11 citations · 44 across the 12 of their papers we have counts for
4 papers · 1 filter
Ranks of Tensor Networks for Eigenspace Projections and the Curse of Dimensionality
Mazen Ali
The hierarchical (multi-linear) rank of an order- tensor is key in determining the cost of representing a tensor as a (tree) Tensor Network (TN). In general, it is known that, f…
-Stability of the -Projection onto Finite Element Spaces on Adaptively Refined Quadrilateral Meshes
Mazen Ali, Stefan A. Funken, Anja Schmidt
The -orthogonal projection onto a finite element (FE) space is called -stable iff $\|\nablaΠ_h u\|_{L^2(Ω)}\leq C\|u\|_…
HT-AWGM: A Hierarchical Tucker-Adaptive Wavelet Galerkin Method for High Dimensional Elliptic Problems
Mazen Ali, Karsten Urban
This paper is concerned with the construction, analysis and realization of a numerical method to approximate the solution of high dimensional elliptic partial differential equation…
Reduced Basis Methods Based Upon Adaptive Snapshot Computations
Mazen Ali, Kristina Steih, Karsten Urban
We use asymptotically optimal \emph{adaptive} numerical methods (here specifically a wavelet scheme) for snapshot computations within the offline phase of the Reduced Basis Method…