Analytical approximations for real values of the Lambert W-function

Barry, D.A, Parlange, J.Y., Li, L., Prommer, H., Cunningham, C.J. and Stagnitti, E. (2000) Analytical approximations for real values of the Lambert W-function. Mathematics and Computers in Simulation, 53 1-2: 95-103. doi:10.1016/S0378-4754(00)00172-5

Author Barry, D.A
Parlange, J.Y.
Li, L.
Prommer, H.
Cunningham, C.J.
Stagnitti, E.
Title Analytical approximations for real values of the Lambert W-function
Journal name Mathematics and Computers in Simulation   Check publisher's open access policy
ISSN 0378-4754
Publication date 2000-08
Sub-type Article (original research)
DOI 10.1016/S0378-4754(00)00172-5
Volume 53
Issue 1-2
Start page 95
End page 103
Total pages 9
Place of publication Amsterdam, Netherlands
Publisher Elsevier
Language eng
Formatted abstract
The Lambert W is a transcendental function defined by solutions of the equation W exp(W) = x. For real values of the argument, x, the W-function has two branches, W 0 (the principal branch) and W -1 (the negative branch). A survey of the literature reveals that, in the case of the principal branch (W 0), the vast majority of W-function applications use, at any given time, only a portion of the branch viz. the parts defined by the ranges -1 ≤ W 0 ≤ 0 and 0 ≤ W 0. Approximations are presented for each portion of W 0, and for W -1. It is shown that the present approximations are very accurate with relative errors down to around 0.02% or smaller. The approximations can be used directly, or as starting values for iterative improvement schemes.
Keyword Computer science, interdisciplinary applications
Computer ccience, software engineering
Mathematics, applied
Analytical approximations
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ
Additional Notes Erratum to “Analytical approximations for real values of the Lambert W-function” [Mathematics and Computers in Simulation 53 (2000) 95–103]

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Civil Engineering Publications
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Created: Mon, 13 Aug 2007, 11:56:25 EST