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

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

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.

Suggested Citation

  • Campos, Beatriz & Canela, Jordi & Rodríguez-Arenas, Alberto & Vindel, Pura, 2025. "Computing parameter planes of iterative root-finding methods with several free critical points," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 52-72.
    • Handle: RePEc:eee:matcom:v:228:y:2025:i:c:p:52-72
    DOI: 10.1016/j.matcom.2024.08.013
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    References listed on IDEAS

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    1. Behl, Ramandeep & Cordero, Alicia & Motsa, Sandile S. & Torregrosa, Juan R., 2015. "Construction of fourth-order optimal families of iterative methods and their dynamics," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 89-101.
    2. Cordero, Alicia & Gutiérrez, José M. & Magreñán, Á. Alberto & Torregrosa, Juan R., 2016. "Stability analysis of a parametric family of iterative methods for solving nonlinear models," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 26-40.
    3. Argyros, Ioannis K. & Magreñán, Á. Alberto, 2015. "On the convergence of an optimal fourth-order family of methods and its dynamics," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 336-346.
    4. Bahl, Ashu & Cordero, Alicia & Sharma, Rajni & R. Torregrosa, Juan, 2019. "A novel bi-parametric sixth order iterative scheme for solving nonlinear systems and its dynamics," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 147-166.
    5. Campos, B. & Vindel, P., 2021. "Dynamics of subfamilies of Ostrowski–Chun methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 57-81.
    6. Campos, Beatriz & Cordero, Alicia & Torregrosa, Juan R. & Vindel, Pura, 2016. "Dynamics of a multipoint variant of Chebyshev–Halley’s family," Applied Mathematics and Computation, Elsevier, vol. 284(C), pages 195-208.
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