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A Schur algorithm and linearly connected processor array for Toeplitz-plus-Hankel matrices

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1 Author(s)
Zarowski, C.J. ; Dept. of Electr. Eng., Queen''s Univ., Kingston, Ont., Canada

A Levinson-Durbin type algorithm for solving Toeplitz-plus-Hankel (T+H) linear systems of equations is used to induce a Schur-type algorithm for such systems. A Schur-type algorithm is defined as one which efficiently computes the LDU-decomposition of the matrix. On the other hand, Levinson-Durbin type algorithms are defined as those algorithms which efficiently compute the UDL-decomposition of the inverse of a matrix. It is shown that the Schur algorithm so obtained is amenable to efficient implementation on a linearly connected array of processors in a manner which generalizes the results of S.-Y. Kung and Y.H. Ku (1983) for symmetric Toeplitz matrices. Specifically, if T+H is of order n, then the Schur algorithm runs on O(n ) processors in O(n) time

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Signal Processing, IEEE Transactions on  (Volume:40 ,  Issue: 8 )