{
  "abstract": "This paper develops projection methods for computing low-rank solutions to large-scale coupled generalized Sylvester equations. The dominant subspaces of these solutions are shown to be spanned by specific resolvent directions, motivating a Petrov--Galerkin projection framework. Conditions for the unique solvability of the projected coupled generalized Sylvester equations are also discussed. Based on these dominant subspaces, two algorithms are proposed: an extended Krylov-based projection algorithm and a rational Krylov-based projection algorithm. The former uses fixed shifts, whereas the latter uses adaptive shifts. Numerical experiments on large-scale benchmark problems demonstrate that the proposed methods achieve high accuracy and fast convergence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30804",
  "author_total": 1,
  "authors": [
    {
      "name": "Umair Zulfiqar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4mpk9qrqmkghx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30804",
  "fulltext_url": null,
  "id": "4mpk9qrqmkghx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30804",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
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      "arxiv",
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      "arxiv",
      "eess.SY"
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      "openalex",
      "1703|Matrix Theory and Algorithms"
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  "openalex": "W7223362966",
  "pdf_url": "https://arxiv.org/pdf/2610.30804",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4mpk9qrqmkghx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30804",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30804"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Numerical Solution of Large-Scale Low-Rank Coupled Generalized Sylvester Equations",
  "title_text": "Numerical Solution of Large-Scale Low-Rank Coupled Generalized Sylvester Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/4mpk9qrqmkghx",
  "venue": "arXiv",
  "versions": []
}