A generalization of the Schur-Cohn test: the singular cases

A generalization is presented of the well known Schur-Cohn procedure. The root distribution results for the unit circle are obtained from the `inertia´ of a certain so called quasi-Toeplitz Bezoutian form. Inertia is computed via Schur complementation which leads to the Schur-Cohn test in the regular case. In a singular case the corresponding Schur complement does not exist and a block Schur complement must be computed. This paper provides a fast and completely recursive procedure for doing so. This is the first general purpose Schur-Cohn type procedure that handles the regular and the singular cases in the same way