Hi Fivexthethird -
perhaps this might be interesting for you: I've made a discussion of the Newtonian method in comparision with the diagonalization-approach in 2008; perhaps today I could write this better (but unfortunately usually don't have time for this); see here: http://go.helms-net.de/math/tetdocs/Bino...zation.htm
I came to tetration via consideration of infinite matrices and powers of them, so possibly the whole article looks strange to you but I hope it is self-expalining enough. Don't hesitate to ask if something might look explainable by not too much effort...
Gottfried
perhaps this might be interesting for you: I've made a discussion of the Newtonian method in comparision with the diagonalization-approach in 2008; perhaps today I could write this better (but unfortunately usually don't have time for this); see here: http://go.helms-net.de/math/tetdocs/Bino...zation.htm
I came to tetration via consideration of infinite matrices and powers of them, so possibly the whole article looks strange to you but I hope it is self-expalining enough. Don't hesitate to ask if something might look explainable by not too much effort...
Gottfried
Gottfried Helms, Kassel