27 citations · 59 across the 5 of their papers we have counts for
6 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…
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…
Principal bundle structure of matrix manifolds
Marie Billaud-Friess, Antonio Falco, Anthony Nouy
In this paper, we introduce a new geometric description of the manifolds of matrices of fixed rank. The starting point is a geometric description of the Grassmann manifold $\mathbb…
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…
Proper Generalized Decomposition for Nonlinear Convex Problems in Tensor Banach Spaces
Antonio Falco, Anthony Nouy
Tensor-based methods are receiving a growing interest in scientific computing for the numerical solution of problems defined in high dimensional tensor product spaces. A family of…