{
  "abstract": "Krylov subspace methods, such as the Conjugate Gradient (CG) and BiCGSTAB methods, are widely used in scientific computing for solving linear systems. In this study, we propose a new framework for solving large Sylvester equations in a low-rank format by reconstructing matrix-oriented Krylov subspace methods. The framework realizes efficient algorithms that are mathematically equivalent to the matrix-oriented Krylov subspace methods by exploiting the mathematical properties of the Sylvester operator and the low-rank structure of the right-hand side. Specifically, by leveraging these properties, approximate solutions can be expressed in a low-rank factorized form, enabling efficient computation and reduced memory requirements. The effectiveness of our algorithms is demonstrated through numerical experiments.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.28274",
  "author_total": 4,
  "authors": [
    {
      "name": "Yuki Satake"
    },
    {
      "name": "Takeshi Fukaya"
    },
    {
      "name": "Tomohiro Sogabe"
    },
    {
      "name": "Shao-Liang Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2sp5smap14h2a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.28274",
  "fulltext_url": null,
  "id": "2sp5smap14h2a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.28274",
  "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",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7162662390",
  "pdf_url": "https://arxiv.org/pdf/2605.28274",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2sp5smap14h2a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2605.28274",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.28274"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Factorized Krylov subspace methods for solving large Sylvester equations",
  "title_text": "Factorized Krylov subspace methods for solving large Sylvester equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/2sp5smap14h2a",
  "venue": "arXiv",
  "versions": []
}