February 4th, 2015, 5:28 am
QuoteYes, we have different attitudes for that, here I would prefer to havea good initial instead of a generic approach or naming methods. And soavoiding probably expansive methods.Well, it is (can be??) usually a requirement to have a non-linear solver that works for all combinations of input parameters. It's a mathematical problem in the main and this is why homotopy etc. are used in many application areas.Concerning efficiency, fixed point method 4 can be extended by Aitken to get 2nd order convergence comparable to that of NR, e.g. M = 0.1, eps = 0.8 converges in 4 iterations. Or bracketing with NR is also not bad.NR is very fast when it does converge but I prefer bracketing the solution first as it is easier IMO than finding a seed. It's a choice, I suppose.A follow-on is a two-dimensional NR method and then how do I choose seeds? e.g. let's say fitting the ir yield and vol.. Which is the most robust of the above 10 methods?
Last edited by
Cuchulainn on February 3rd, 2015, 11:00 pm, edited 1 time in total.