Split Levinson algorithm for Toeplitz matrices with singular sub-matrices

The split Levinson algorithm, which is computationally superior to the classical Levinson algorithm, is used for solving linear systems with real symmetric Toeplitz matrices, with no restriction on the ranks of their nested submatrices. The algorithm is based on the observation that the singular predictor polynomials are either the same as or closely related to the predictor polynomials when the corresponding Toeplitz submatrix is singular. A numerical example and a flowchart of the algorithm are presented to illustrate the proposed method