Generalized Hurwitz polynomials

Details Generalized Hurwitz polynomials Generalized Hurwitz polynomials

2010-05-17

arxiv.org/abs/1005.3032v1

Mathematics

Classical Analysis and ODEs

59 pages

Scientific paper

We describe a wide class of polynomials, which is a natural generalization of Hurwitz stable polynomials. We also give a detailed account of so-called self-interlacing polynomials, which are dual to Hurwitz stable polynomials but have only real and simple zeroes. All proofs are given using properties of rational functions mapping the upper half-plane of the complex plane to the lower half-plane. Matrices with self-interlacing spectra and other applications of generalized Hurwitz polynomials are discussed.

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