Approximating zeros of an analytic function by homotopy method
type: Item
instance of: scholarly article
title: Approximating zeros of an analytic function by homotopy method
zbMATH Open document ID: 0701.65037
author: M. Mohseni Moghadam
published in: Bulletin of the Iranian Mathematical Society
publication date: 1989-01-01T00:00:00Z
review text: Like the method of \textit{L. M. Delves} and \textit{J. N. Lyness} [Math. Comp. 21, 543-560 (1967; Zbl 0153.179)] the one proposed here is based on applying the residue theorem to \(z^ kf'(z)/f(z)\), \(k=0,1,...,s\), and an appropriately chosen closed contour C. To find M roots inside C simultaneously one has to set up and solve a polynomial equation of degree M. Using strong classical algebraic results the author derives a special homotopy method that allows him to convert the problem to a system of ordinary differential equations which he then solves numerically with standard software.
reviewed by: Martin H. Gutknecht
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 65H20
Mathematics Subject Classification ID: 65E05
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 4149465
zbMATH Keywords: zeros of analytic function
zbMATH Keywords: continuation method
zbMATH Keywords: nonlinear equation
zbMATH Keywords: analytic equation
zbMATH Keywords: homotopy method
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4149465