A bound for the error term in the Brent-McMillan algorithm
Numerical Analysis
2015-08-18 v1
Abstract
The Brent-McMillan algorithm B3 (1980), when implemented with binary splitting, is the fastest known algorithm for high-precision computation of Euler's constant. However, no rigorous error bound for the algorithm has ever been published. We provide such a bound and justify the empirical observations of Brent and McMillan. We also give bounds on the error in the asymptotic expansions of functions related to modified Bessel functions.
Cite
@article{arxiv.1312.0039,
title = {A bound for the error term in the Brent-McMillan algorithm},
author = {Richard P. Brent and Fredrik Johansson},
journal= {arXiv preprint arXiv:1312.0039},
year = {2015}
}
Comments
10 pages, 1 table