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.

翻译：我们开发了一个工具箱,用于根据生成序列、Cauchy的主要成分方法以及分析组合实验的简单结果,对含有常数或多数值的线性重现进行错误分析。我们用几个非三元应用实例来说明这一方法的力量。这些例子包括对计算Bernoulli数字的算法进行的新的最坏分析,以及用来评估间距计算中不同限制功能并避免间断爆炸的新算法。