Split Levinson algorithm is weakly stable

The authors explore the numerical stability properties of the split Levinson algorithm for computing the predictor polynomial associated with a positive-definite real symmetric Toeplitz matrix. Various bounds on the residual vector are derived for the fixed-point and floating-point implementation of the algorithm. These bounds are similar in form to the bounds derived by G. Cybenko (1980) for the Levinson algorithm and are obtained by converting a three-term recurrence for the error vector to an equivalent two-term recurrence. The split Levinson algorithm is shown to be weakly stable