Volume 58, pp. 196-227, 2023.

Rounding error analysis of linear recurrences using generating series

Marc Mezzarobba


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 the Bernoulli numbers and a new algorithm for evaluating differentially finite functions in interval arithmetic while avoiding interval blow-up.

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Key words

rounding error, rigorous computing, complex variable, majorant series, Bernoulli numbers, vibrating string, differentially finite function

AMS subject classifications

65G50, 65Q30, 65L70, 05A15

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