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arXiv · 1611.09156

Self-interlacing polynomials

Mikhail Tyaglov
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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 Li\'enard-Chipart criterions for stable polynomials. A criterion of Hurwitz stability of polynomials in terms of minors of certain Hankel matrices is established.

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Mikhail Tyaglov. 2016-11-28. Self-interlacing polynomials. https://doi.org/10.1016/j.laa.2017.08.020

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