Newton’s method iteratively updates the solution as:
\mathbf{x}_{k+1} = \mathbf{x}_k - \mathbf{J}_k^{-1} \mathbf{F}(\mathbf{x}_k),where \mathbf{J}_k = \mathbf{J}(\mathbf{x}_k) is the Jacobian matrix of \mathbf{F} evaluated at \mathbf{x}_k . However, computing \mathbf{J}_k and its inverse at each iteration can be computationally expensive.