Perturbation expansions in polynomial root tracking

An alternative for root tracking algorithms that compute the roots explicitly is presented. The proposed method is first based on using any preferred algorithm to track the transversal model parameters and subsequently on the second-order perturbation expansion for the associated companion matrix to approximate a single root of interest. An application to EEG signal analysis is discussed and it is shown that the second-order approximation yields root location estimates that are more accurate than the first-order approximation.