This Julia package implements an approximation of the two real branches of Lambert's W function, W = W(x), defined as a solution of the equation W*exp(W) = x
The approximation is based on an iterative method.
I made this package to try out Julia, but unfortunately I did not register it before an official LambertW package occured.
To compute W_k(x), where k being either 0 or -1 denotes the branch, use
lambertw(x, k)
A third, optional argument specifies the precision which by default is eps().
The initial approximations are described in
- D.A. Barry, J.-Y. Parlange, L. Li, H. Prommer, C. J. Cunningham, F. Stagnitti, "Analytical approximations for real values of the Lambert W-function", Mathematics and Computers in Simulation, volume 53, 2000, page 95--103. DOI: 10.1016/S0378-4754(00)00172-5
- The erratum to the above article; DOI: 10.1016/S0378-4754(02)00051-4
The iterative refinement is calculated using Fritsch’s method as mentioned in e.g.
- Darko Veberic, "Lambert W function for applications in physics", Computer Physics Communications, volume 183, 2012, page 2622-–2628. DOI: 10.1016/j.cpc.2012.07.008. arXiv: 1209.0735 [cs.MS].