Non-linear systems

[Thanh Dang Nguyen <nguyet1@Eng.Auburn.EDU>]

Hi,

> I got another problem, I have to solve 31 non linear equations for 
> 31 unknowns, can anyone tell me about theoritical methods to solve it 

It's a very general question, and even the fact that you have exactly
31 equations doesn't help anything at all :-) Moreover, many beautiful
things will no longer work for the non-linear problems, and in most
cases you need to face a serious numerical problem which can be
solved mostly using some sort of iterative methods.

If you don't assume anything about the nature of your system, then
you can still solve the problem using some well-known gradient algorithms
such as steepest descent, conjugate gradient, Gauss-Newton etc. Matlab
has a general least-squares command which allows you to solve non-linear
systems blindly, or with user-supplied gradients (it may help a lot).
As with any non-linear system, convergence is also a big issue, since
you may not end up with the global, but local minimum. I think Matlab 
has no guarantee for this, due to the nature of the gradient methods.

In short, non-linear optimization is a tough problem, and the more you
know of the nature of your system, the better chance you have in finding
a suitable algorithm for it.

Good luck!

-Thanh