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Journal Articles Numerical Algorithms Year : 2020

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

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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Origin : Files produced by the author(s)
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)

Dates and versions

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

Identifiers

Cite

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

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