Comments on "numerical evaluation of the Lambert W function and application to generation of generalized Gaussian noise with exponent 1/2"

The Lambert W function appears in a wide variety of circumstances, including the recent application to signal processing referred to in the paper under discussion. Besides applications, a sizable body of mathematical analysis has been reported. The original paper presented a numerical algorithm for computation of W-1. An existing, similar algorithm is presented. Iterative improvement of the W-1 estimates is also discussed, and issues concerning computational efficiency and possible sources of rounding error in fixed precision computational environments are identified. Existing, public-domain software takes into account all the identified numerical issues and produces estimates of W to near the precision available on the host machine.