Polynomials generated by a three term recurrence relation: bounds for complex zeros
type: Item
instance of: scholarly article
title: Polynomials generated by a three term recurrence relation: bounds for complex zeros
zbMATH Open document ID: 1067.30015
author: A. Sri Ranga
author: Alex P. da Silva
published in: Linear Algebra and its Applications
publication date: 2005-05-04T00:00:00Z
full work available at URL: http://hdl.handle.net/11449/21746
review text: The authors investigate bounds for the zeros of polynomials \(Q_m(z)\) defined by the three-term recurrence relation \[ Q_{m+1}(z)=(z+\beta_{m+1})Q_m(z)-\alpha_{m+1}zQ_{m-1}(z),\quad m=1,2,\ldots \] with \(Q_0=1\) and \(Q_1(z)=z+\beta_1\), under a variety of assumptions on the complex numbers \(\alpha_m\) and \(\beta_m\) (the results are too technical to be reported here). Applications to Szegö polynomials, para-orthogonal polynomials, and polynomials with non-zero complex coefficients are also discussed.
reviewed by: Vania Mascioni
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 2165364
zbMATH Keywords: three term recurrence relations
zbMATH Keywords: eigenvalue problems
zbMATH Keywords: zeros of polynomials
MaRDI profile type: Publication
OpenAlex ID: W2153354766
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DOI: 10.1016/J.LAA.2004.11.005
description: scientific article; zbMATH DE number 2165364