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

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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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Dates and versions

hal-01519823 , version 1 (09-05-2017)
hal-01519823 , version 2 (12-03-2020)

Identifiers

  • HAL Id : hal-01519823 , version 1

Cite

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