Numerical evaluation of the Lambert W function and application to generation of generalized Gaussian noise with exponent 1/2

@article{ChapeauBlondeau2002NumericalEO,
  title={Numerical evaluation of the Lambert W function and application to generation of generalized Gaussian noise with exponent 1/2},
  author={François Chapeau-Blondeau and Abdelilah Monir},
  journal={IEEE Trans. Signal Process.},
  year={2002},
  volume={50},
  pages={2160-2165}
}
We address the problem of synthesizing a generalized Gaussian noise with exponent 1/2 by means of a nonlinear memoryless transformation applied to a uniform noise. We show that this transformation is expressable in terms of a special function known under the name of the Lambert W function. We review the main methods for numerical evaluation of the relevant branch of the (multivalued) Lambert W function with controlled accuracy and complement them with an original rational function approximation… 

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