Newton's Method

[Han]

Snorre,

I think your program is fine, but it doesn't match exactly with the math above your code. The math presumes f(x) is a column vector whereas it appears you have a row vector. Strangely the CAS seems to not mind this and allows the multiplication to go through as is. Nice find!

I was planning to write something similar (to incorporate into the equation library program), but basically had a few extra lines in mind (that now seem unnecessary). I was thinking it was necessary to transpose the f vector to ensure valid multiplication. The CAS seems to be rather flexible in this respect!

Lastly, defining the jacobi as you did vs leaving it untransposed (how I thought about doing it) comes down to deciding between two transposes vs a single transpose (needed prior to taking inverse). I think the latter choice would give a slight speedup in cases where the number of iterations is significantly large.

As for experience, I doubt I have any more experience than anyone here -- perhaps more chunks of free time to tinker, maybe.

Edit: I think there may be a few other ways to exit the iterations. You've listed a few, but we could also exit based on whether max|f(x_i)| is within a certain tolerance as suggested by: http://ocw.usu.edu/Civil_and_Environment...Matlab.pdf