The guaranteed convergence of Laguerre-like method
type: Item
instance of: scholarly article
title: The guaranteed convergence of Laguerre-like method
zbMATH Open document ID: 1053.65036
DOI: 10.1016/S0898-1221(03)90028-9
author: M. S. Petković
author: L. D. Petković
author: Snežana Ilić
publication date: 2004-08-06T00:00:00Z
review text: The authors continue their study of a Laguerre-like method for the simultaneous computation of all zeros of polynomial. The method, recently presented by the first author [J. Comput. Appl. Math. 152, No. 1--2, 451--465 (2003; Zbl 1022.65053)], is recalled together with estimates and inequalities necessary for the convergence analysis. The main result of the paper is a theorem which gives a condition assuring fourth order convergence when the Laguerre-like method is applied to a polynomial of degree \(\geq 3\) with simple zeros. A numerical example of the method is given at the end of the paper.
reviewed by: Luigi Gatteschi
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 26C10
Mathematics Subject Classification ID: 12Y05
zbMATH DE Number: 2082581
zbMATH Keywords: zeros of polynomials
zbMATH Keywords: point estimation
zbMATH Keywords: approximate zeros
zbMATH Keywords: simultaneous zeros
zbMATH Keywords: guaranteed convergence
zbMATH Keywords: Laguerre-like method
MaRDI profile type: Publication
cites work: The fundamental theorem of algebra and complexity theory
cites work: Approximate Zeros of Quadratically Convergent Algorithms
cites work: On zero finding methods of higher order from data at one point
cites work: On Approximate Zeros and Rootfinding Algorithms for a Complex Polynomial
cites work: Q4720691
cites work: Convergence of Newton’s method and inverse function theorem in Banach space
cites work: The theory of Smale's point estimation and its applications
cites work: Q4894319
cites work: Weierstrass formula and zero-finding methods
cites work: Point estimation of simultaneous methods for solving polynomial equations: A survey
cites work: Q4254885
cites work: Q4060241
cites work: Q4072022
cites work: Some modifications of Laguerre's method
cites work: Q2765622
cites work: Laguerre-like inclusion method for polynomial zeros
cites work: Q3959347
full work available at URL: s0898-1221(03)90028-9
OpenAlex ID: W1965159190
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2082581