Frequency response computation by direct frequency evaluation using Hyman´s method

Two basically possible approaches for the computation of the frequency response of linear multivariable systems are outlined: the calculation of the frequency response matrix via a prior calculation of the transfer function matrix (algebraic inversion) with subsequent frequency evaluation and the direct computation of the frequency response matrix for each discrete frequency value (numerical inversion). Regarding numerical inversion, this paper reports a new efficient algorithm for computing the frequency response by Hyman´s method. Utilizing real arithmetics, the algorithm is based on a single transformation to upper Hessenberg form followed by a double back-substitution for each frequency value.