Computing the Poles of Autoregressive Models from the Reflection Coefficients

A new approach to the computation of the poles of a stable autoregressive system from the reflection coefficients is proposed. Equivalently, we compute the zeros of Szego polynomials from the associated Schur parameters. The numerical method utilizes an efficient algorithm for computing the (unimodular) zeros of a unitary Hessenberg matrix; this step can be regarded as the computation of the poles of an associated lossless system. These eigenvalues are then used as starting points for a continuation procedure for finding the zeros of the desired polynomial. The procedure is efficient and parallelizable, and may therefore be suitable for real-time applications