11 citations · 44 across the 12 of their papers we have counts for
12 papers
On the Ordering of Sites in the Density Matrix Renormalization Group using Quantum Mutual Information
Mazen Ali
The density matrix renormalization group (DMRG) of White 1992 remains to this day an integral component of many state-of-the-art methods for efficiently simulating strongly correla…
Approximation Theory of Tree Tensor Networks: Tensorized Multivariate Functions
Mazen Ali, Anthony Nouy
We study the approximation of multivariate functions with tensor networks (TNs), providing some answers to the following two questions: ``what are the approximation capabilities of…
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\|_…
Approximation of Smoothness Classes by Deep Rectifier Networks
Mazen Ali, Anthony Nouy
We consider approximation rates of sparsely connected deep rectified linear unit (ReLU) and rectified power unit (RePU) neural networks for functions in Besov spaces …
Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions -- Part II
Mazen Ali, Anthony Nouy
We study the approximation by tensor networks (TNs) of functions from classical smoothness classes. The considered approximation tool combines a tensorization of functions in $L^p(…
Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions -- Part I
Mazen Ali, Anthony Nouy
We study the approximation of functions by tensor networks (TNs). We show that Lebesgue -spaces in one dimension can be identified with tensor product spaces of arbitrary orde…
Singular Value Decomposition in Sobolev Spaces: Part II
Mazen Ali, Anthony Nouy
Under certain conditions, an element of a tensor product space can be identified with a compact operator and the singular value decomposition (SVD) applies to the latter. These con…
Low-Rank Approximability and Entropy Area Laws for Ground States of Unbounded Hamiltonians
Mazen Ali
We show how local bounded interactions in an unbounded Hamiltonian lead to eigenfunctions with favorable low-rank properties. To this end, we utilize ideas from quantum entanglemen…
Singular Value Decomposition in Sobolev Spaces: Part I
Mazen Ali, Anthony Nouy
A well known result from functional analysis states that any compact operator between Hilbert spaces admits a singular value decomposition (SVD). This decomposition is a powerful t…
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…