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Iteration functions for pth roots of complex numbers

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Abstract

A novel way of generating higher-order iteration functions for the computation of pth roots of complex numbers is the main contribution of the present work. The behavior of some of these iteration functions will be analyzed and the conditions on the starting values that guarantee the convergence will be stated. The illustration of the basins of attractions of the pth roots will be carried out by some computer generated plots. In order to compare the performance of the iterations some numerical examples will be considered.

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Authors and Affiliations

  1. Instituto Superior de Engenharia de Coimbra, Rua Pedro Nunes, 3030-199, Coimbra, Portugal

    João Ribeiro Cardoso & Ana F. Loureiro

  2. Institute of Systems and Robotics, University of Coimbra, Pólo II, 3030-290, Coimbra, Portugal

    João Ribeiro Cardoso

  3. Centro de Matemática da Universidade do Porto, Rua do Campo Alegre, 687, 4169-007, Porto, Portugal

    Ana F. Loureiro

Authors
  1. João Ribeiro Cardoso
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  2. Ana F. Loureiro
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Correspondence to João Ribeiro Cardoso.

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Cardoso, J.R., Loureiro, A.F. Iteration functions for pth roots of complex numbers. Numer Algor 57, 329–356 (2011). https://doi.org/10.1007/s11075-010-9431-8

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  • DOI: https://doi.org/10.1007/s11075-010-9431-8

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