Breaking the curse of dimensionality
In modern science, efficient numerical treatment of high-dimensional problems becomes more and more important. A fundamental insight of the theory of information-based complexity (IBC for short) is that the computational hardness of a problem cannot be described properly only by the rate of convergence. There exist problems for which an exponential number of information operations is needed in order to reduce the initial error, although there are algorithms which provide an arbitrarily large rate...