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 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2021 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.1186/s13662-021-03649-6
  • Title of Journal : ADVANCES IN DIFFERENCE EQUATIONS
  • Keywords: Multiple roots, Polynomial equation, Iterative methods, Simultaneous methods, Computational efficiency and CPU-time, SIMULTANEOUS APPROXIMATION, CONVERGENCE, ZEROS

Abstract

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.