The Split Levinson Algorithm is Weakly Stable
Hari Krishna, Yunbiao Wang · SIAM Journal on Numerical Analysis · 1993
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 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 Cybenko for the Levinson algorithm and are obtained by converting a three-term recurrence for the error vector to an equivalent two-term recurrence. From the bounds the conclusion is that the split Levinson algorithm is weakly stable.