On the application of different

Motivated by some control problems requiring the extraction of the null-space of large polynomial matrices, we introduce two fast numerical linear algebra algorithms to perform this task. These fast algorithms are based on the displacement structure theory and the generalized Schur algorithm. We present a full analysis of the performance of both algorithms and a comparison with the performance of the classical algorithms proposed in the first part of this work [12]. We also discuss briefly the numerical stability of the algorithms.