Exponential Convergence of an Approximation Problem for Infinitely Differentiable Multivariate Functions

We study approximation problems for infinitely differentiable multivariate functions in the worst-case setting. Using a series of information-based algorithms as approximation tools, in which each algorithm is constructed by performing finitely many standard information operations, we prove that the $L_\infty$-approximation problem is exponentially convergent. As a corollary, we show that the corresponding integral problem is exponentially convergent as well.