Fast algorithms for computing QR and Cholesky factors of Toeplitz operators

Levinson, Lattice and Schur recursions provide alternative ways of computing reflection coefficients for stationary time series. The authors show that when a Toeplitz correlation matrix is a product of two Toeplitz data matrices, as in the correlation method of linear prediction, then the Levinson recursions can be used to derive the Lattice recursions and the Lattice recursions can be used to derive the Schur recursions. They explore the close relation between QR and Cholesky algorithms in the Toeplitz case, and present the underlying matrix factorization