Condition number of system of non-linear equations

Question

I've a system of non-linear equations. The system has only two unknowns but 6 equations (thus over-determined). Solving the system of equations are not a problem. However, I need an indication of how well-conditioned the system of equations is. I know the condition number is typically used to do this. Any advice on exactly how this procedure works will be appreciated.

Thanks

Answer 1

My answer can be totally off topic, so please forgive me if it is.

Let say that you have $N$ equations for $M$ unknowns ($N > M$). You can consider minimizing of the norm $$\Phi(x_1,x_2,x_3,..,x_M)=\sum _{i=1}^N g_i(x_1,x_2,x_3,..,x_M)^2$$ hoping that at solution $\Phi$ will be zero. The Jacobian of the system leads to a square $M \times M$ system.