Paper's Title:

On Perturbed Reflection Coefficients

Author(s):

J. L. Díaz-Barrero and J. J. Egozcue

Applied Mathematics III,
Universidad Politécnica de Cataluña,
Barcelona, Spain
jose.luis.diaz@upc.edu
juan.jose.egozcue@upc.edu

Abstract:

Many control and signal processing applications require testing stability of polynomials. Classical tests for locating zeros of polynomials are recursive, but they must be stopped whenever the so called "singular polynomials" appear. These ``singular cases'' are often avoided by perturbing the "singular polynomial". Perturbation techniques although always successful are not proven to be well-founded. Our aim is to give a mathematical foundation to a perturbation method in order to overcome "singular cases" when using Levinson recursion as a testing method. The non-singular polynomials are proven to be dense in the set of all polynomials respect the L²-norm on the unit circle . The proof is constructive and can be used algorithmically.

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