Can we prove the existence of a unique solution of a square system of nonlinear equations? Where the number of equations equal the number of constraints and all equations are indepedent.
Consider the square, nonlinear, independant equations:
x² + y² = 0
x² + y² = 1
In short, the answer is no.
How about convergence to a solution, is that provable?
Convergence of a solution? Convergence is normally described for a function, not an equation. I'm not sure what you mean by convergence in this context.
Sorry I'm not articulate enough.
What I meant is if I have a set of nolinear equations, how can I prove that there is indeed a solution to that system?