Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Albert Cohen, Giovanni Migliorati, Fabio Nobile

We analyze the accuracy of the discrete least-squares approximation of a function $u$ in multivariate polynomial spaces ${\mathbb{P}}_{\Lambda }:=\mathrm{span}\{y\mapsto y^{\nu }:\nu \in \Lambda \}$ wit…