Efficient iterative methods for finding simultaneously all the multiple roots of polynomial equation

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Shams M., Rafiq N., Kausar N., Agarwal P., Park C., Momani S.

ADVANCES IN DIFFERENCE EQUATIONS, vol.2021, no.1, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2021 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1186/s13662-021-03649-6
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: Multiple roots, Polynomial equation, Iterative methods, Simultaneous methods, Computational efficiency and CPU-time, SIMULTANEOUS APPROXIMATION, CONVERGENCE, ZEROS
  • Yıldız Technical University Affiliated: No


Two new iterative methods for the simultaneous determination of all multiple as well as distinct roots of nonlinear polynomial equation are established, using two suitable corrections to achieve a very high computational efficiency as compared to the existing methods in the literature. Convergence analysis shows that the orders of convergence of the newly constructed simultaneous methods are 10 and 12. At the end, numerical test examples are given to check the efficiency and numerical performance of these simultaneous methods.