Structured matrices, continued fractions, and root localization of polynomials

• Autores: Olga Holtz, Mikhail Tyaglov
• Localización: SIAM Review, ISSN 0036-1445, Vol. 54, Nº. 3, 2012, págs. 421-509
• Idioma: inglés
• DOI: 10.1137/090781127
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• Resumen

  • 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.