Analytical approximations for real values of the Lambert W -function
By D. Barry, J. Parlange, Ling Li, H. Prommer, C. Cunningham, F. Stagnitti. 2000
233 citations recorded by the source corpus.
The Lambert W is a transcendental function defined by solutions of the equation Wexp(W)=x. For real values of the argument, x, the W-function has two branches, W0 (the principal branch) and W−1 (the negative branch). A survey of the literature reveals that, in the case of the principal branch (W0), 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≤W0≤0 and 0≤W0. Approximations are presented for each portion of W0, 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.
Subfields: Biomedical Engineering, Orthopedics and Sports Medicine, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/e5d82f6dc85b9b506fc6b7247dc7ce57ca474685
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In Statistical and Nonlinear Physics
Citations in the corpus
- The QCD running coupling (2016, background): “An accurate approximation of W−1 can be found in [28].”
- Exact Kolmogorov and total variation distances between some familiar discrete distributions (2006, unknown): “[2], and the references therein).”
- Image Resolution in Optical Nanoscopy (2013, methodology): “A useful analytical approximation for the Lambert W-function is W (y) ≈ ln (2y)− ln (ln (1 + 2y)) [21].”
- Joint Depth and Color Camera Calibration with Distortion Correction (2012, methodology): “Hence, we use a spatially varying offset that decays as the Kinect disparity increases: dk ¼ dþD ðu; vÞ expð 0 1dÞ; ð6Þ where d is the distorted disparity as returned by the Kinect, D contains the spatial distortion pattern, and ¼ ½ 0; 1 models the decay of the distortion effect.”