Consider a system of n nonlinear equations:
\mathbf{F}(\mathbf{x}) = \mathbf{0},where \mathbf{F}: \mathbb{R}^n \to \mathbb{R}^n is a vector-valued function, and \mathbf{x} \in \mathbb{R}^n is the vector of unknowns. The goal is to find \mathbf{x}^* such that \mathbf{F}(\mathbf{x}^*) = \mathbf{0} .