论文标题
使用生成序列对线性复发的四舍五入误差分析
Rounding Error Analysis of Linear Recurrences Using Generating Series
论文作者
论文摘要
我们开发了一个工具箱，以基于生成序列，库奇的主要内容方法以及分析组合学的简单结果，用于具有恒定或多项式系数的线性复发的误差分析。我们通过几个非平凡的应用示例来说明该方法的力量。在这些示例中，有针对计算Bernoulli数字的算法的新最坏情况分析，以及一种用于评估间隔算术差异有限函数的新算法，同时避免间隔爆炸。
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.
