Performance Analysis of the Taylor Expansion Coefficients Computation as Implemented by the Software Package TADIFF

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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