An Optimal Thirty-Second-Order Iterative Method for Solving Nonlinear Equations and a Conjecture

  1. Varona, Juan Luis 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Año de publicación: 2022

Volumen: 21

Número: 2

Tipo: Artículo

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DOI: 10.1007/S12346-022-00572-3 DIALNET GOOGLE SCHOLAR lock_openDialnet editor

Otras publicaciones en: Qualitative theory of dynamical systems

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Resumen

Many multipoint iterative methods without memory for solving non-linear equations in one variable are found in the literature. In particular, there are methods that provide fourth-order, eighth-order or sixteenth-order convergence using only, respectively, three, four or five function evaluations per iteration step, thus supporting the Kung-Traub conjecture on the optimal order of convergence. This paper shows how to find optimal high order root-finding iterative methods by means of a general scheme based in weight functions. In particular, we explicitly give an optimal thirty-second-order iterative method; as long as we know, an iterative method with that order of convergence has not been described before. Finally, we give a conjecture about optimal order multipoint iterative methods with weights.

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