Computing the Lambert W function in arbitrary-precision complex interval arithmetic
Mathematical Software
2017-05-10 v1 Numerical Analysis
Abstract
We describe an algorithm to evaluate all the complex branches of the Lambert W function with rigorous error bounds in interval arithmetic, which has been implemented in the Arb library. The classic 1996 paper on the Lambert W function by Corless et al. provides a thorough but partly heuristic numerical analysis which needs to be complemented with some explicit inequalities and practical observations about managing precision and branch cuts.
Cite
@article{arxiv.1705.03266,
title = {Computing the Lambert W function in arbitrary-precision complex interval arithmetic},
author = {Fredrik Johansson},
journal= {arXiv preprint arXiv:1705.03266},
year = {2017}
}
Comments
16 pages, 4 figures