A modification of the Delves-Lyness method for locating the zeros of analytic functions
type: Item
instance of: scholarly article
title: A modification of the Delves-Lyness method for locating the zeros of analytic functions
zbMATH Open document ID: 0607.65020
DOI: 10.1016/0021-9991(85)90125-1
author: E. G. Anastasselou
author: N. I. Ioakimidis
published in: Journal of Computational Physics
publication date: 1985-01-01T00:00:00Z
review text: One of the variants of this general class of methods involves integrating the function \(z^ kf'(z)/f(z)\) round a closed contour. When this is done numerically one can avoid derivative evaluations by using integration by parts exploiting \(f'(z)/f(z)=d(\log f(z))/dz\). However, one is now left with the problem of keeping track of the argument of a multivalued analytic function as it winds round the origin (there being n winds when the number of zeros within the contour is n). This paper proposes a method which apparently reduces the chance of being misled. However, to use it one needs to know the numerical value of n. This reviewer's experience is that, when using these methods, the main problem is the determination of n. By the time enough information to be reasonably certain of this is available, locating the zeros is a simple ''spinoff'' calculation.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 3982404
zbMATH Keywords: Delves-Lyness method
zbMATH Keywords: zeros of an analytic function
zbMATH Keywords: zero finding
zbMATH Keywords: multivalued analytic function
reviewed by: James N. Lyness
MaRDI profile type: Publication
full work available at URL: 0021-9991(85)90125-1
OpenAlex ID: W2049236760
cites work: Solution of equations involving analytic functions
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description: scientific article; zbMATH DE number 3982404