Phase shifting is a well-established technique for phase measurements in interferometry and 3D profiling, which requires at least three sinusoidal intensity patterns with certain phase-shifts. In this paper, two phase-shifting schemes are analyzed, which have been used to minimize absolute phase errors due to the phase-shift error. The first one is the advance iterative algorithm (AIA) and the second is based on the Levenberg-Marquardt method (LM). In order to show their performance, these schemes are evaluated using synthetic data and taking into account the numerical accuracy, the order of convergence, and the detuning error. The results show that both methods reduce the phase error linearly; however, the AIA scheme significantly improves the accuracy and reduces the processing time. This work sheds light to the advantages and disadvantages of using the linear and non-linear solutions.