Numerical and symbolic computation of polynomial matrix determinant

The determinant of a polynomial matrix is frequently computed in analysis and/or design of control systems via polynomial approach. The computation can either be done symbolically using general symbolic procedures for determinant (MATHEMATICA^TM, MAPLE^TM) or by special numeric procedures (POLYNOMIAL TOOLBOX FOR MATLAB^TM). This paper aims to compare the performance of the symbolic procedure built-in Mathematica with the best existing numerical routine based on the Fast Fourier Transform algorithm (FFT), coded for this purpose also in Mathematica. The new tailored numerical algorithm appears to be substantially more efficient than the general-purpose symbolic one. As it is also reasonably accurate, it is recommended for industrial applications of polynomial matrices