Self-interlacing polynomials

Abstract

We describe a new subclass of the class of real polynomials with real simple roots called self-interlacing polynomials. This subclass is isomorphic to the class of real Hurwitz stable polynomials (all roots in the open left half-plane). In the work, we present basic properties of self-interlacing polynomials and their relations with Hurwitz and Hankel matrices as well as with Stiltjes type of continued fractions. We also establish "self-interlacing" analogues of the well-known Hurwitz and Liénard-Chipart criterions for stable polynomials. A criterion of Hurwitz stability of polynomials in terms of minors of certain Hankel matrices is established.

The journal version with corrected typos

References in corpus (3)

• Polynomials, roots, and interlacing
• Generalized Hurwitz polynomials
• Self-interlacing polynomials II: Matrices with self-interlacing spectrum

Cited by in corpus (2)

• A Fractal Eigenvector
• Hermite-Poulain theorems for linear finite difference operators