How to improve computing time of fsolver()

I'm solving a system of equations in order to find numerically the steady state of a dynamic system, my system is of around 80 equations and variables. I can get exact analytic solution for around 10 variables, which I use as first guess of the corresponding variables, but for the other variables I do not have a better initial guess than any number between 1 and 100.

I'm trying to solve this system using those initial values using fsolve(), but it takes extremely long. Particularly, the report of the iterations show that the column "f(x)" (which I think is some kind of norm of the function, correct me if I'm wrong) decreases to around 2 fastly, but from then it starts to decrease very very slow, what would you recommend me in such a case? Thanks!

Answer 1

[Walter Roberson]

sometimes (but definitely not always!!) you can get faster resolution by transforming the set of equations into a sum-of-squared-error system. So if before you had

fsolve(@fun, x0)

then instead

SSE = @(x) sum(fun(x).^2)

and now use a minimizer on it. I tend to have a bit better results using fminsearch() -- unless there are constraints, in which case fmincon() may be necessary.

[Turing Machine]

Thanks for your answer! Indeed my solution is constrained, I'll be checking the fmincon() alternative.