This book provides a systematic survey of classical and recent results on hyperbolic cross
approximation. Motivated by numerous applications, the last two decades have seen great …

This paper is a contemporary review of QMC ('quasi-Monte Carlo') methods, that is, equal-
weight rules for the approximate evaluation of high-dimensional integrals over the unit cube …

The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the
engineering, mathematical, and scientific communities with significant developments in …

The present paper is dedicated to the application of the pivoted Cholesky decomposition to
compute low-rank approximations of dense, positive semi-definite matrices. The resulting …

In this article, we study the approximation of a probability measure μ on Rd by its empirical
measure ˆμN interpreted as a random quantization. As error criterion we consider an …

In this paper we propose and analyze stable variational formulations for convection diffusion
problems starting from concepts introduced by Sangalli. We derive efficient and reliable a …

We derive and analyse a scheme for the approximation of order d tensors [Formula: see text]
in the hierarchical (H-) Tucker format, a dimension-multilevel variant of the Tucker format …

This book is a survey on multivariate approximation. The 20th century was a period of
transition from univariate problems to multivariate problems in a number of areas of …

We review two similar concepts of hierarchical rank of tensors (which extend the matrix rank
to higher order tensors): the TT-rank and the H-rank (hierarchical or H-Tucker rank). Based …

In this paper, we present algorithms for the approximation of multivariate periodic functions
by trigonometric polynomials. The approximation is based on sampling of multivariate …