same indices used at every Fourier frequency. This common-index constraint requires a new analysis. Under frequency-alignment and frequency-wise rank-growth assumptions, we prove an expected-error bound and recover the matrix ARP factor $r+1$ when the frequency-wise sampling distributions are aligned. We also derive bounds for tensor cross approximation and t-DEIM. The numerical experiments show that both proposed methods give accurate tensor approximations and perform favorably against the considered slice-selection baselines. A separate full-enumeration experiment verifies the assumptions and the expected-error bound for common-index T-ARP.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.26688",
  "author_total": 3,
  "authors": [
    {
      "name": "Ahmadsho Akdodshoev"
    },
    {
      "name": "Valentin Leplat"
    },
    {
      "name": "Salman Ahmadi-Asl"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4a71nzwxz8ss9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.26688",
  "fulltext_url": null,
  "id": "4a71nzwxz8ss9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.26688",
  "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",
      "2605|Tensor decomposition and applications"
    ]
  ],
  "openalex": "W7166116956",
  "pdf_url": "https://arxiv.org/pdf/2606.26688",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4a71nzwxz8ss9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2606.26688",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.26688"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Adaptive Randomized Pivoting for Tensor Cross Approximation in the T-Product Framework",
  "title_text": "Adaptive Randomized Pivoting for Tensor Cross Approximation in the T-Product Framework",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/4a71nzwxz8ss9",
  "venue": "arXiv",
  "versions": []
}