Improved validated bounds for Taylor coefficients and for Taylor remainder series

Authors:
M. Neher
Affiliations:
Institut für Angewandte Mathematik, Universität Karlsruhe (TH), 76128 Karlsruhe, Germany
Venue:
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Year:
2003

Citing 4
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Abstract

This paper presents methods for the validated computation of bounds for Taylor coefficients and bounds for Taylor remainder series of analytic functions. These bounds are derived from modifications of Cauchy's estimate. The proposed methods have been implemented in mathematical software called ACETAF. Interval arithmetic is used to restore mathematical rigour to practical calculations. The performance of ACETAF is demonstrated with numerical examples.