Efficient procedures for stepup and stepdown computations

The stepup (stepdown) procedure is an algorithm for computing the predictor polynomial (reflection) coefficients from the knowledge of the reflection coefficients (predictor polynomial). Here, both real as well as complex cases are considered, and several computationally efficient algorithms for the stepup and stepdown computations are presented. They are intimately related to recently reported alternative algorithms for computing the predictor polynomial associated with real, symmetric, and Hermitian Toeplitz matrices