ON A NEW THREE-TERM RECURRENCE RELATION IN TOEPLITZ SYSTEM THEORY by P. DELSARTE and Y. GENIN

This paper is concerned with a novel three-term recurrence relation for a well-defined family of symmetric or antisymmetrie polynomials. In the context where it was originally discovered, this recurrence yields a method for checking whether a given polynomial is devoid of zeros in the closed unit disc. As shown in this paper, the same recurrence, used in reverse order, gives rise to a new algorithm for solving the classicallinear prediction problem relative to a given positive definite Toeplitz matrix. This algorithm can be viewed as a split version of a suitable analogue of the well-known Levinson algorithm.