Title: Error analysis of a derivative-free algorithm for computing zeros of holomorphic functions
Authors: Kravanja, Peter ×
Sakurai, LT
Van Barel, Marc #
Issue Date: 2003
Publisher: Springer-verlag wien
Series Title: Computing vol:70 issue:4 pages:335-347
Abstract: We consider the quadrature method developed by Kravanja and Van Barel (Computing 63(1):69-91, 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.
ISSN: 0010-485X
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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