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math.NA2020
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…
math.NA2020
A new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of matrix manifolds
Marie Billaud-Friess, Antonio Falcó, Anthony Nouy
In this paper, we propose a new splitting algorithm for dynamical low-rank approximation motivated by the fibre bundle structure of the set of fixed rank matrices. We first introdu…