The behaviour of approximations of the SOR Weierstrass method
type: Item
instance of: scholarly article
title: The behaviour of approximations of the SOR Weierstrass method
zbMATH Open document ID: 0868.65028
DOI: 10.1016/0898-1221(96)00160-5
publication date: 1997-02-19T00:00:00Z
review text: The Weierstrass method is one of the most efficient methods for the simultaneous approximation of the simple roots of a polynomial. The choice of initial approximations plays a crucial role in the applications. Practical experience shows that the method converges for almost all distinct initial values. This paper deals with the successive overrelaxation (SOR) Weierstrass method with acceleration parameter. It is shown that for a given polynomial and acceleration parameter, there exists a unique divergence point from \(\mathbb{C}\). This is a very interesting result.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 12Y05
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 980334
zbMATH Keywords: divergence sets
zbMATH Keywords: convergence
zbMATH Keywords: Weierstrass method
zbMATH Keywords: roots of a polynomial
zbMATH Keywords: successive overrelaxation
author: Nikolay Kyurkchiev
author: M. S. Petković
reviewed by: Liu Xinguo
MaRDI profile type: Publication
full work available at URL: 0898-1221(96)00160-5
OpenAlex ID: W1998103765
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published in: Computers & Mathematics with Applications
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description: scientific article; zbMATH DE number 980334