I was doing some simulations for the solution of a system of Non-Linear Equations using Newton Method and found that the convergence is linear. I went through the literature for Newton method and found that this behavior is expected for equations having a root of multiplicity greater that one.
How do we define the idea of the multiplicity of a solution for a Non-Linear system of equations? And how do we check that if the system of non-linear equations has a solution whose multiplicity is greater than one?