A hybrid method for polynomial complex zero
type: Item
instance of: scholarly article
title: A hybrid method for polynomial complex zero
zbMATH Open document ID: 0724.65048
DOI: 10.1016/0898-1221(91)90097-N
author: M. S. Petković
author: Ljiljana Cvetković
publication date: 1991-01-01T00:00:00Z
review text: The paper deals with an iterative algorithm for finding isolated simple complex zeroes of a polynomial. Using Weierstrass' interval formula for the simultaneous inclusion of all zeroes of the polynomial and rectangular floating-point arithmetic, a hybrid method with high computational efficiency is presented. Furthermore, error bounds of the approximate solution are determined. In a second part, a computationally verifiable test for the existence of a zero in a given disc is established. A numerical example is given, too.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 65E05
zbMATH DE Number: 4195053
zbMATH Keywords: rectangular arithmetic
zbMATH Keywords: iterative algorithm
zbMATH Keywords: isolated simple complex zeroes
zbMATH Keywords: polynomial
zbMATH Keywords: Weierstrass' interval formula
zbMATH Keywords: simultaneous inclusion
zbMATH Keywords: floating-point arithmetic
zbMATH Keywords: hybrid method
zbMATH Keywords: error bounds
zbMATH Keywords: numerical example
reviewed by: Hartje Kriete
describes a project that uses: Pascal-SC
MaRDI profile type: Publication
cites work: Q3345690
cites work: Iterative methods for interval inclusion of fixed points
cites work: Further Applications of Circular Arithmetic: Schroeder-Like Algorithms with Error Bounds for Finding Zeros of Polynomials
cites work: The numerical stability of simultaneous iterations via square-rooting
cites work: Circular arithmetic and the determination of polynomial zeros
cites work: Q4072022
cites work: Q3780406
cites work: An interval version of the secant method
cites work: On Halley-Like Algorithms for Simultaneous Approximation of Polynomial Complex Zeros
cites work: Iterative methods for simultaneous inclusion of polynomial zeros
cites work: On the efficiency of some combined methods for polynomial complex zeros
cites work: Hybrid inclusion algorithms for polynomial multiple complex zeros in rectangular arithmetic
cites work: A computational test for the existence of a polynomial zero
cites work: The numerical stability of the generalised root iterations for polynomial zeros
full work available at URL: 0898-1221(91)90097-n
OpenAlex ID: W2018314172
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4195053