Performance analysis of the Taylor expansion coefficients computation as implemented by the software package TADIFF. (English) Zbl 1432.65004

D’Amore, L.; Arcucci, R.; Marcellino, L.; Murli, A.

JNAIAM, J. Numer. Anal. Ind. Appl. Math. 8, No. 1-4, 1-12 (2013).

Summary: 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.

MSC:

65B99	Acceleration of convergence in numerical analysis
65Y10	Numerical algorithms for specific classes of architectures
65Y20	Complexity and performance of numerical algorithms

Keywords:

algorithmic differentiation; Taylor expansion coefficients; TADIFF

Software:

TADIFF; ReLIADiff