A LOOK-AHEAD BLOCK SCHUR-ALGORITHM FOR TOEPLITZ-LIKE MATRICES

We derive a look-ahead recursive algorithm for the block triangular factorization of Toeplitz-like matrices. The derivation is based on combining the block Schur/Gauss reduction procedure with displacement structure and leads to an efficient block-Schur complementation algorithm. For an n x n Toeplitz-like matrix, the overall computational complexity of the algorithm is O(rn(2) + n(3)/t) operations, where r is the matrix displacement rank and t is the number of diagonal blocks. These blocks can be of any desirable size. They may, for example, correspond to the smallest nonsingular leading submatrices or, alternatively to numerically well-conditioned blocks.