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：我们开发了一套基于生成级数、柯西强函数法及解析组合学简易结论的线性常系数与多项式系数递归误差分析工具箱，并通过多个非平凡应用实例展示了该方法的能力。这些实例包括：伯努利数计算算法的新型最坏情况分析，以及一种在区间算术中避免区间膨胀的微分有限函数求值新算法。