Is an Inverse-Free Newton's Method Possible for Matrix Inversions?

[tangodirt]

Does anyone know of a Newton's method derivative that does not require an inverted Jacobian? I am attempting to port my code from one language to another, and rather than rely on outside libraries for matrix inversions (like I am now), I would prefer to simply do away with the inverted matrix altogether. Also, porting outside "general-purpose" libraries from one language to another is not something I want to do, especially when I just need a "problem specific" method. I.E. reusability is not high on my requirement list.

The easier to implement in code, the better.

http://benisrael.net/InverseFreeMethod.pdf" is the closest thing I can find, but I am having a hard time making the leap from the "theory" to "application."

All of my equations are already in the form f(x1, x2, x3, etc.) = 0 and do not change. Only the input parameters (value assigned to x1, x2, x3, etc.) change.

 

[hunt_mat]

I have been using this method for a while now, the basic equation for Newtons method with lots of dimensions is:
$$(x_{n+1}-x_{n})J(x_{n})=-f(x_{n})$$
Now this is basically a linear algebra problem. MATLAB has inbuilt routines for this, or you can code up your own pivot method.