During the last years, low‐rank tensor approximation has been established as a new tool in
scientific computing to address large‐scale linear and multilinear algebra problems, which …

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

Usually one avoids numerical algorithms involving operations with large, fully populated
matrices. Instead one tries to reduce all algorithms to matrix-vector multiplications involving …

We propose algorithms for the solution of high-dimensional symmetrical positive definite
(SPD) linear systems with the matrix and the right-hand side given and the solution sought in …

Large-scale problems have always been a challenge for numerical computations. An
example is the treatment of fully populated n× n matrices when n2 is close to or beyond the …

A robust and efficient time integrator for dynamical tensor approximation in the tensor train or
matrix product state format is presented. The method is based on splitting the projector onto …

Hierarchical tensors can be regarded as a generalisation, preserving many crucial features,
of the singular value decomposition to higher-order tensors. For a given tensor product …

The numerical treatment of partial differential equations splits into two different parts. The
first part are the discretisation methods and their analysis. This led to the author's …

A new method for structured representation of matrices and vectors is presented. The
method is based on the representation of a matrix as ad-dimensional tensor and applying …

In this paper, we propose a method for the numerical solution of linear systems of equations
in low rank tensor format. Such systems may arise from the discretisation of PDEs in high …