I tried to make a simple sheet that would show the path the Newton-Raphson approximation takes to get to a solution based on an initial guess.
The problem I'm having is that it's very slow with anything more than 2/3 iterations.
I'm not sure why it is slow. I can simulate the loop in steps and none of the calcs are slow outside of the loop.
Any ideas as to why this is so slow for i>2. i=3 is still okay, but is gets eternal after that.
In this particular case, the solution converges at the 7th iteration for two decimal places of accuracy.
This is a snip of 4 iterations, which takes well over 2 minutes...


Any input would be much appreciated.
Thanks,
Newton-Raphson Approximation.sm (10 KiB) downloaded 52 time(s).

I changed optimization of for loop to Numeric. It runs in less than a second on my machine.

Newton-Raphson Approximation.sm (11 KiB) downloaded 57 time(s).

I knew it was going to be something simple like this. Thanks!