Publication
Title
On locating clusters of zeros of analytic functions
Author
Abstract
Given an analytic function f and a Jordan curve γ that does not pass through any zero of f, we consider the problem of computing all the zeros of f that lie inside γ, together with their respective multiplicities. Our principal means of obtaining information about the location of these zeros is a certain symmetric bilinear form that can be evaluated via numerical integration along γ. If f has one or several clusters of zeros, then the mapping from the ordinary moments associated with this form to the zeros and their respective multiplicities is very ill-conditioned. We present numerical methods to calculate the centre of a cluster and its weight, i.e., the arithmetic mean of the zeros that form a certain cluster and the total number of zeros in this cluster, respectively. Our approach relies on formal orthogonal polynomials and rational interpolation at roots of unity. Numerical examples illustrate the effectiveness of our techniques.
Language
English
Source (journal)
Bit : numerical mathematics. - Lund
Publication
Lund : 1999
ISSN
0006-3835
Volume/pages
39:4(1999), p. 646-682
ISI
000084736100004
Full text (Publisher's DOI)
Full text (publisher's version - intranet only)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
External links
Web of Science
Record
Identification
Creation 17.04.2012
Last edited 11.09.2017