So suppose I want to solve a system of $n$ quadratic equations given by $f: \mathbb{R}^n \rightarrow \mathbb{R}^n $ using the Newton method, $x_{n+1} = x_n - J^{-1}(x_n)f(x_n)$. Do there exist general results on the coefficients of $f(x)$ which guarantee convergence of the Netwon iterator?
For quadratic $f: \mathbb{C} \rightarrow \mathbb{C}$ there exist some general results but I was curious if this has been studied in an $n$-dimensional setting.