Computing the Lambert W function in arbitrary-precision complex interval arithmetic
This work provides a rigorous and practical implementation of the Lambert W function for arbitrary-precision interval arithmetic, benefiting researchers and engineers who require guaranteed error bounds in complex analysis and numerical computing.
The authors present an algorithm for computing all complex branches of the Lambert W function with rigorous error bounds in interval arithmetic, implemented in the Arb library. The algorithm achieves high precision and reliability, addressing gaps in the heuristic numerical analysis from the classic 1996 paper.
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.