Abstract
Abstract : The major problem for the present contract period was to extend fast algorithms based on displacement structure to matrices with zero minors the socalled singular case. Almost all the literature, of about a hundred years, deals with the socalled regular or nonsingular cases, with particular success in the case of Hankel and Hankel-related matrices. These results are related to the now well known Berlekamp-Massey algorithm (for solving Hankel linear equations). For Toeplitz and Toeplitz-related matrices, there were only some partial and rather complicated solutions. In the Ph.D. research of D. Pal a complete and elegant solution is given to this problem for the case of Toeplitz and quasi- Toeplitz matrices. While not as general as one would have liked, the latter class of matrices allowed one to get the first general solution to the much- studied stability and root-distribution problems for discrete-time systems. Additional results appear in the list of publications in the appendix.
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