Rounding error analysis of linear recurrences using generating series
نویسندگان
چکیده
We develop a toolbox for the error analysis of linear recurrences with constant or polynomial coefficients, based on generating series, Cauchy's method majorants, and simple results from analytic combinatorics. illustrate power approach by several nontrivial application examples. Among these examples are new worst-case an algorithm computing Bernoulli numbers, evaluating differentially finite functions in interval arithmetic while avoiding blow-up.
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ژورنال
عنوان ژورنال: Electronic Transactions on Numerical Analysis
سال: 2023
ISSN: ['1068-9613', '1097-4067']
DOI: https://doi.org/10.1553/etna_vol58s196