Luisa D’Amore2, Valeria Melea and Almerico Murlib
aUniversity of Naples Federico II, Naples, ITALY,
bSouthern Partnership for Advanced Computational Infrastructures (SPACI), c/o
University of Naples, Federico II, Naples
and CMCC - Centro Euro-Mediterraneo per i Cambiamenti Climatici, Lecce, ITALY
Received 29 October, 2012; accepted in revised form 24 April, 2013
Abstract: A detailed rounding errors analysis for the computation of Taylor expansion
coefficients of an analytic real function with respect to one variable, as implemented by
TADIFF, a software package written in C++ specialized for computing Taylor expansion
coefficients using Algorithmic Differentiation, is performed. The error analysis is carried
out in a finite precision arithmetic system satisfying the IEEE standard 754. Furthermore,
time and space complexity of such a computation is discussed. Experimental results aimed
to validate both the accuracy and the complexity estimates are presented.
Keywords: Algorithmic Differentiation, Taylor expansion coefficients, TADIFF
Mathematics Subject Classification: AMS: 65G50; 65Y20; 68Q25
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