An algorithm for locating all zeros of a real polynomial
type: Item
instance of: scholarly article
title: An algorithm for locating all zeros of a real polynomial
zbMATH Open document ID: 0844.65042
DOI: 10.1007/BF02238233
author: F. Locher
author: Michael-Ralf Skrzipek
published in: Computing
publication date: 1995-07-25T00:00:00Z
review text: The authors present a globally convergent algorithm for calculating all zeros of a polynomial \(p_n\) with real coefficients. The calculation procedure starts with the stability test allowing to decide whether all zeros of \(p_n\) lie in the interior of the unit circle of the complex plane. It is also possible to get the exact number of zeros in the interior, on the boundary and in the exterior of a circle. Later the approximations of the zeros are calculated by appropriate iterative algorithms (e.g. Newton's or Bairstrow's type at the final stage).
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 769259
zbMATH Keywords: zeros of a real polynomial
zbMATH Keywords: global convergence
zbMATH Keywords: Newton method
zbMATH Keywords: Bairstrow method
zbMATH Keywords: stability test
zbMATH Keywords: iterative algorithms
MaRDI profile type: Publication
cites work: Q5558293
cites work: Detection and validation of clusters of polynomial zeros
cites work: A stability test for real polynomials
cites work: A bibliography on roots of polynomials
cites work: Q5641060
cites work: Counting Zeros of Real Polynomials within the Unit Disk
cites work: A Global Bisection Algorithm for Computing the Zeros of Polynomials in the Complex Plane
full work available at URL: https://doi.org/10.1007/bf02238233
OpenAlex ID: W1587987493
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description: scientific article; zbMATH DE number 769259