Computing parameter planes of iterative root-finding methods with several free critical points

Beatriz Campos, Jordi Canela, Alberto Rodríguez-Arenas and Pura Vindel

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 228, issue C, 52-72

Abstract: In this paper we present an algorithm to obtain the parameter planes of families of root-finding methods with several free critical points. The parameter planes show the joint behaviour of all critical points. This algorithm avoids the inconsistencies arising from the relationship between the different critical points as well as the indeterminacy caused by the square roots involved in their computation.

Keywords: Root-finding algorithms; Newton-like algorithms; Parameter planes; Several critical points (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:228:y:2025:i:c:p:52-72

DOI: 10.1016/j.matcom.2024.08.013

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