Hi,Are there any experts on Newton Ralphson out there? I got a problem here. Sometimes it seems that it will never converge. Thank you!

Being an expert in Newton-Raphson is like being a master of classic 3x3 tic-tac-toe.The method converges well when you have a function like ln(x) or exp(x)-2 which is fairly smooth, and the first derivative doesn't oscilate much. Cases like cos(x) seeded with x=0 and really wavy functions tend to work the least well. If you have a range, fall back on the bisection method.

The problem with me is that after several iterations, the value doesn't get updated at alot, no change in the first 5 dicimal points and so it doesn't add any more value by processing more iterations. Hence, it doesn't converge. Any fixes?

I presume you are talking about newton-raphson (ralphson??)One easy thing to try is to start off with the bisection method and then polish withnewton-raphson once your interval is "sufficiently small"For more see here

What is the behavior of your algorithm before it stalls out? Is it moving towards the correct answer for the first few iterations? This might be a data precision problem then. Are the numbers you are working with really small? You wouldn’t by chance be trying to find the implied volatility for deep out of the money options? If so, test the boundary conditions listed in any decent basic options text (Hull, for example) to see if the implied vol is even computable before calling your algorithm. What are you using for a seed value? The better the seed the more likely Newton is to converge and the more rapidly as well.

the bevaviour of newton raphson depend a lot on your starting value. It is possible that it converge very slowly when you have a bad problem and a bad starting point. There are many algoriths which do not have this problem for example BFGS Methods which are the most useful Newton Methods. (if you still want to use your newton-raphson just include a gradient step) But first of all the problem solver you use depend on your problem: do you have box-restricitions or nonlinear restrictions? And Remember: Do you look for local minima/minima or global minima , newton algorithms just find local minima...