Schur-Cohn sub-transforms of a polynomial
type: Item
instance of: scholarly article
title: Schur-Cohn sub-transforms of a polynomial
zbMATH Open document ID: 0809.12001
published in: Journal of Symbolic Computation
publication date: 1995-04-04T00:00:00Z
review text: Let \(P\) be a polynomial of degree \(d\). The number of zeros of \(P\) lying inside \(| z|<1\) can be found (with some exceptions) by the Schur- Cohn algorithm. This constructs a sequence of polynomials \(TP, T^ 2 P,\dots\) where the degree of \(T^ k P\) is deemed to be \(d-k\) even if the coefficient of \(x^{d-k}\) is zero. (For details see, e.g., \textit{P. Henrici} [Applied and computational complex analysis. Vol. I, 493-496 (Wiley, 1988; Zbl 0635.30001)].) The coefficients in the sequence grow exponentially, but it is permissible to divide through each \(T^ i P\) by a numerical factor, and in the present paper it is shown that this can be done in such a way that the coefficients, while still integers, grow much more slowly, thus speeding up the computation.
Mathematics Subject Classification ID: 12D10
Mathematics Subject Classification ID: 65Y20
zbMATH DE Number: 627601
zbMATH Keywords: Schur-Cohn algorithm
zbMATH Keywords: complexity
zbMATH Keywords: polynomials
author: Philippe Saux Picart
reviewed by: H. J. Godwin
MaRDI profile type: Publication
full work available at URL: jsco.1993.1031
OpenAlex ID: W1988057096
DOI: 10.1006/JSCO.1993.1031
description: scientific article; zbMATH DE number 627601