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

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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