This paper shows an analysis of a fast solution method for the system of linear equations encountered in the semi-parametric spectral estimation problem. Spectral analysis forms the basis of a major part of signal processing applications typically used for tracking and distinguishing signals of interest, and for estimating dominant harmonics in signals. Power utility companies uses spectral analysis in analysing signals recorded from the power system. The signals recorded during power system disturbances could be analysed to determine the characteristics of the disturbance. The test results show that an increase in the order of the local polynomial filter used in the semi- parametric method affects the condition number of the coefficient matrix, and this results in an inaccurate solution.