Nonlinear magnetic field problems can be solved by using the polarization method. After applying the Finite Element Method (FEM), a system of nonlinear equations can be derived, which can only be solved by iterative techniques. The fixed point iteration scheme and the Newton-Raphson technique are the most widely used algorithms to solve nonlinear equations. The first is known as a convergent, but slow algorithm, while the other is a fast solver, which convergence can be critical. This paper presents and compares the two methods.