I'm working on a nonlinear system of 2 equations and try to solve it with the Newton-Raphson method. I have a function $f(x,y)$. In order to use the method, I have to find a starting vector $(x,y)$. But the method will only converge for specific starting vectors.
Is there a formula that gives the convergence of the Newton-Raphson method on a system of equations ?
Thank you all.