用生成级数分析线性递归的舍入误差
Rounding Error Analysis of Linear Recurrences Using Generating Series
摘要：
我们开发了一个工具箱的误差分析的线性递归常数或多项式系数，生成系列的基础上，柯西的方法的majorants，从分析组合学的简单结果。我们说明了几个不平凡的应用程序的例子的方法的力量。在这些例子中，有一个新的最坏情况下的分析算法计算伯努利数，和一个新的算法，用于评估差分有限函数的区间运算，同时避免区间爆破。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
