{
  "abstract": "In the present paper, we investigate the local and the semilocal convergence of a recently constructed family of accelerated simultaneous methods with two corrections applied to polynomials with simple and multiple zeros. A new local convergence theorem that provides explicit domains of initial conditions and error estimates ensuring the Q-convergence of the methods from the first iteration is established. Based on this result, we derive a semilocal convergence theorem, for simple zeros, with computable initial conditions and an error estimate, making it directly applicable in practice. Three numerical tests illustrate the applicability of the theoretical results.",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, 4000 Plovdiv, Bulgaria",
    "Faculty of Physics and Technology, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria",
    "Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Ivan Ginchev"
    },
    {
      "affs": [
        1
      ],
      "name": "Stoil I. Ivanov",
      "orcid": "0000-0002-0082-7791"
    },
    {
      "affs": [
        2
      ],
      "name": "Boyan Zlatanov",
      "orcid": "0000-0002-5857-9372"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8t1cbwnqh7xrh.bib",
  "cited_by": 0,
  "doi": "10.3390/axioms15100733",
  "fulltext_url": null,
  "id": "8t1cbwnqh7xrh",
  "issns": [
    "2075-1680"
  ],
  "landing_url": "https://www.mdpi.com/2075-1680/15/10/733",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2612|Iterative Methods for Nonlinear Equations"
    ]
  ],
  "openalex": "W7216170283",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/8t1cbwnqh7xrh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:30Z",
      "native_id": "10.3390/axioms15100733",
      "source": "crossref",
      "url": "https://www.mdpi.com/2075-1680/15/10/733"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2612|Iterative Methods for Nonlinear Equations",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Convergence of a Family of Accelerated Schröder-like Methods for the Simultaneous Extraction of Simple and Multiple Polynomial Zeros",
  "title_text": "Convergence of a Family of Accelerated Schröder-like Methods for the Simultaneous Extraction of Simple and Multiple Polynomial Zeros",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:30Z",
  "url": "https://research.draconitic.com/paper/8t1cbwnqh7xrh",
  "venue": "Axioms",
  "versions": []
}