Publication
Title
A derivative-free algorithm for computing zeros of analytic functions
Author
Abstract
LetW be a simply connected region inC, f : W !Canalytic inW and a positively oriented Jordan curve in W that does not pass through any zero of f . We present an algorithm for computing all the zeros of f that lie in the interior of . It proceeds by evaluating certain integrals along numerically and is based on the theory of formal orthogonal polynomials. The algorithm requires only f and not its first derivative f 0. We have found that it gives accurate approximations for the zeros. Moreover, it is self-starting in the sense that it does not require initial approximations. The algorithmworks for simple zeros as well as multiple zeros, although it is unable to compute the multiplicity of a zero explicitly. Numerical examples illustrate the effectiveness of our approach.
Language
English
Source (journal)
Computing: archives for informatics and numerical computation. - Wien
Publication
Wien : 1999
ISSN
0010-485X
Volume/pages
63:1(1999), p. 69-91
ISI
000081744400004
Full text (Publishers DOI)
Full text (publishers version - intranet only)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
External links
Web of Science
Record
Identification
Creation 17.04.2012
Last edited 18.04.2017