Rounding Error Analysis of Linear Recurrences Using Generating Series
Numerical Analysis
2023-03-02 v5 Numerical Analysis
Symbolic Computation
Abstract
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.
Cite
@article{arxiv.2011.00827,
title = {Rounding Error Analysis of Linear Recurrences Using Generating Series},
author = {Marc Mezzarobba},
journal= {arXiv preprint arXiv:2011.00827},
year = {2023}
}