Displacement structure approach to singular root distribution problems: the imaginary axis case

A general theory of tabular form root distribution procedures based on LDL* factorization of Bezoutians has been presented in this paper. In particular, we have concentrated on the singular cases arising in the Routh test. A one-to-one correspondence has been 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 (1989), it has been possible to extend the new unified approach of Lev-Ari, Bistritz, and Kailath (1991) to the singular cases. By doing so not only did we obtain all the known procedures but we also obtained new results.<
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