# Numerical Approximation to Roots

1. Apr 27, 2010

### Kreizhn

1. The problem statement, all variables and given/known data
I'm trying to find a root-finding method for a function
[tex] f: \mathbb R^n \to \mathbb R [/itex]

2. Relevant equations
x is a root of f(x) if f(x) = 0

3. The attempt at a solution
There is lots of work done for this problem when n=1, and also lots of work done when $f: \mathbb R^n \to \mathbb R^n$. It seems like there should be a Newton method that can be applied here, but it's not entirely obvious to me. I've had some results by using the generalized Moore-Penrose inverse on $\nabla f$ but it's not something I would like to depend on in general. Does anyone know if there's an algorithm for solving this?