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.

中文翻译：

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使用生成序列的线性递归的舍入误差分析

我们开发了一个工具箱，用于具有常数或多项式系数的线性递归的误差分析，基于生成序列、柯西的majorants 方法和分析组合学的简单结果。我们通过几个重要的应用示例来说明该方法的强大功能。其中包括对计算伯努利数的算法的新最坏情况分析，以及在区间算术中评估微分有限函数同时避免区间爆炸的新算法。