27 citations · 94 across the 7 of their papers we have counts for
8 papers
Geometry of tree-based tensor formats in tensor Banach spaces
Antonio Falcó, Wolfgang Hackbusch, Anthony Nouy
In the paper `On the Dirac-Frenkel Variational Principle on Tensor Banach Spaces', we provided a geometrical description of manifolds of tensors in Tucker format with fixed multili…
Post-Processing of High-Dimensional Data
Mike Espig, Wolfgang Hackbusch, Alexander Litvinenko +2
Scientific computations or measurements may result in huge volumes of data. Often these can be thought of representing a real-valued function on a high-dimensional domain, and can…
Numerical approximation of Poisson problems in long domains
Michel Chipot, Wolfgang Hackbusch, Stefan Sauter +1
In this paper, we consider the Poisson equation on a "long" domain which is the Cartesian product of a one-dimensional long interval with a (d-1)-dimensional domain. The right-hand…
Tree-based tensor formats
Antonio Falco, Wolfgang Hackbusch, Anthony Nouy
The main goal of this paper is to study the topological properties of tensors in tree-based Tucker format. These formats include the Tucker format and the Hierarchical Tucker forma…
On the Dirac-Frenkel Variational Principle on Tensor Banach Spaces
A. Falcó, W. Hackbusch, A. Nouy
The main goal of this paper is to extend the so-called Dirac-Frenkel Variational Principle in the framework of tensor Banach spaces. To this end we observe that a tensor product of…
Geometric Structures in Tensor Representations (Final Release)
Antonio Falco, Wolfgang Hackbusch, Anthony Nouy
The main goal of this paper is to study the geometric structures associated with the representation of tensors in subspace based formats. To do this we use a property of the so-cal…