Quasi-Monte Carlo quadratures for multivariate smooth functions

We compute approximations of multivariate smooth functions by fitting random and quasi-random data to reduced size Tchebychef polynomial approximation models. We discuss the optimization of the data used in the least square method by testing several quasi-random sequences. Points built from optimal quadratic quantization are especially efficient. Very accurate approximation type quadrature formulas are obtained avoiding the usual periodisation problems when using lattices rules. Some numerical tests confirm the efficiency of our quadratures compared to standard methods.