On the basins of attraction of root-finding algorithms

Autors/ores

  • David Rosado Rodríguez

Paraules clau:

dynamical systems, root-finding algorithms, Newton’s method, Traub’s method.

Resum

Els algoritmes de cerca d’arrels han estat històricament utilitzats per resoldre numèricament equacions no lineals de la forma f(x) = 0. Aquest treball explora la dinàmica dels mètodes de la família Traub parametritzada Tp,δ aplicada a polinomis. Aquests mètodes inclouen un ventall des del mètode de Newton (δ = 0) fins al mètode de Traub (δ = 1). El nostre enfocament rau a investigar diverses propietats topològiques de les conques d’atracció, particularment la seva simple connectivitat i la no acotació, que són crucials per identificar un conjunt universal de condicions inicials que assegurin la convergència a totes les arrels de p.

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Com citar

Rosado Rodríguez, D. (2024). On the basins of attraction of root-finding algorithms. Reports@SCM, 9(1), 103–104. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/154351

Número

Vol. 9 Núm. 1 (2024)

Secció

Extended abstracts

Llicència

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