On the application of displacement structure methods to obtain null-spaces of polynomial matrices

In this paper we present different algorithms to obtain the null-space of a polynomial matrix. These algorithms are based on the computation of the constant null-spaces of some associated block Toeplitz matrices. For the case of large block Toeplitz matrices we introduce two fast numerical methods to compute their constant null-spaces and we compare the performance of these fast methods with the classical orthogonal methods. We also discuss briefly the numerical stability of the developed algorithms.