Selected aspects of tractability analysis (Q6564672)

This review paper provides an introductory overview of the general theory of tractability in Hilbert spaces. The results are illustrated by means of examples dealing with numerical integration in \(\mathbb R^d\). It specifically addresses the following questions: (1) Given an error threshold \(\epsilon > 0\) in a \(d\)-dimensional problem, how much information does one need to have in order to guarantee that the approximation is accurate with an error of no more than \(\epsilon\)? (2) What is the precise form of the dependency of the required amount of information on the error bound \(\epsilon\) and on the dimension \(d\)?