Introducing memory to a family of multi-step multidimensional iterative methods with weight function
[EN] In this paper, we construct a derivative-free multi-step iterative scheme based on Steffensen's method. To avoid excessively increasing the number of functional evaluations and, at the same time, to increase the order of convergence, we freeze the divided differences used from the seco...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/204608 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/204608 |
| Access Level: | acceso abierto |
| Palabra clave: | Iterative methods Nonlinear systems Memory schemes Basin of attraction Dynamical plane MATEMATICA APLICADA |
| Sumario: | [EN] In this paper, we construct a derivative-free multi-step iterative scheme based on Steffensen's method. To avoid excessively increasing the number of functional evaluations and, at the same time, to increase the order of convergence, we freeze the divided differences used from the second step and use a weight function on already evaluated operators. Therefore, we define a family of multi-step methods with convergence order 2m, where m is the number of steps, free of derivatives, with several parameters and with dynamic behaviour, in some cases, similar to Steffensen's method. In addition, we study how to increase the convergence order of the defined family by introducing memory in two different ways: using the usual divided differences and the Kurchatov divided differences. We perform some numerical experiments to see the behaviour of the proposed family and suggest different weight functions to visualize with dynamical planes in some cases the dynamical behaviour. |
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