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

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

Software:

TADIFF; ReLIADiff
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