Publication
Title
Error analysis of a derivative-free algorithm for computing zeros of holomorphic functions
Author
Abstract
We consider the quadrature method developed by Kravanja and Van Barel (Computing 63(1):6991, 1999) for computing all the zeros of a holomorphic function that lie inside the unit circle. The algorithm uses only the function values and no (first or higher order) derivatives. Information about the location of the zeros is obtained from certain integrals along the unit circle. In numerical computations these are replaced by their trapezoidal rule approximations. We investigate the resulting quadrature error. Our error analysis shows that the zeros located inside the unit circle do not affect the accuracy of the computed approximations whereas the quadrature error related to the zeros located outside the unit circle tends to zero exponentially as the number of quadrature points tends to infinity.
Language
English
Source (journal)
Computing: archives for informatics and numerical computation. - Wien
Publication
Wien : 2003
ISSN
0010-485X
Volume/pages
70:4(2003), p. 335-347
ISI
000185138000003
Full text (Publisher's DOI)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
External links
Web of Science
Record
Identification
Creation 17.04.2012
Last edited 24.06.2017