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 [itex] f: \mathbb R^n \to \mathbb R^n [/itex]. 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 [itex] \nabla f [/itex] but it's not something I would like to depend on in general. Does anyone know if there's an algorithm for solving this?