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<p>This paper investigates the convergence of a fourth-order iterative method for simultaneously finding all roots of a complex polynomial. The method was introduced by Kyurkchiev in 1983 and, in a completely different form, by Zheng and Sun in 1999. To date, only local convergence results are available for this method. In this study, we provide a comprehensive semilocal convergence analysis for the Kyurkchiev-Zheng-Sun method. The resulting theorem includes fully computable initial conditions, a computable a posteriori error estimate, and a localization for each root of the polynomial. The paper concludes with numerical experiments that demonstrate the effectiveness and applicability of the proposed theorem.</p>

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Fully computable convergence analysis of a fourth order iterative method for finding polynomial roots

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月18日

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  • Petko D. Proinov,
  • Slav I. Cholakov,
  • Maria T. Vasileva

摘要

This paper investigates the convergence of a fourth-order iterative method for simultaneously finding all roots of a complex polynomial. The method was introduced by Kyurkchiev in 1983 and, in a completely different form, by Zheng and Sun in 1999. To date, only local convergence results are available for this method. In this study, we provide a comprehensive semilocal convergence analysis for the Kyurkchiev-Zheng-Sun method. The resulting theorem includes fully computable initial conditions, a computable a posteriori error estimate, and a localization for each root of the polynomial. The paper concludes with numerical experiments that demonstrate the effectiveness and applicability of the proposed theorem.