Displacement Structure Approach to Singular Root Distribution Problems: The UnitCircle Case

摘要

A general theory of tabular form root distribution procedures based on LDLfactorization of Bezoutians is presented in this note. In particular, we concentrate on the singular cases arising in the Schur-Cohn test. A one-to-one correspondence is established between the rank profile of the underlying Bezoutians and the occurrence of the singular cases. Combining this interpretation with the newly developed factorization procedures of pal and Kailath, it is possible to extend the new unified approach of Lev-Ari, Bistritz, and Kailath to the singular cases. By doing so, not only do we derive the well known Schur-Cohn procedure, but we also obtain new results. In fact, we are able to derive a new completely recursive procedure to deal with the first kind of singularity.