Title
Error analysis of a derivative-free algorithm for computing zeros of holomorphic functions Error analysis of a derivative-free algorithm for computing zeros of holomorphic functions
Author
Faculty/Department
Faculty of Social Sciences. Communication Sciences
Publication type
article
Publication
Wien ,
Subject
Computer. Automation
Source (journal)
Computing: archives for informatics and numerical computation. - Wien
Volume/pages
70(2003) :4 , p. 335-347
ISSN
0010-485X
ISI
000185138000003
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
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.
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