Suppose you need to solve $f(\mathbf{x})=\mathbf{0}$ where $f:\mathbb{R}^n \to \mathbb{R}^m$, $m,n>1$. Newton's method relies on first order Taylor expansion of f. Where can I find details of analogous method using second order Taylor expansion? I found at least a dozen numerical analysis books which mention this method, but give no details or applications