Structured matrices, continued fractions, and root localization of polynomials

Details Structured matrices, continued fractions, and root localization of polynomials Structured matrices, continued fractions, and root localization of polynomials

2009-12-23

arxiv.org/abs/0912.4703v3

Mathematics

Classical Analysis and ODEs

79 pages; new material added to the Introduction

Scientific paper

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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