Transmission-Line Models for the Modified Schur Algorithm. (Reannouncement withNew Availability Information)

摘要

We present transmission-line models for the modified Schur algorithm that handlesfunction that are bounded on the unit circle sad have a finite member of poles inside the unit disc. The first application of then models is the physical interpretation of procedures for root distribution with respect to the unit circle: for every polynomial p(z), the transmission-line model for the all-pass p*(z)/p(z) special structure from which the number of stable and unstable zeros can be calculated by inspection. Three other applications are to problems from analytic function theory and linear algebra: the matching of Taylor coefficients, the factorization of certain indefinite Hermitian matrices, and the Schur-Takagi extension problem. We show that these three problems can be solved using the transmission-line models and their physical properties such as causality and energy conservation.