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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.
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https://hal.archives-ouvertes.fr/hal-02984459
Contributor : Marc Mezzarobba <>
Submitted on : Saturday, October 31, 2020 - 9:53:00 AM
Last modification on : Wednesday, November 4, 2020 - 5:30:05 PM

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Distributed under a Creative Commons Attribution 4.0 International License

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  • HAL Id : hal-02984459, version 1
  • ARXIV : 2011.00827

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Marc Mezzarobba. Rounding Error Analysis of Linear Recurrences Using Generating Series. 2020. ⟨hal-02984459⟩

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