Computing the Lambert W function in arbitrary-precision complex interval arithmetic

摘要

We describe an algorithm to evaluate all the complex branches of the Lambert W function with rigorous error bounds in arbitrary-precision interval arithmetic or ball arithmetic. The classic 1996 paper on the Lambert W function by Corless et al. provides a thorough but partly heuristic numerical analysis of the Lambert W function which needs to be complemented with some explicit inequalities and practical observations about managing precision and branch cuts. An implementation is provided in the Arb library.