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Tractability of $L_\infty$-approximation on weighted Banach spaces of smooth functions
Keywords: Tractability; $L_\infty$-approximation
Sun, 14:25--14:50
  • Weimar, Markus (Mathematical Institute, Friedrich-Schiller-University Jena, Germany)

In this talk we study the worst case error of $L_\infty$-approximation for multivariate smooth functions $f \colon [0,1]^d \rightarrow \mathbb{R}$ from certain weighted Banach spaces $F_d^\gamma$. Since it is well-known that we can reach an excellent rate of convergence with respect to $n$, the amount of information on $f$ used by an approximation-algorithm, we especially consider the dependence of the error bounds on the dimension $d$. It turns out that this dependence and therefore also the complexity of the problem are strongly connected to the weight $\gamma$ which characterizes the function space.

We will present necessary and sufficient conditions for tractability in the case of product weights. The talk is based on [1].

[1] Markus Weimar. Tractability results for weighted Banach spaces of smooth functions. Submitted to J. Complexity.