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<p>A new family of iterative methods for finding multiple roots of nonlinear problems is proposed. The family is derivative-free and optimal in the sense of Kung–Traub’s conjecture. The two-step family includes a weight function. The stability analysis uses two different weight functions: a polynomial and a rational function. Furthermore, a numerical benchmark is carried out on these two weight functions, showing the competitiveness concerning similar methods in the literature.</p>

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Derivative-free optimal multiple-root finding family of iterative methods

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月13日

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  • Julissa H. Jerezano,
  • Francisco I. Chicharro,
  • Neus Garrido-Saez

摘要

A new family of iterative methods for finding multiple roots of nonlinear problems is proposed. The family is derivative-free and optimal in the sense of Kung–Traub’s conjecture. The two-step family includes a weight function. The stability analysis uses two different weight functions: a polynomial and a rational function. Furthermore, a numerical benchmark is carried out on these two weight functions, showing the competitiveness concerning similar methods in the literature.