Rounding Error Analysis of Linear Recurrences Using Generating Series

Marc Mezzarobba (1)

1 PEQUAN - Performance et Qualité des Algorithmes Numériques

We develop a toolbox for the error analysis of linear recurrences with constant or polynomial coefficients, based on generating series, Cauchy's method of majorants, and simple results from analytic combinatorics. We illustrate the power of the approach by several nontrivial application examples. Among these examples are a new worst-case analysis of an algorithm for computing Bernoulli numbers, and a new algorithm for evaluating differentially finite functions in interval arithmetic while avoiding interval blow-up.

Domaines: Analyse numérique [cs.NA]; Arithmétique des ordinateurs; Calcul formel [cs.SC]

Marc Mezzarobba. Rounding Error Analysis of Linear Recurrences Using Generating Series. 2021. ⟨hal-02984459v2⟩