{
  "abstract": "We propose Regularized Newton-SLRA (RN-SLRA), a regularized Newton-type method for local manifold--affine intersection problems motivated by structured low-rank approximation. Classical Newton-SLRA achieves fast local convergence under transversality, but its tangent-space intersection step may become ill-defined, singular, or severely ill-conditioned when transversality fails. RN-SLRA overcomes this difficulty by replacing the exact tangent-space intersection step with a regularized quadratic subproblem over the affine space. Under intrinsic transversality, RN-SLRA with regularization parameter $μ_k=c r_k^ρ$ converges locally with Q-order at least $1+ρ$ for $0<ρ\\le1$, including quadratically for $ρ=1$, and linearly for $ρ=0$. We also analyze an inexact variant based on $σ$-quasioptimal manifold projections. It retains the $1+ρ$ order for $0<ρ\\leq1$, and converges linearly for fixed regularization when $qσ<1$, where $q$ is the local one-step alternating-projection factor. Experiments support the predicted quadratic behavior on an analytically clean but nontransversal SLRA instance, where the classical Newton tangent system is severely ill-conditioned, and show reduced projection costs for the inexact method on large-scale Hankel problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.31738",
  "author_total": 2,
  "authors": [
    {
      "name": "Dengyu Zheng"
    },
    {
      "name": "Shixiang Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2s1tsf0whnps7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.31738",
  "fulltext_url": null,
  "id": "2s1tsf0whnps7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.31738",
  "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"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "2612|Advanced Optimization Algorithms Research"
    ]
  ],
  "openalex": "W7166882039",
  "pdf_url": "https://arxiv.org/pdf/2606.31738",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2s1tsf0whnps7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2606.31738",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.31738"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "A Regularized Newton-Type Method for Manifold--Affine Intersection Problems under Intrinsic Transversality",
  "title_text": "A Regularized Newton-Type Method for Manifold--Affine Intersection Problems under Intrinsic Transversality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/2s1tsf0whnps7",
  "venue": "arXiv",
  "versions": []
}