{
  "abstract": "We analyze two fixed-point iterations for computing the principal square root of an M-matrix $A$. Although these iterations, with customary initialization, converge sublinearly when $A$ is a singular M-matrix, we show that, under suitable mild conditions on the initial approximation, the convergence is linear. Moreover, we provide component-wise accurate versions of these iterations, which allow us to approximate the principal square root with a component-wise relative error uniformly bounded by a small multiple of the machine precision. Numerical experiments demonstrating the effectiveness of the proposed algorithms for certain classes of problems are presented.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27520",
  "author_total": 4,
  "authors": [
    {
      "name": "Dario Andrea Bini"
    },
    {
      "name": "Bruno Iannazzo"
    },
    {
      "name": "Beatrice Meini"
    },
    {
      "name": "Jie Meng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5pva1b9k2vavm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27520",
  "fulltext_url": null,
  "id": "5pva1b9k2vavm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27520",
  "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": "W7214217068",
  "pdf_url": "https://arxiv.org/pdf/2609.27520",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5pva1b9k2vavm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27520",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27520"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Component-wise accurate fixed point iterations for computing the square root of a singular M-matrix",
  "title_text": "Component-wise accurate fixed point iterations for computing the square root of a singular M-matrix",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/5pva1b9k2vavm",
  "venue": "arXiv",
  "versions": []
}