We study the information complexity in the randomized setting of solving a general elliptic
PDE of order 2m in a smooth, bounded domain Q⊂ Rd with smooth coefficients and …

We study the minimal number n (ɛ, d) of information evaluations needed to compute a worst
case ɛ-approximation of a linear multivariate problem. This problem is defined over a …

The query complexity of the following numerical problem is studied in the quantum model of
computation: consider a general elliptic partial differential equation of order 2m in a smooth …

We study the intrinsic difficulty of solving linear parabolic initial-value problems numerically
at a single point. We present a worst-case analysis for deterministic as well as for …

The thesis contains an analysis of two computational problems. The first problem is discrete
quantum Boolean summation. This problem is a building block of quantum algorithms for …

We give a short introduction to quantum computing and its relation to numerical analysis. We
survey recent research on quantum algorithms and quantum complexity theory for two basic …

Using a new and elegant reduction approach we derive a lower bound of quantum
complexity for the approximation of imbeddings from anisotropic Sobolev classes B (W pr …