Implementation of polynomial algebra via spectra

Polynomial methods are an effective method for the synthesis of control systems. The calculation of certain functions with polynomial matrices which are represented by coefficients of polynomials can be time consuming. If, however, the polynomial matrix is represented as a matrix of spectra of polynomials, in many cases it is possible to make significant savings on time and to reduce demands on memory. The time burden of the matrix product above the spectra increases linearly with the degree of the polynomials, whereas for calculations above coefficients of polynomials, it increases quadratically. For the calculation of the spectra, the generally-known and well implemented discrete Fourier transform is used.