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Computing the Lambert W function in arbitrary-precision complex interval arithmetic (1705.03266v1)
Published 9 May 2017 in cs.MS and cs.NA
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.