So my teacher asked me to find out the rate of convergence and the asymptotic constant for Newthons method based on this experiment's graphs. We were searching for a simple root in the first case, and for multiple root in the second case. I've compared the graphs with the graphs demoing different rates of convergence on wiki and concluded that it's quadratic in the first case and linear in the second. But can I actually tell anything about the asymptotic constant by just looking at a graph? Is there a way to calculate it? (Didn't find one on Google. ) Thanks for your time!
[for simple root][1] : https://i.stack.imgur.com/XwiPa.png
[for multiple root][2]: https://i.stack.imgur.com/Ed2ha.png
