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arXiv · 0912.4703

Structured matrices, continued fractions, and root localization of polynomials

Olga Holtz·Mikhail Tyaglov
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Abstract

We give a detailed account of various connections between several classes of objects: Hankel, Hurwitz, Toeplitz, Vandermonde and other structured matrices, Stietjes and Jacobi-type continued fractions, Cauchy indices, moment problems, total positivity, and root localization of univariate polynomials. Along with a survey of many classical facts, we provide a number of new results.

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Olga Holtz, Mikhail Tyaglov. 2009-12-23. Structured matrices, continued fractions, and root localization of polynomials. https://doi.org/10.1137/090781127

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