Optimal quantization has been recently revisited in multi-dimensional numerical
integration, multi-asset American option pricing, control theory and nonlinear filtering theory. In this paper, we enlighten some numerical procedures
in order to get some accurate optimal quadratic quantization of the Gaussian distribution in
one and higher dimensions. We study in particular Newton method in the deterministic case
(dimension d = 1) and stochastic gradient in higher dimensional case (d ≥ 2). Some heuristics
are provided which concern the step in the stochastic gradient method. Finally numerical
examples borrowed from mathematical finance are used to test the accuracy of our Gaussian
This quarterly published journal presents original articles on the theory and applications of Monte Carlo and Quasi-Monte Carlo methods. Launched in 1995 the journal covers all stochastic numerics topics with emphasis on the theory of Monte Carlo methods and new applications in all branches of science and technology.