Structured matrices, continued fractions, and root localization of polynomials
Classical Analysis and ODEs
2012-07-06 v3 Complex Variables
History and Overview
Rings and Algebras
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.
Cite
@article{arxiv.0912.4703,
title = {Structured matrices, continued fractions, and root localization of polynomials},
author = {Olga Holtz and Mikhail Tyaglov},
journal= {arXiv preprint arXiv:0912.4703},
year = {2012}
}
Comments
79 pages; new material added to the Introduction