A Schur algorithm for Hermitian Toeplitz matrices with singular leading principal submatrices

It is shown to be possible to develop a Schur-type algorithm for Hermitian Toeplitz matrices in the singular case. This algorithm is shown to be amenable to implementation on a parallel processing system consisting of a linear array of O(n) processors. The resulting machine executes the proposed algorithm in O(n) time. It is important to note that the present algorithm and that of Delsarte et al. (1985) are very practical algorithms when the Toeplitz matrix in question has elements over a finite field (as opposed to the field of rational, real, or complex numbers). This is because their is now no problem with errors due to quantization of results.<>