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On the Convergence of a New Family of Multi-Point Ehrlich-Type Iterative Methods for Polynomial Zeros

Author

Listed:
  • Petko D. Proinov

    (Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria)

  • Milena D. Petkova

    (Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 Tzar Asen, 4000 Plovdiv, Bulgaria)

Abstract

In this paper, we construct and study a new family of multi-point Ehrlich-type iterative methods for approximating all the zeros of a uni-variate polynomial simultaneously. The first member of this family is the two-point Ehrlich-type iterative method introduced and studied by Trićković and Petković in 1999. The main purpose of the paper is to provide local and semilocal convergence analysis of the multi-point Ehrlich-type methods. Our local convergence theorem is obtained by an approach that was introduced by the authors in 2020. Two numerical examples are presented to show the applicability of our semilocal convergence theorem.

Suggested Citation

  • Petko D. Proinov & Milena D. Petkova, 2021. "On the Convergence of a New Family of Multi-Point Ehrlich-Type Iterative Methods for Polynomial Zeros," Mathematics, MDPI, vol. 9(14), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1640-:d:592980
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    References listed on IDEAS

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    1. Sergio Amat & Ioannis Argyros & Sonia Busquier & Miguel Ángel Hernández-Verón & María Jesús Rubio, 2019. "A Unified Convergence Analysis for Some Two-Point Type Methods for Nonsmooth Operators," Mathematics, MDPI, vol. 7(8), pages 1-12, August.
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