Generalized Hurwitz polynomials
Generalized Hurwitz polynomials
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广义 Hurwitz 多项式
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
M. Tyaglov
中科院分区：
文献类型：
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作者：
M. Tyaglov
我们描述了一类广泛的多项式，它是Hurwitz稳定多项式的自然推广。我们还给出了所谓的自交错多项式的详细说明，它是对偶于Hurwitz稳定多项式，但只有实零点和单零点。所有的证明都是利用复平面上半平面到下半平面映射的有理函数的性质给出的。讨论了广义Hurwitz多项式的自交错谱矩阵及其其它应用。
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.