Friday September 25th, 2020 | |
| Time: | 2:30 PM - 3:30 PM |
| Title: | The Weierstrass root-finder is not generally convergent |
| Speaker: | Bernhard Reinke, Aix-Marseille University |
| Abstract: | |
| We will give an overview of root-finding methods and their interpretation as complex dynamical systems. The main focus will be the Weierstrass/Durand-Kerner method and its similarities and differences to the Newton and the Ehrlich-Aberth methods. In particular, we will show how to use methods from computer algebra to investigate (and/or establish) the existence of attracting periodic cycles, as well as diverging orbits, and present explicit examples of both phenomena for the Weierstrass method. This talk is based on joint work with Dierk Schleicher and Michael Stoll. | |