Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 57 min ago
Peer-reviewedCC BY 4.0Axioms

Convergence of a Family of Accelerated Schröder-like Methods for the Simultaneous Extraction of Simple and Multiple Polynomial Zeros

  • Ivan Ginchev1
  • Stoil I. Ivanov2
  • Boyan Zlatanov3
  1. 1Independent Researcher, 4000 Plovdiv, Bulgaria
  2. 2Faculty of Physics and Technology, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria
  3. 3Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria
Open at sourceDOICite

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.

Related

  1. Combining Exponential and Polynomial Convergence Rates for Accelerated Extremum Seeking: A High-Order Lie Bracket Approach
    Victoria Grushkovskaya, Sameh Eisa
    arXivPreprintarXiv licenceFull textOptimisation & controlarXiv
  2. Simultaneous popular differences for polynomial and linear progressions in finite fields
    Xuancheng Shao, Weiwen Zhang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  3. Simultaneous popular polynomial differences in higher dimensions
    Guo-Dong Hong
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  4. Simultaneous Global Convergence Failure of Newton's and Halley's Methods in Degree Four
    Alessio Basti, Tommaso Cremaschi
    arXivPreprintCC BY-NC-SA 4.0Full textNumerical analysis & scientific computingarXiv
  5. Weak and Error-Bound Linear Convergence of a Safeguarded Anderson-Accelerated Subgradient Extragradient Method
    Austine Efut Ofem, Adhir Maharaj, Virath Singh
    MathematicsPeer-reviewedCC BY 4.0General mathematicsCrossref

Cite

BibTeXRIS
BibTeX
@article{ginchev2026convergence,
  title = {{Convergence of a Family of Accelerated Schröder-like Methods for the Simultaneous Extraction of Simple and Multiple Polynomial Zeros}},
  author = {Ivan Ginchev and Stoil I. Ivanov and Boyan Zlatanov},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15100733},
  url = {https://www.mdpi.com/2075-1680/15/10/733},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Convergence of a Family of Accelerated Schröder-like Methods for the Simultaneous Extraction of Simple and Multiple Polynomial Zeros
AU  - Ivan Ginchev
AU  - Stoil I. Ivanov
AU  - Boyan Zlatanov
PY  - 2026
DA  - 2026/10/01
JO  - Axioms
DO  - 10.3390/axioms15100733
UR  - https://www.mdpi.com/2075-1680/15/10/733
AB  - 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.
SN  - 2075-1680
ER  -