TY - JOUR
T1 - Analytical approximations for real values of the Lambert W-function
AU - Barry, D. A.
AU - Parlange, J. Y.
AU - Li, L.
AU - Prommer, H.
AU - Cunningham, C. J.
AU - Stagnitti, F.
PY - 2000/8/15
Y1 - 2000/8/15
N2 - 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, 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.
AB - 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, 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.
KW - Algorithms
KW - Analytical approximations
KW - Iteration scheme
UR - https://www.scopus.com/pages/publications/0001951498
M3 - Article
AN - SCOPUS:0001951498
SN - 0378-4754
VL - 53
SP - 95
EP - 103
JO - Mathematics and Computers in Simulation
JF - Mathematics and Computers in Simulation
IS - 1-2
ER -