Computing the zeros of analytic functions
type: Item
instance of: scholarly article
title: Computing the zeros of analytic functions
zbMATH Open document ID: 0945.65018
author: Peter Kravanja
author: Marc van Barel
published in: Lecture Notes in Mathematics
publication date: 2000-05-15T00:00:00Z
review text: The authors study the zeros of analytic function and several related problems in computational complex analysis. Using a logarithmic residue based quadrature method, the authors develop the algorithm for computing all the zeros of an analytic function \(f\) that lie inside a positively oriented Jordan curve \(\gamma.\) The same method is used to approximate the center of a cluster and the total number of zeros of the analytic function in this cluster. The authors also show how the logarithmic residue based approach can be used to compute all the zeros and poles of a meromorphic function that lie in the interior of a Jordan curve. They consider systems of analytic equations and use a multidimensional logarithmic residue formula to compute the zeros and corresponding multiplicities of analytics functions. This book provides useful methods and software for computing zeros of analytic functions which leads to a rich blend of mathematics and numerical analysis.
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 30C10
Mathematics Subject Classification ID: 65-02
zbMATH DE Number: 1446983
zbMATH Keywords: zeros
zbMATH Keywords: analytic function
zbMATH Keywords: computational complex analysis
zbMATH Keywords: textbook
zbMATH Keywords: logarithmic residue
zbMATH Keywords: quadrature method
zbMATH Keywords: poles
zbMATH Keywords: meromorphic function
reviewed by: Matthew He
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bfb0103927
OpenAlex ID: W384065554
DOI: 10.1007/BFB0103927
description: scientific article; zbMATH DE number 1446983