Performance analysis of the computation of the Taylor series coefficients as performed in TADIFF

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.