Displacement structure approach to singular root distribution problems: the unit circle case

A general theory of tabular form root distribution procedures based on LDL* factorization of Bezoutians is presented. In particular, the authors 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(1991) to the singular cases. By doing so, not only do the authors derive the well known Schur-Cohn procedure, but they also obtain new results. In fact, the authors are able to derive a new completely recursive procedure to deal with the “first kind of singularity”