Order of the method

The numerical example in appendix shows that the error decreases very quickly. Some experiments have been performed with a large number of significant digits (100 digits). These experiments seem to show the method would be of order 2. This order is not very impressive. However, the main strength of the method is that its starts very quickly, even for very flat ellipses. The example shows that in a quite difficult case we already have $0.013^\circ$ after only one iteration.

This order should be analyzed more precisely.