Resumen de Structured matrices, continued fractions, and root localization of polynomials

Olga Holtz, Mikhail Tyaglov

• 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.