Iteration functions for pth roots of complex numbers

作者：Cardoso Joao Ribeiro^*; Loureiro Ana F

来源：Numerical Algorithms, 2011, 57(3): 329-356.

DOI：10.1007/s11075-010-9431-8

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

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.

• 出版日期2011-7