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 …

Shearlets emerged in recent years among the most successful frameworks for the efficient
representation of multidimensional data. Indeed, after it was recognized that traditional …

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 …

Compressed sensing (CS) is a relatively new approach to signal acquisition which has as its
goal to minimize the number of measurements needed of the signal in order to guarantee …

We discuss the calculus of variations in tensor representations with a special focus on tensor
networks and apply it to functionals of practical interest. The survey provides all necessary …

In this article, we describe an efficient approximation of the stochastic Galerkin matrix which
stems from a stationary diffusion equation. The uncertain permeability coefficient is assumed …

This paper analyzes the continuum model/complete electrode model in the electrical
impedance tomography inverse problem of determining the conductivity parameter from …

In this paper, we suggest approximate algorithms for the reconstruction of sparse high-
dimensional trigonometric polynomials, where the support in frequency domain is unknown …