Rounding Error Analysis of Linear Recurrences Using Generating Series - Archive ouverte HAL Access content directly
Journal Articles Electronic Transactions on Numerical Analysis Year : 2023

Rounding Error Analysis of Linear Recurrences Using Generating Series

Abstract

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.
Fichier principal
Vignette du fichier
recrnderr.pdf (495.68 Ko) Télécharger le fichier
recrnderr_supplementary_material.zip (638.61 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Licence : CC BY - Attribution
Licence : CC BY - Attribution

Dates and versions

hal-02984459 , version 1 (31-10-2020)
hal-02984459 , version 2 (23-04-2021)
hal-02984459 , version 3 (21-02-2023)

Licence

Attribution

Identifiers

Cite

Marc Mezzarobba. Rounding Error Analysis of Linear Recurrences Using Generating Series. Electronic Transactions on Numerical Analysis, 2023, 58, pp.196--227. ⟨10.1553/etna_vol58s196⟩. ⟨hal-02984459v3⟩
140 View
223 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More