Divide-and-conquer solutions of least-squares problems for matrices with displacement structure

A divide-and-conquer implementation of a generalized Schur algorithm enables (exact and) least-squares solutions of various block-Toeplitz or Toeplitz-block systems of equations with $O ( \alpha ^3 n\log ^2 n )$ operations to be obtained, where the displacement rank $\alpha $ is a small constant (typically between two to four for scalar near-Toeplitz matrices) independent of the size of the matrices.