The two treated methods are called the method of successive linear problems (MSLP) and augmented Newton and are widely used in the literature. We prove several explicit formulas for for both methods. Formulas for both methods are found for simple as well as double eigenvalues. In some cases, we observe in examples that the limit as does not exist. For cases where this limit does not appear to exist, we prove other limiting expressions such that a characterization of in the limit is still possible.