Iteration functions for \(p\)th roots of complex numbers. (English) Zbl 1221.30065
Summary: A novel way of generating higher-order iteration functions for the computation of the \(p\)th roots of complex numbers is the main contribution of the present work. The behavior of some of these iteration functions is analyzed, and conditions on the starting values that guarantee convergence are stated. The illustration of the basins of attractions of the \(p\)th roots are carried out by some computer generated plots. In order to compare the performance of the iterations some numerical examples are considered.
MSC:
| 30D05 | Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable |
| 11A07 | Congruences; primitive roots; residue systems |
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