{
  "abstract": "We consider the adjoint-free random-plane iteration algorithm for finding the top eigenvector of a matrix proposed in (SIAM J. Matrix Anal. Appl. 47 (2026), 1349-1374). Unlike standard methods such as the power method or gradient descent, the above algorithm lacked linear convergence guarantees in the presence of a spectral gap. In this paper, we establish explicit spectral-gap-dependent global linear convergence rates in expectation, providing quantitative guarantees for the empirically observed convergence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.42071",
  "author_total": 2,
  "authors": [
    {
      "name": "Jonas Bresch"
    },
    {
      "name": "Oleh Melnyk"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2nx9vms3awqwc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.42071",
  "fulltext_url": null,
  "id": "2nx9vms3awqwc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.42071",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.42071",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2nx9vms3awqwc.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.42071",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.42071"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Stochastic Rayleigh-Ritz Ascent: Global Linear Convergence under a Spectral Gap",
  "title_text": "Stochastic Rayleigh-Ritz Ascent: Global Linear Convergence under a Spectral Gap",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/2nx9vms3awqwc",
  "venue": "arXiv",
  "versions": []
}