THE SPLIT LEVINSON ALGORITHM IS WEAKLY STABLE

The numerical stability properties of the split Levinson algorithm for computing the pedictor polynomial associated with a positive-definite real symmetric Toeplitz matrix are explored. Various bounds on the re sidual vector are derived for the fixed-point and floating-point imple mentation of the algorithm. These bounds are similar in form to the bo unds derived by Cybenko for the Levinson algorithm and are obtained by converting a three-term recurrence for the error vector to an equival ent two-term recurrence. From the bounds the conclusion is that the sp lit Levinson algorithm is weakly stable.