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An Optimal Thirty-Second-Or...
An Optimal Thirty-Second-Order Iterative Method for Solving Nonlinear Equations and a Conjecture
2022

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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Título:
An Optimal Thirty-Second-Order Iterative Method for Solving Nonlinear Equations and a Conjecture [ electronic resource]
Editorial:
2022
Tipo Audiovisual:
Multipoint iterative methods Simple root Order of convergence Kung and Traub's conjecture Basins of attraction
Documento fuente:
Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022
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application/pdf
Restricciones de acceso:
Open access content. Open access content star
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Lengua:
English
Enlace a fuente de información:
Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022

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