Numerical Algorithms

, Volume 57, Issue 3, pp 329–356 | Cite as

Iteration functions for pth roots of complex numbers

  • João Ribeiro Cardoso
  • Ana F. Loureiro
Original Paper


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.


Basins of attraction Higher-order convergence Iteration function pth root Residual 


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Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  1. 1.Instituto Superior de Engenharia de CoimbraCoimbraPortugal
  2. 2.Institute of Systems and RoboticsUniversity of CoimbraCoimbraPortugal
  3. 3.Centro de Matemática da Universidade do PortoPortoPortugal

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