Schur algorithms for Hermitian Toeplitz, and Hankel matrices withsingular leading principal submatrices |
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Authors: | Zarowski C.J. |
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Affiliation: | Dept. of Electr. Eng., Queen's Univ., Kingston, Ont.; |
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Abstract: | It is shown how a simple matrix algebra procedure can be used to induce Schur-type algorithms for the solution of certain Toeplitz and Hankel linear systems of equations when given Levinson-Durbin algorithms for such problems. The algorithm of P. Delsarte et al. (1985) for Hermitian Toeplitz matrices in the singular case is used to induce a Schur algorithm for such matrices. An algorithm due to G. Heinig and K. Rost (1984) for Hankel matrices in the singular case is used to induce a Schur algorithm for such matrices. The Berlekamp-Massey algorithm is viewed as a kind of Levinson-Durbin algorithm and so is used to induce a Schur algorithm for the minimal partial realization problem. The Schur algorithm for Hermitian Toeplitz matrices in the singular case is shown to be amenable to implementation on a linearly connected parallel processor array of the sort considered by Kung and Hu (1983), and in fact generalizes their result to the singular case |
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