An error analysis of two related quadrature methods for computing zeros of analytic functions

Authors:
Tetsuya Sakurai;Peter Kravanja;Hiroshi Sugiura;Marc Van Barel
Affiliations:
Institute of Information Sciences and Electronics, University of Tsukuba, Tennodai 1-1-1, Tsukuba, Ibraraki, 305-8573, Japan;Katholieke Universiteit Leuven, Department of Computer Science, Celestijnenlaan 200 A, B-3001 Heverlee, Belgium;Graduate School of Engineering, Nagoya University, Nagoya 464-8603, Japan;Katholieke Universiteit Leuven, Department of Computer Science, Celestijnenlaan 200 A, B-3001 Heverlee, Belgium
Venue:
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Year:
2003

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Abstract

We present an error analysis for two related quadrature methods (the Delves-Lyness method and its modification by Kravanja, Sakurai and Van Barel) for computing all the zeros of an analytic function that lie inside the unit circle. We consider the forward as well as the backward approximation error in case the integrals are computed via the trapezoidal rule on the unit circle. Contrary to the Delves-Lyness method, the quadrature error that arises from the zeros located inside the unit circle does not affect the results of the approach of Kravanja et al. Numerical experiments illustrate our main results.