ON A GENERALIZATION OF THE SZEGO-LEVINSON RECURRENCE AND ITS APPLICATION IN LOSSLESS INVERSE SCATTERING

Predictor polynomials corresponding to nested Toeplitz matrices are known to be connected by the Szego-Levinson recurrence relation. This paper is concerned with a generalization of that result, where the relevant reduction process for Toeplitz matrices (of decreasing order) is defined by an elementary one-parameter linear transformation. The descending and ascending versions of the corresponding generalized Szego-Levinson recurrence relations are discussed in detail. In particular, these relations are shown to be essentially the same as the extraction formulas for canonical Schur and Brune sections in the Dewilde-Dym recursive solution of the lossless inverse scattering problem. The paper also deals with some extensions of the Levinson algorithm for linear prediction and of the Schur-Cohn algorithm for polynomial stability test.