Low-rank tensor representations can provide highly compressed approximations of
functions. These concepts, which essentially amount to generalizations of classical …

Bei der numerischen Behandlung partieller Differentialgleichungen treten oft überraschende
Phänomene auf. Neben der zügigen Behandlung der klassischen Theorie, die bis an die …

Parametrized families of PDEs arise in various contexts such as inverse problems, control
and optimization, risk assessment, and uncertainty quantification. In most of these …

Deterministic Galerkin approximations of a class of second order elliptic PDEs with random
coefficients on a bounded domain D⊂ ℝ d are introduced and their convergence rates are …

With respect to space-time tensor-product wavelet bases, parabolic initial boundary value
problems are equivalently formulated as bi-infinite matrix problems. Adaptive wavelet …

Abstract In [Math. Comp, 70 (2001), 27–75] and [Found. Comput. Math., 2 (3)(2002), 203–
245], Cohen, Dahmen and DeVore introduced adaptive wavelet methods for solving …

The origins of wavelets go back to the beginning of the last century and wavelet methods are
by now a well-known tool in image processing (jpeg2000). These functions have, however …

The numerical approximation of parametric partial differential equations is a computational
challenge, in particular when the number of involved parameter is large. This paper …

Adaptive tensor product wavelet methods are applied for solving Poisson's equation, as well
as anisotropic generalizations, in high space dimensions. It will be demonstrated that the …

We present convergence estimates of two types of greedy algorithms in terms of the metric
entropy of underlying compact sets. In the first part, we measure the error of a standard …