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

Fredrik Johansson 1, 2
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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.
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https://hal.inria.fr/hal-01519823
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Submitted on : Tuesday, May 9, 2017 - 12:51:11 PM
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Fredrik Johansson. Computing the Lambert W function in arbitrary-precision complex interval arithmetic. 2017. ⟨hal-01519823⟩

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