A Robust Approximation to a Lambert-Type Function

2015/04/08 by K. Roberts, Roberts, Ken
Economics, Econometrics and Finance · Engineering · Physics and Astronomy · #Experimental and Theoretical Physics Studies #FOS: Mathematics #Numerical Analysis (math.NA) #Sports Analytics and Performance #Sports Dynamics and Biomechanics

paper · pdf · doi:10.48550/arxiv.1504.01964

openalex publication_date 2015/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The function y = g(x) = log(W(e^x)), where W() denotes the Lambert W function, is the solution to the equation y + e^y = x. It appears in various problem situations, for instance the calculation of current-voltage curves for solar cells. A direct calculation of g(x) may be inaccurate because of arithmetic underflow or overflow. We present a simple algorithm for calculating g(x) that is robust, in that it will work for almost all x values which are representable in the arithmetic of one's chosen computer language. The algorithm does not assume that the chosen computer language implements the Lambert W function.

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