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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
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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Preprints, Working Papers, ...
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Submitted on : Tuesday, May 9, 2017 - 12:51:11 PM
Last modification on : Friday, December 3, 2021 - 12:20:06 PM
Long-term archiving on: : Thursday, August 10, 2017 - 1:01:14 PM


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  • HAL Id : hal-01519823, version 1



Fredrik Johansson. Computing the Lambert W function in arbitrary-precision complex interval arithmetic. 2017. ⟨hal-01519823v1⟩



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