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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
2 IMB - Institut de Mathématiques de Bordeaux
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 : Thursday, March 12, 2020 - 3:38:16 PM
Last modification on : Wednesday, February 2, 2022 - 3:54:26 PM
Long-term archiving on: : Saturday, June 13, 2020 - 12:30:51 PM

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Fredrik Johansson. Computing the Lambert W function in arbitrary-precision complex interval arithmetic. Numerical Algorithms, Springer Verlag, 2020, 83 (1), pp.221-242. ⟨10.1007/s11075-019-00678-x⟩. ⟨hal-01519823v2⟩

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