Exponential tractability of L2-approximation with function values

We study the complexity of high-dimensional approximation in $L_2$-norm when different classes information are available; we compare power function evaluations with arbitrary continuous linear measurements. Here, discuss situation number measurements required to achieve an error $\varepsilon \in (0,1)$ dimension $d\in\mathbb{N}$ depends only poly-logarithmically on $\varepsilon^{-1}$. This corresponds exponential order convergence error, which often happens applications. However, it does not mean that problem is easy, main difficulty usually lies within dependence $d$. determine extent amount changes, if allow evaluation instead information. It turns out this case lose very little, and can even restrict algorithms. In particular, several notions tractability hold simultaneously for both types available