A Refined Probabilistic Error Bound for Sums
Numerical Analysis
2021-04-15 v1 Numerical Analysis
Abstract
This paper considers a probabilistic model for floating-point computation in which the roundoff errors are represented by bounded random variables with mean zero. Using this model, a probabilistic bound is derived for the forward error of the computed sum of n real numbers. This work improves upon existing probabilistic bounds by holding to all orders, and as a result provides informative bounds for larger problem sizes.
Cite
@article{arxiv.2104.06531,
title = {A Refined Probabilistic Error Bound for Sums},
author = {Eric Hallman},
journal= {arXiv preprint arXiv:2104.06531},
year = {2021}
}