On initial conditions for the convergence of simultaneous root finding methods
type: Item
instance of: scholarly article
title: On initial conditions for the convergence of simultaneous root finding methods
zbMATH Open document ID: 0862.65029
DOI: 10.1007/BF02276878
published in: Computing
publication date: 1997-05-25T00:00:00Z
review text: This paper addresses the convergence of a number of numerical methods for the simultaneous approximation of all complex roots of a polynomial. The theorems involve only the polynomial degree and the initial approximations to the roots. The convergence theorems apply to the Weierstrass-Dichov, the Börsch-Supan-Nourein, the Maehly-Ehrlich and the square root method in ordinary complex arithmetic and to the Weierstrass interval, the Gargantini-Henrici, the Börsch-Supan-like interval, the square root interval and the Halley-like interval method in complex interval arithmetic.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 936852
zbMATH Keywords: polynomial roots
zbMATH Keywords: simultaneous rootfinding
zbMATH Keywords: Weierstrass-Dochev method
zbMATH Keywords: Börsch-Supan-Nourein method
zbMATH Keywords: Maehly-Ehrlich method
zbMATH Keywords: Gargantini-Henrici interval method
zbMATH Keywords: Weierstrass interval method
zbMATH Keywords: Börsch-Supan interval method
zbMATH Keywords: square root interval method
zbMATH Keywords: convergence
zbMATH Keywords: complex roots
zbMATH Keywords: polynomial
zbMATH Keywords: square root method
zbMATH Keywords: Halley-like interval method
zbMATH Keywords: complex interval arithmetic
author: M. S. Petković
reviewed by: Claus Bendtsen
MaRDI profile type: Publication
cites work: Q3345690
cites work: Residuenabschätzung für Polynom-Nullstellen mittels Lagrange-Interpolation
cites work: On iteration methods without derivatives for the simultaneous determination of polynomial zeros
cites work: A modified Newton method for polynomials
cites work: Parallel Laguerre iterations: The complex case
cites work: Circular arithmetic and the determination of polynomial zeros
cites work: Zur iterativen Auflösung algebraischer Gleichungen
cites work: On the convergence order of a modified method for simultaneous finding polynomial zeros
cites work: An iteration formula for the simultaneous determination of the zeros of a polynomial
cites work: On a generalisation of the root iterations for polynomial complex zeros in circular interval arithmetic
cites work: On an iterative method for simultaneous inclusion of polynomial complex zeros
cites work: Iterative methods for simultaneous inclusion of polynomial zeros
cites work: On Halley-Like Algorithms for Simultaneous Approximation of Polynomial Complex Zeros
cites work: A note on some improvements of the simultaneous methods for determination of polynomial zeros
cites work: On some improvements of square root iteration for polynomial complex zeros
cites work: Weierstrass formula and zero-finding methods
cites work: Q3327628
cites work: Q3223805
full work available at URL: https://doi.org/10.1007/bf02276878
OpenAlex ID: W1530287661
description: scientific article; zbMATH DE number 936852