Attractive cycles in the iteration of meromorphic functions
type: Item
instance of: scholarly article
title: Attractive cycles in the iteration of meromorphic functions
zbMATH Open document ID: 0541.30016
DOI: 10.1007/BF01389489
author: James Lucien Howland
author: Rémi Vaillancourt
published in: Numerische Mathematik
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/132999
review text: The existence of attractive cycles constitutes a serious impediment to the solution of nonlinear equations by iterative methods. This problem is illustrated in the case of the solution of the equation \(z \tan z=c,\) for complex values of c, by Newton's method. Relevant results from the theory of the iteration of rational functions are cited and extended to the analysis of this case, in which a meromorphic function is iterated. Extensive numerical results, including many attractive cycles, are summarized.
Mathematics Subject Classification ID: 30D05
Mathematics Subject Classification ID: 30-04
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 65H05
zbMATH DE Number: 3859460
zbMATH Keywords: attractive cycles
zbMATH Keywords: iteration of rational functions
zbMATH Keywords: meromorphic function
MaRDI profile type: Publication
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OpenAlex ID: W2094876055
description: scientific article; zbMATH DE number 3859460