Editing Newton's method (section)

===Error for {{math|n>1}} variables===
If we seek the root of a single function <math>f : \mathbf{R}^n \to \mathbf{R}</math>
then the error <math>\epsilon_n=x_n-\alpha</math> is a vector such that its components obey <math>\epsilon^{(n+1)}_k = \frac{1}{2} (\epsilon^{(n)})^T Q_k \epsilon^{(n)} + O(\|\epsilon^{(n)}\|^3)</math> where <math>Q_k</math> is a quadratic form:
<math>(Q_k)_{i,j} = \sum_{\ell} ((D^2 f)^{-1})_{i,\ell} \frac{\partial^3f}{\partial x_j \partial x_k \partial x_\ell}</math>
evaluated at the root <math>\alpha</math>
(where <math>D^2f</math> is the 2nd derivative Hessian matrix).