{
  "abstract": "Discrete-time non-symmetric algebraic Riccati equations (DTNAREs) arise in game-theoretic computations of Nash equilibria. Solving such equations at large scale is often computationally prohibitive. This paper develops a numerical approach for large-scale DTNAREs whose solutions are low rank. A low-rank alternating direction implicit (ADI) method is introduced that recursively constructs a low-rank stabilizing solution without explicitly solving any projected DTNARE. Through the pole-placement property of the low-rank ADI iteration, the method ensures that the implicitly solved projected DTNARE always admits a stabilizing solution. An automatic shift-generation strategy is also developed for the ADI iterations. Once an initial shift is provided, the algorithm computes the low-rank solution without further user intervention. Numerical experiments on DTNAREs with dimensions between \\(10^6\\) and \\(10^7\\) demonstrate the accuracy and efficiency of the method. The results confirm that the proposed low-rank ADI algorithm is an effective solver for large-scale DTNAREs that would otherwise be computationally prohibitive.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21282",
  "author_total": 1,
  "authors": [
    {
      "name": "Umair Zulfiqar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5st5vvax1em1g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21282",
  "fulltext_url": null,
  "id": "5st5vvax1em1g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21282",
  "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",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "1703|Matrix Theory and Algorithms"
    ]
  ],
  "openalex": "W7213898108",
  "pdf_url": "https://arxiv.org/pdf/2609.21282",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5st5vvax1em1g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21282",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21282"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A Low-rank ADI Algorithm for the Numerical Solution of Large Discrete-time Non-symmetric Algebraic Riccati Equations",
  "title_text": "A Low-rank ADI Algorithm for the Numerical Solution of Large Discrete-time Non-symmetric Algebraic Riccati Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/5st5vvax1em1g",
  "venue": "arXiv",
  "versions": []
}